Previous Page
   Next Page
 
Evokation
  
 
Index
  

 

 

THE NUCLEAR FAMILY 1969

 

 

 

 

 

 

 

 

...

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

....

 

 

A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

"As all the words in the English language are composed out of the twenty-six letters of the alphabet,.."

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

"By writing the 26 letters of the alphabet in a certain order one may put down almost any message (this book 'is written with the same letters' as the Encyclopaedia Britannica and Winnie the Pooh, only the order of the letters differs). In the same way Nature is able to convey with her language how a cell and a whole organism is to be constructed and how it is to function. Nature has succeeded better than we humans; for the genetic code there is only one universal language which is the same in a man, a bean plant and a bacterium."

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
J
K
L
M
N
O
P
Q
R
10
11
12
13
14
15
16
17
18
1+0
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
S
T
U
V
W
X
Y
Z
I
19
20
21
22
23
24
25
26
9
1+9
2+0
2+1
2+2
2+3
2+4
2+5
2+6
ME
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
I
ME
I
ME
I
ME
I
ME
I
9
18
9
18
9
18
9
18
9
=
1+8
=
1+8
=
1+8
=
1+8
=
=
9
=
9
=
9
=
9
=
I
ME
I
ME
I
ME
I
ME
1
9
9
9
9
9
9
9
9
9
I
ME
I
ME
I
ME
I
ME
1

 

 

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-
-
-
-
-
-
-
-
-
 1+0 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+0 2+1 2+2 2+3 2+4 2+5 2+6
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
 -
-
-
-
-
-
-
-
-
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

"Perhaps the most famous of the early Jewish mystical texts is the fifth century Sefer Yezirah (The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time"

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320 or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

T
H
E
-
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
20
8
5
-
13
21
19
9
3
-
15
6
-
20
8
5
-
19
16
8
5
18
5
19
2
8
5
-
4
3
1
9
3
-
6
6
-
2
8
5
-
1
7
8
5
9
5
1
T
H
E
-
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
 
 
 
 
 
 
1
 
 
 
 
 
 
 
 
 
 
1
 
 
 
 
 
1
2
 
 
 
 
 
 
 
 
 
 
 
 
2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3
 
 
3
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5
 
 
 
 
 
 
 
 
 
 
 
 
5
 
 
 
 
5
 
5
 
 
 
 
 
 
 
 
 
 
 
6
6
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
7
 
 
 
 
 
 
8
 
 
 
 
 
 
 
 
 
 
 
 
8
 
 
 
 
8
 
 
 
 
 
 
 
 
 
 
 
9
 
 
 
 
 
 
 
 
 
 
 
 
 
9
 
 
T
H
E
-
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S

 

 

1
occurs
x
3
=
3
-
-
3
2
occurs
x
2
=
4
-
-
4
3
occurs
x
2
=
6
-
-
6
4
occurs
x
1
=
4
-
-
4
5
occurs
x
4
=
20
2+0
=
2
6
occurs
x
2
=
12
1+2
=
3
7
occurs
x
1
=
7
-
-
7
8
occurs
x
3
=
24
2+4
=
6
9
occurs
x
2
=
18
1+8
=
9
45
First Total
-
20
-
98
-
-
44
4+5
Reduce
-
2+0
-
9+8
-
-
4+4
9
Second Total
-
2
-
17
-
-
4
-
Reduce
-
-
-
1+7
-
-
-
9
Final Total
-
2
-
8
-
-
8

 

 

17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
`-
13
21
19
9
3
-
15
6
-
20
8
5
-
19
16
8
5
18
5
19
+
=
209
2+0+9
=
11
1+1
2
-
4
3
1
9
3
-
6
6
-
2
8
5
-
1
7
8
5
9
5
1
+
=
83
8+3
=
11
1+1
2
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-

 

 

-
-
-
17
MUSIC OF THE SPHERES
S
=
1
--
S
19
10
1
-
-
-
-
--
S
19
10
1
3
-
-
-
--
S
19
10
1
-
T
=
2
-
T
20
2
2
2
U
=
3
-
U
21
3
3
-
C
=
-
-
C
3
3
3
2
M
=
4
-
M
13
4
4
1
E
=
5
-
E
5
5
5
-
-
-
-
-
E
5
5
5
3
-
-
-
-
E
5
5
5
-
O
=
6
-
O
15
6
6
2
F
-
-
-
F
6
6
6
-
P
=
7
-
P
16
7
7
1
H
=
8
-
H
8
8
8
-
-
-
-
-
H
8
8
8
2
I
=
9
-
I
9
9
9
-
-
-
-
-
R
18
9
9
2
9
-
45
17
MUSIC OF THE SPHERES
-
-
-
17
-
-
4+5
-
-
-
-
-
 1+7
9
-
9
17
MUSIC OF THE SPHERES
-
-
-
8

 

 

1
occurs
x
3
=
3
-
-
3
2
occurs
x
1
=
2
-
-
2
3
occurs
x
2
=
6
-
-
6
4
occurs
x
1
=
4
-
-
4
5
occurs
x
3
=
15
1+5
=
6
6
occurs
x
2
=
12
1+2
=
3
7
occurs
x
1
=
7
-
-
7
8
occurs
x
2
=
16
1+6
=
7
9
occurs
x
2
=
18
1+8
=
9
45
First Total
-
17
-
83
-
-
47
4+5
Reduce
-
1+7
-
8+3
-
-
4+7
9
Second Total
-
8
-
11
-
-
11
-
Reduce
-
-
-
1+1
-
-
-
9
Final Total
-
8
-
2
-
-
2

 

 

17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
`-
13
21
19
9
3
-
15
6
-
20
8
5
-
19
16
8
5
18
5
19
+
=
209
2+0+9
=
11
1+1
2
-
4
3
1
9
3
-
6
6
-
2
8
5
-
1
7
8
5
9
5
1
+
=
83
8+3
=
11
1+1
2
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-

 

 

q-
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
9
-
-
6
-
-
-
8
-
-
1
-
8
-
-
-
1
+
=
34
3+4
=
7
=
7
=
7
-
-
-
-
19
9
-
-
15
-
-
-
8
-
-
19
-
8
-
-
-
19
+
=
97
9+7
=
16
1+6
7
=
7
q-
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
-
-
-
-
4
3
-
-
3
-
-
6
-
2
-
5
-
-
7
-
5
9
5
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
13
21
-
-
3
-
-
6
-
20
-
5
-
-
16
-
5
18
5
-
+
=
112
1+1+2
=
4
=
4
=
4
q-
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
-
-
-
-
13
21
19
9
3
-
15
6
-
20
8
5
-
19
16
8
5
18
5
19
+
=
209
2+0+9
=
11
1+1
2
=
2
-
-
4
3
1
9
3
-
6
6
-
2
8
5
-
1
7
8
5
9
5
1
+
=
83
8+3
=
11
1+1
2
=
2
-
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
3
-
-
3
-
--
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
45
-
-
17
-
83
-
47
4+5
1+7
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
4+5
-
-
1+7
-
8+3
-
4+7
9
8
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
9
-
-
8
-
11
-
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+1
-
1+1
9
8
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
9
-
-
8
-
2
-
2

 

 

17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-
`-
13
21
19
9
3
-
15
6
-
20
8
5
-
19
16
8
5
18
5
19
+
=
209
2+0+9
=
11
1+1
2
-
4
3
1
9
3
-
6
6
-
2
8
5
-
1
7
8
5
9
5
1
+
=
83
8+3
=
11
1+1
2
17
M
U
S
I
C
-
O
F
-
T
H
E
-
S
P
H
E
R
E
S
-
-
-
-
-
--
-
-

 

 

Musica universalis - Wikipedia
https://en.wikipedia.org/wiki/Musica_universalis
Musica universalis (literally universal music), also called Music of the spheres or Harmony of the Spheres, is an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica (the Medieval Latin term for music).

 

music of the spheres - The William Herschel Society
www.williamherschel.org.uk/wp-content/uploads/.../Harmony-of-the-Spheres.doc

Its founder, Pythagoras (532-497? BC), was probably the first person to associate strictly music and astronomy. He used the word “cosmos” to describe a ...

 

MUSIC OF THE SPHERES

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
5
MUSIC
65
29
2
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
20
-
5
-
65
29
20
-
-
-
-
-
-
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
7
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
-
12
-
2
-
21
123
12
-
-
-
-
-
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
12
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
13
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
15
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
17
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
36
-
7
-
90
547
36
-
3
2
6
4
15
12
7
16
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
1+2
-
1+6
1+8
-
-
83
-
17
MUSIC
65
29
2
-
3
2
6
4
6
3
7
7
9
-
-
8+3
-
1+7
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
8
THE
33
15
6
-
3
2
6
4
6
3
7
7
9
-
-
1+1
-
-
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
First Total
209
110
20
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Add to Reduce
2+0+9
1+1+0
2+0
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Second Total
11
2
2
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Reduce to Deduce
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Essence of Number
2
2
9
-
3
2
6
4
6
3
7
7
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
5
MUSIC
65
29
2
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
7
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
12
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
13
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
15
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
17
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
2
6
4
15
12
7
16
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
1+2
-
1+6
1+8
-
-
83
-
17
MUSIC
65
29
2
-
3
2
6
4
6
3
7
7
9
-
-
8+3
-
1+7
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
8
THE
33
15
6
-
3
2
6
4
6
3
7
7
9
-
-
1+1
-
-
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
First Total
209
110
20
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Add to Reduce
2+0+9
1+1+0
2+0
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Second Total
11
2
2
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Reduce to Deduce
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Essence of Number
2
2
9
-
3
2
6
4
6
3
7
7
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
5
MUSIC
65
29
2
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
17
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
7
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
12
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
13
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
15
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
3
2
6
4
15
12
7
16
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
1+2
-
1+6
1+8
-
-
83
-
17
MUSIC
65
29
2
-
3
2
6
4
6
3
7
7
9
-
-
8+3
-
1+7
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
-
-
11
-
8
THE
33
15
6
-
3
2
6
4
6
3
7
7
9
-
-
1+1
-
-
SPHERES
90
54
9
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
First Total
209
110
20
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Add to Reduce
2+0+9
1+1+0
2+0
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Second Total
11
2
2
-
3
2
6
4
6
3
7
7
9
-
-
-
-
-
Reduce to Deduce
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
8
Essence of Number
2
2
9
-
3
2
6
4
6
3
7
7
9

 

 

-
-
-
17
MUSIC OF THE SPHERES
S
=
1
--
S
19
10
1
-
-
-
--
S
19
10
1
-
-
-
--
S
19
10
1
T
=
2
-
T
20
2
2
U
=
3
-
U
21
3
3
C
=
-
-
C
3
3
3
M
=
4
-
M
13
4
4
E
=
5
-
E
5
5
5
-
-
-
-
E
5
5
5
-
-
-
-
E
5
5
5
O
=
6
-
O
15
6
6
F
-
-
-
F
6
6
6
P
=
7
-
P
16
7
7
H
=
8
-
H
8
8
8
-
-
-
-
H
8
8
8
I
=
9
-
I
9
9
9
-
-
-
-
R
18
9
9
9
-
45
-
MUSIC OF THE SPHERES
-
-
-
-
-
4+5
-
-
-
-
-
9
-
9
17
MUSIC OF THE SPHERES
-
-
-

 

 

T
=
2
-
3
THE
33
15
6
N
=
5
-
9
NUMERICAL
96
42
6
S
=
1
-
5
SCALE
40
13
4
-
-
8
4
17
First Total
169
70
16
-
-
-
-
1+7
Add to Reduce
1+6+9
7+0
1+6
-
-
8
-
8
Second Total
16
7
7
-
-
-
-
-
Reduce to Deduce
1+6
-
-
-
-
8
-
8
Essence of Number
7
7
7

 

 

 

 

 

 

alphabet, alphabetos, from alpha + beta, first two letters of the Greek alphabet. athlete, athletes "contestant in the games," from athlein "to contest for ... www.nvtc.gov/lotw/months/february/greek.

 

The word "alphabet" came into Middle English from the Late Latin Alphabetum, which in turn originated in the Ancient Greek Alphabetos, from alpha and beta, ... in.answers.yahoo.com/question/index

 

 

-
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
-
=
8
=
8
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
-
=
8
=
8
-
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
-
1
3
7
-
1
2
5
2
3
4
+
=
21
2+1
=
3
=
3
-
-
1
12
16
-
1
2
5
20
21
13
+
=
57
5+7
=
12
1+2
3
-
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
-
1
12
16
8
1
2
5
20
21
13
+
=
99
9+9
=
18
1+8
9
-
-
1
3
7
8
1
2
5
2
3
4
+
=
36
3+6
=
9
=
9
-
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
-
-
2
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
-
5
-
-
-
=
=
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
=
=
9
-
-
-
-
-
15
10
A
L
P
H
A
B
E
T
U
M
-
-
30
-
-
10
-
36
1+5
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
-
1+0
-
3+6
6
1
A
L
P
H
A
B
E
T
U
M
-
-
3
-
-
1
-
9
-
-
1
3
7
8
1
2
5
2
3
4
-
-
-
-
-
-
-
-
6
1
A
L
P
H
A
B
E
T
U
M
-
-
3
-
-
1
-
9

 

 

10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
-
=
8
=
8
-
-
-
-
8
-
-
-
-
-
-
+
=
8
-
=
8
=
8
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
1
3
7
-
1
2
5
2
3
4
+
=
21
2+1
=
3
=
3
-
1
12
16
-
1
2
5
20
21
13
+
=
57
5+7
=
12
1+2
3
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
--
-
-
-
1
12
16
8
1
2
5
20
21
13
+
=
99
9+9
=
18
1+8
9
-
1
3
7
8
1
2
5
2
3
4
+
=
36
3+6
=
9
=
9
10
A
L
P
H
A
B
E
T
U
M
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
-
2
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
5
-
-
-
=
=
5
occurs
x
1
=
5
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
10
A
L
P
H
A
B
E
T
U
M
-
-
30
-
-
10
-
36
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
-
1+0
-
3+6
1
A
L
P
H
A
B
E
T
U
M
-
-
3
-
-
1
-
9
-
1
3
7
8
1
2
5
2
3
4
-
-
-
-
-
-
-
-
1
A
L
P
H
A
B
E
T
U
M
-
-
3
-
-
1
-
9

 

 

-
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
1
+
=
15
1+5
=
6
=
6
-
-
-
-
-
8
-
-
-
-
15
19
+
=
42
4+2
=
6
=
6
-
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
-
1
3
7
-
1
2
5
2
-
-
+
=
21
2+1
=
3
=
3
-
-
1
12
16
-
1
2
5
20
-
-
+
=
57
5+7
=
12
1+2
3
-
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
-
1
12
16
8
1
2
5
20
15
19
+
=
99
9+9
=
18
1+8
9
-
-
1
3
7
8
1
2
5
2
6
1
+
=
36
3+6
=
9
=
9
-
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
3
=
3
-
-
-
-
-
-
-
2
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
=
=
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
=
=
9
-
-
-
-
-
13
10
A
L
P
H
A
B
E
T
O
S
-
-
32
-
-
10
-
36
1+3
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
-
1+0
-
3+6
4
1
A
L
P
H
A
B
E
T
O
S
-
-
5
-
-
1
-
9
-
-
1
3
7
8
1
2
5
2
6
1
-
-
-
-
-
-
-
-
4
1
A
L
P
H
A
B
E
T
O
S
-
-
5
-
-
1
-
9

 

 

10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
1
+
=
15
1+5
=
6
=
6
-
-
-
-
8
-
-
-
-
15
19
+
=
42
4+2
=
6
=
6
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
1
3
7
-
1
2
5
2
-
-
+
=
21
2+1
=
3
=
3
-
1
12
16
-
1
2
5
20
-
-
+
=
57
5+7
=
12
1+2
3
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
1
12
16
8
1
2
5
20
15
19
+
=
99
9+9
=
18
1+8
9
-
1
3
7
8
1
2
5
2
6
1
+
=
36
3+6
=
9
=
9
10
A
L
P
H
A
B
E
T
O
S
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
3
=
3
-
-
-
-
-
-
2
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
-
5
-
-
-
=
=
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
-
-
=
=
9
-
-
-
-
-
10
A
L
P
H
A
B
E
T
O
S
-
-
32
-
-
10
-
36
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
-
1+0
-
3+6
1
A
L
P
H
A
B
E
T
O
S
-
-
5
-
-
1
-
9
-
1
3
7
8
1
2
5
2
6
1
-
-
-
-
-
-
-
-
1
A
L
P
H
A
B
E
T
O
S
-
-
5
-
-
1
-
9

 

 

-
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
-
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
-
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
1
3
7
-
1
2
5
2
+
=
21
2+1
=
3
=
3
-
-
1
12
16
-
1
2
5
20
+
=
57
5+7
=
12
1+2
3
-
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
1
12
16
8
1
2
5
20
+
=
65
6+5
=
11
1+1
2
-
-
1
3
7
8
1
2
5
2
+
=
29
2+9
=
11
1+1
2
-
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
5
-
=
=
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
=
=
9
NINE
9
-
-
-
19
8
A
L
P
H
A
B
E
T
-
-
26
-
-
8
-
29
1+9
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+9
10
8
A
L
P
H
A
B
E
T
-
-
8
-
-
8
-
11
1+0
-
1
3
7
8
1
2
5
2
-
-
-
-
-
-
-
1+1
1
8
A
L
P
H
A
B
E
T
-
-
8
-
-
8
-
2

 

 

8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
1
3
7
-
1
2
5
2
+
=
21
2+1
=
3
=
3
-
1
12
16
-
1
2
5
20
+
=
57
5+7
=
12
1+2
3
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
1
12
16
8
1
2
5
20
+
=
65
6+5
=
11
1+1
2
-
1
3
7
8
1
2
5
2
+
=
29
2+9
=
11
1+1
2
8
A
L
P
H
A
B
E
T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
-
-
2
-
2
-
-
2
occurs
x
2
=
4
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
-
5
-
=
=
5
occurs
x
1
=
5
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
8
A
L
P
H
A
B
E
T
-
-
26
-
-
8
-
29
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+9
8
A
L
P
H
A
B
E
T
-
-
8
-
-
8
-
11
-
1
3
7
8
1
2
5
2
-
-
-
-
-
-
-
1+1
8
A
L
P
H
A
B
E
T
-
-
8
-
-
8
-
2

 

 

I

THAT

AM ALWAYS AM

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly. too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the /Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry In the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 360° in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, Incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillarta adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

Thee Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted
mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656.years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, .multiply this by 2 and again we have.the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as.- the interest-
ing number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes. difficult to escape the suspicion that many signs (number and otherwise) -indicate that early man observed the results.. of the movement of Precession . and that the-.transmission of this information was .considered of prime importance.

'With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would
have constituted the construction-of a 'Unified Field Theory' for nothing .less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced.,that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two,four.Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radiusekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up. his piece of striped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

All about the planets in our Solar System. The nine planets that orbit the sun are (in order from the sun): Mercury,Venus, Earth, Mars, Jupiter, Saturn, ... www.enchantedlearning.com/subjects/astronomy/planets

Our solar system consists of the sun, eight planets, moons, dwarf planets, an asteroid belt, comets, meteors, and others. The sun is the center of our solar system; the planets, their moons, the asteroids, comets, and other rocks and gas all orbit the sun.

The nine planets that orbit the sun are (in order from the sun): Mercury,Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto (a dwarf planet). A belt of asteroids (minor planets made of rock and metal) lies between Mars and Jupiter. These objects all orbit the sun in roughly circular orbits that lie in the same plane, the ecliptic (Pluto is an exception; it has an elliptical orbit tilted over 17° from the ecliptic).

 

 

N
=
5
-
2
NO
29
11
2
T
=
2
-
4
TIME
47
20
2
L
=
3
-
4
LIKE
37
19
1
T
=
2
-
3
THE
33
15
6
P
=
7
-
7
PRESENT
97
34
7
S
-
19
4
20
First Total
243
99
18
-
-
1+9
-
2+0
Add to Reduce
2+4+3
9+9
1+8
-
-
10
-
2
Second Total
9
18
9
-
-
1+0
4
-
Reduce to Deduce
-
1+8
-
-
-
1
5
2
Essence of Number
9
9
9

 

 

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

ZEROREZ

 

 

 

THE

SUN RED SUN

 

 

-
RED
-
-
-
1
R
18
9
9
2
E+D
9
9
9
3
RED
27
18
18
-
-
2+7
1+8
1+8
3
RED
9
9
9

 

 

-
3
R
E
D
-
-
-
-
-
--
-
-
-
-
18
5
4
+
=
27
2+7
=
9
=
9
-
-
9
5
4
+
=
18
1+8
=
9
=
9
-
3
R
E
D
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
=
-
5
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
27
3
R
E
D
-
-
18
-
-
3
-
18
2+7
-
9
-
-
-
-
1+8
-
-
-
-
1+8
9
3
R
E
D
-
-
9
-
-
3
-
9

 

 

3
R
E
D
-
-
-
-
-
--
-
-
-
18
5
4
+
=
27
2+7
=
9
=
9
-
9
5
4
+
=
18
1+8
=
9
=
9
3
R
E
D
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
-
5
-
-
-
5
occurs
x
1
=
5
-
9
-
-
-
-
9
occurs
x
1
=
9
3
R
E
D
-
-
18
-
-
3
-
18
-
9
-
-
-
-
1+8
-
-
-
-
1+8
3
R
E
D
-
-
9
-
-
3
-
9

 

 

THE

SUN GOD

RE

 

-
2
R
E
-
-
-
-
-
--
-
-
-
-
18
5
+
=
23
2+3
=
5
=
5
-
-
9
5
+
=
14
1+4
=
5
=
5
-
2
R
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
4
-
-
-
-
-
-
=
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
31
2
R
E
-
-
14
-
-
2
-
14
3+1
-
9
-
-
-
1+4
-
-
-
-
1+4
4
2
R
E
-
-
5
-
-
2
-
5

 

 

2
R
E
-
-
-
-
-
--
-
-
-
18
5
+
=
23
2+3
=
5
=
5
-
9
5
+
=
14
1+4
=
5
=
5
2
R
E
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
9
-
-
-
9
occurs
x
1
=
9
2
R
E
-
-
14
-
-
2
-
14
-
9
-
-
-
1+4
-
-
-
-
1+4
2
R
E
-
-
5
-
-
2
-
5

 

 

 

 

THE FINGERPRINTS OF THE GODS

Graham Hancock 1995

Page 273

"The precessional numbers highlighted by Sellers in the Osiris myth are 360, 72, 30 and 12."

"These he joined to the 360 days of which the year then consisted (emphasis added)."

"Elsewhere the myth informs us that the 360 - day year consists of "12 months of 30 days each".

Note 6

And in general,as Sellers observes , "phrases are used which prompt simple mental calculations and an attention to numbers ". note 7 "Elsewhere the myth informs us that the 360-day year consists of '12 months of 30 days each'.

Thus far we have been provided with three of Seller's precessional: 360, 12 and 30. The fourth number,which occurs later in the text, is by far the most important. As we saw in Chapter Nine, the evil deity known as Set led a group of conspirators in a plot to kill Osiris. The number of these conspirators was 72."

 

 

P
=
7
-
10
PRECESSION
123
69
6
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
E
=
5
-
9
EQUINOXES
129
57
3
-
-
20
-
24
Add to Reduce
306
153
18
-
-
2+0
-
2+4
Reduce to Deduce
3+0+6
1+5+3
1+8
-
-
2
-
6
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PRECESSION
123
69
6
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EQUINOXES
129
57
3
-
-
-
-
-
-
-
-
-
-
-
-
20
-
24
-
306
153
18
-
1
2
3
4
5
6
7
8
9
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
Q
=
8
-
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
10
PRECESSION
123
69
6
-
3
2
6
4
35
30
7
16
27
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
3+5
3+0
-
1+6
2+7
T
=
2
-
3
THE
33
15
6
-
3
2
6
4
8
3
7
7
9
E
=
5
-
9
EQUINOXES
129
57
3
-
-
-
-
-
-
-
-
-
-
-
-
18
-
24
Add to Reduce
306
153
18
-
3
2
6
4
8
3
7
7
9
-
-
1+8
-
2+4
Reduce to Deduce
3+0+6
1+5+3
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
3
2
6
4
8
3
7
7
9

 

LETTERS TRANSPOSED INTO NUMBER RE-ARRANGED NUMERICAL;LY

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
10
PRECESSION
123
69
6
-
-
-
-
-
-
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EQUINOXES
129
57
3
-
-
-
-
-
-
-
-
-
-
-
-
20
-
24
-
306
153
18
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
-
-
4
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
4
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
4
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
4
-
-
-
-
-
C
=
3
-
1
C
3
3
3
-
-
-
3
4
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
4
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
4
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
4
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
4
-
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
4
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
4
-
-
-
8
-
Q
=
8
-
1
Q
17
8
8
-
-
-
-
4
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
4
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
4
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
10
PRECESSION
123
69
6
-
3
2
6
4
35
30
7
16
27
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
3+5
3+0
-
1+6
2+7
T
=
2
-
3
THE
33
15
6
-
3
2
6
4
8
3
7
7
9
E
=
5
-
9
EQUINOXES
129
57
3
-
-
-
-
-
-
-
-
-
-
-
-
18
-
24
Add to Reduce
306
153
18
-
3
2
6
4
8
3
7
7
9
-
-
1+8
-
2+4
Reduce to Deduce
3+0+6
1+5+3
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
3
2
6
4
8
3
7
7
9

 

 

10
PRECESSION
123
69
6
2
OF
21
12
3
3
THE
33
15
6
9
EQUINOXES
129
57
3
24
Add to Reduce
306
153
18
2+4
Reduce to Deduce
3+0+6
1+5+3
1+8
6
Essence of Number
9
9
9

 

 

A
=
1
6
AUTUMN
90
18
9
S
=
1
6
SUMMER
89
26
8
W
=
5
6
WINTER
89
35
8
S
=
1
6
SPRING
83
38
2
-
-
8
24
Add to Reduce
351
117
27
-
-
-
2+4
Reduce to Deduce
3+5+1
1+1+7
2+7
-
-
8
6
Essence of Number
9
9
9

 

 

-
-
-
-
-
WORLD-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
W
=
5
1
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
50
-
5
WORLD
72
27
27
-
1
2
3
4
5
6
7
8
9
-
-
5+0
-
-
-
7+2
2+7
2+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
WORLD
9
9
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
WORLD
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
--
-
--
-
EARTH
-
--
-
E
=
5
-
1
E
5
5
5
A
=
1
-
1
A
1
1
1
R
=
9
-
1
R
18
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
-
-
25
-
5
EARTH
52
25
25
-
-
2+5
-
-
-
5+2
2+5
2+5
-
-
7
-
5
EARTH
7
7
7

 

 

-
-
-
-
-
EARTH-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
25
-
5
EARTH
52
25
25
-
1
2
3
4
5
6
7
8
9
-
-
2+5
-
-
-
5+2
2+5
2+5
-
-
-
-
-
-
-
-
-
-
-
-
7
-
5
EARTH
7
7
7
-
1
2
3
4
5
6
7
8
9

 

EARTH WORLD

 

-
-
-
-
10
EARTHWORLD
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
EARTH-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
25
-
5
EARTH
52
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
WORLD
-
-
-
-
-
-
-
-
-
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
27
-
5
-
72
27
27
-
-
-
-
-
-
-
-
-
-
-
-
52
-
-
EARTHWORLD
124
52
52
-
1
2
3
4
5
6
7
8
18
-
-
2+7
-
-
-
1+2+4
5+2
5+2
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
10
EARTHWORLD
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
EARTH-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
7
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
52
-
-
EARTHWORLD
124
52
52
-
1
2
3
4
5
6
7
8
18
-
-
2+7
-
-
-
1+2+4
5+2
5+2
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
10
EARTHWORLD
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
EARTH-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
7
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
52
-
-
EARTHWORLD
124
52
52
-
1
2
3
4
5
6
7
8
18
-
-
2+7
-
-
-
1+2+4
5+2
5+2
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
EARTHWORLD
7
7
7
-
1
2
3
4
5
6
7
8
9

 

 

3
SUN
54
9
9
5
EARTH
52
25
7
4
MOON
57
21
3
12
First Total
163
55
19
1+2
Add to Reduce
1+6+3
5+5
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
7
7
7

 

 

5
EARTH
52
25
7
3
AIR
28
19
1
4
FIRE
38
29
2
5
WATER
67
22
4
17
First Total
185
95
14
1+7
Add to Reduce
1+8+5
9+5
1+4
8
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
8
Essence of Number
5
5
5

 

 

A
=
1
3

AIR
28
19
1
F
=
6
4

FIRE
38
29
2
E
=
5
5

EARTH
52
25
7
W
=
5
5

WATER
67
22
4
H
=
8
5

HUMAN
57
21
3
S
=
1
6

SPIRIT
91
37
1
-
-
26
28
-
333
153
18
-
-
2+6
10
-
3+3+3
1+5+3
1+8
-
-
8
1
-
9
9
9

 

 

Everything in nature is made up of five basic elements: earth, water, fire, air, and space.

SPACE THE PACES OF SPACE

 

E
=
5
-
5
EARTH
52
25
7
A
=
1
-
3
AIR
28
19
1
F
=
6
-
4
FIRE
38
29
2
W
=
5
-
5
WATER
67
22
4
-
-
17
-
17
Add
185
95
14
-
-
1+7
-
1+7
Reduce
1+8+5
9+5
1+4
-
-
8
-
8
 Total
14
14
5
-
-
-
-
-
Deduce
1+4
1+4
-
-
-
8
-
8
Essence
5
5
5

 

EARTH FIRE AIR WATER

 

-
-
-
-
10
EARTH AIR FIRE WATER
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EARTH-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
25
-
5
EARTH
52
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
AIR
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
19
-
3
AIR
28
19
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FIRE
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
29
-
4
FIRE
38
29
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
WATER
-
-
-
-
-
-
-
-
-
-
-
-
-
W
=
5
13
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
14
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
17
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
22
-
5
WATER
67
22
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
95
-
17
EARTH AIR FIRE WATER
185
95
14
-
3
4
3
4
20
6
7
8
54
-
-
9+5
-
1+7
-
1+8+5
9+5
1+4
-
-
-
-
-
2+0
-
-
-
5+4
-
-
14
-
8
EARTH AIR FIRE WATER
14
14
5
-
3
4
3
4
2
6
7
8
9
-
-
1+4
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
EARTH AIR FIRE WATER
5
5
5
-
3
4
3
4
2
6
7
8
9

 

 

-
-
-
-
10
EARTH AIR FIRE WATER
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
A
=
1
2
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
R
=
9
3
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
T
=
2
4
1
T
20
2
2
-
-
2
3
4
-
-
7
-
-
H
=
8
5
1
H
8
8
8
-
-
-
3
4
-
-
7
8
-
A
=
1
6
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
I
=
9
7
1
I
9
9
9
-
-
-
3
4
-
-
7
-
9
R
=
9
8
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
F
=
6
9
1
F
6
6
6
-
-
-
3
4
-
6
7
-
-
I
=
9
10
1
I
9
9
9
-
-
-
3
4
-
-
7
-
9
R
=
9
11
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
E
=
5
12
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
W
=
5
13
1
W
23
5
5
-
-
-
3
4
5
-
7
-
-
A
=
1
14
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
T
=
2
15
1
T
20
2
2
-
-
2
3
4
-
-
7
-
-
E
=
5
16
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
R
=
9
17
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
95
-
17
EARTH AIR FIRE WATER
185
95
14
-
3
4
3
4
20
6
7
8
54
-
-
9+5
-
1+7
-
1+8+5
9+5
1+4
-
-
-
-
-
2+0
-
-
-
5+4
-
-
14
-
8
EARTH AIR FIRE WATER
14
14
5
-
3
4
3
4
2
6
7
8
9
-
-
1+4
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
EARTH AIR FIRE WATER
5
5
5
-
3
4
3
4
2
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
10
EARTH AIR FIRE WATER
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
A
=
1
6
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
A
=
1
14
1
A
1
1
1
-
1
-
3
4
-
-
7
-
-
T
=
2
15
1
T
20
2
2
-
-
2
3
4
-
-
7
-
-
T
=
2
4
1
T
20
2
2
-
-
2
3
4
-
-
7
-
-
E
=
5
1
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
E
=
5
12
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
W
=
5
13
1
W
23
5
5
-
-
-
3
4
5
-
7
-
-
E
=
5
16
1
E
5
5
5
-
-
-
3
4
5
-
7
-
-
F
=
6
9
1
F
6
6
6
-
-
-
3
4
-
6
7
-
-
H
=
8
5
1
H
8
8
8
-
-
-
3
4
-
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
I
=
9
7
1
I
9
9
9
-
-
-
3
4
-
-
7
-
9
R
=
9
8
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
I
=
9
10
1
I
9
9
9
-
-
-
3
4
-
-
7
-
9
R
=
9
11
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
R
=
9
17
1
R
18
9
9
-
-
-
3
4
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
95
-
17
EARTH AIR FIRE WATER
185
95
14
-
3
4
3
4
20
6
7
8
54
-
-
9+5
-
1+7
-
1+8+5
9+5
1+4
-
-
-
-
-
2+0
-
-
-
5+4
-
-
14
-
8
EARTH AIR FIRE WATER
14
14
5
-
3
4
3
4
2
6
7
8
9
-
-
1+4
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
EARTH AIR FIRE WATER
5
5
5
-
3
4
3
4
2
6
7
8
9

 

 

-
-
-
-
10
EARTH AIR FIRE WATER
-
-
-
-
1
2
5
6
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
14
1
A
1
1
1
-
1
-
-
-
-
-
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
5
-
-
-
W
=
5
13
1
W
23
5
5
-
-
-
5
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
5
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
6
-
-
H
=
8
5
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
9
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
9
R
=
9
17
1
R
18
9
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
95
-
17
EARTH AIR FIRE WATER
185
95
14
-
3
4
20
6
8
54
-
-
9+5
-
1+7
-
1+8+5
9+5
1+4
-
-
-
2+0
-
-
5+4
-
-
14
-
8
EARTH AIR FIRE WATER
14
14
5
-
3
4
2
6
8
9
-
-
1+4
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
5
-
8
EARTH AIR FIRE WATER
5
5
5
-
3
4
2
6
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

 

Greenwich Mean Time - Wikipedia
https://en.wikipedia.org › wiki › Greenwich_Mean_Time

Greenwich Mean Time Zone

Description
Greenwich Mean Time is the mean solar time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given.

Greenwich Mean Time (GMT) is the mean solar time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon;[1] as a consequence, it cannot be used to specify a particular time unless a context is given.

English speakers often use GMT as a synonym for Coordinated Universal Time (UTC):[2] in modern usage, this is incorrect – GMT is now a time zone, not a time reference.[3][4] For navigation, it is considered equivalent to UT1 (the modern form of mean solar time at 0° longitude); but this meaning can differ from UTC by up to 0.9 s. The term GMT should not thus be used for purposes that require precision.[5]

Because of Earth's uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy calculated by the equation of time. Noon GMT is the annual average (i.e. "mean") moment of this event, which accounts for the word "mean" in "Greenwich Mean Time".

Originally, astronomers considered a GMT day to start at noon, while for almost everyone else it started at midnight. To avoid confusion, the name Universal Time was introduced to denote GMT as counted from midnight.[6] Astronomers preferred the old convention to simplify their observational data, so that each night was logged under a single calendar date. Today, Universal Time usually refers to UTC or UT1.[4]

The term "GMT" is especially used by bodies connected with the United Kingdom, such as the BBC World Service, the Royal Navy, and the Met Office; and others particularly in Arab countries, such as the Middle East Broadcasting Centre and OSN. It is a term commonly used in the United Kingdom and countries of the Commonwealth, including Australia, New Zealand, South Africa, India, Pakistan, Bangladesh and Malaysia; and in many other countries of the Eastern Hemisphere.

 

Greenwich Mean Time | History & Definition | Britannica

https://www.britannica.com › ... › Matter & Energy

Greenwich Mean Time (GMT), the name for mean solar time of the longitude (0°) of the Royal Greenwich Observatory in England. The meridian at this longitude ...

WRITTEN BY

Jonathan D. Betts
Curator of Horology, Royal Observatory Greenwich, National Maritime Museum.

See Article History

Alternative Title:GMT


Greenwich Mean Time (GMT), the name for mean solar time of the longitude (0°) of the Royal Greenwich Observatory in England. The meridian at this longitude is called the prime meridian or Greenwich meridian. Greenwich Mean Time (GMT) has been used to clearly designate epoch by avoiding confusing references to local time systems (zones).

Historically, astronomers used Greenwich Mean Astronomical Time (GMAT), in which the astronomical day began at noon at longitude (0°), in accord with scientific tradition. In 1925 GMT was adopted by astronomers so that the astronomical day began at midnight, the same time as the civil day. Some confusion in terminology resulted, though, and in 1928 the International Astronomical Union changed the designation of the standard time of the Greenwich meridian to Universal Time. Universal Time remains in general use in a modified form as Coordinated Universal Time (UTC), which serves to accommodate the timekeeping differences that arise between atomic time (derived from atomic clocks) and solar time. The term Greenwich Mean Time is still used to represent the civil time in Britain.

Jonathan D. Betts

Alternative Title:prime meridian


Greenwich meridian, imaginary line used to indicate 0° longitude that passes through Greenwich, a borough of London, and terminates at the North and South poles. An international conference held in Washington, D.C., in 1884 designated “the meridian passing through the centre of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.” The observatory (renamed the Royal Greenwich Observatory) was moved to Hailsham, East Sussex, during the 1950s, but the original site continues to serve as the location for 0° longitude.

As the prime meridian, the north-south line at Greenwich is used as the reference for all other meridians of longitude, which are numbered east or west of it. The Greenwich meridian also serves as the basis for the world’s standard time zone system. The mean solar time at Greenwich is now called Universal Time (q.v.) and was formerly called Greenwich Mean Time (q.v.). Theoretically, standard time becomes successively one hour earlier at each 15° longitude west of the Greenwich meridian and one hour later at each 15° longitude east. (See standard time.)

Greenwich meridian

) and was formerly called Greenwich Mean Time (q.v.). Theoretically, standard time becomes successively one hour earlier at each 15° longitude west of the Greenwich meridian and one hour later at each 15° longitude east. (See standard time.)…

solar time

Solar time, time measured by Earth’s rotation relative to the Sun. Apparent solar time is that measured by direct observation of the Sun or by a sundial. Mean solar time, kept by most clocks and watches, is the solar time that would be measured by observation if the Sun traveled…

 

Greenwich Mean Time is the mean solar time

Alternative Title:prime meridian

 

-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
G
=
7
-
9
GREENWICH
92
56
2
M
=
4
-
4
MEAN
33
15
6
T
=
2
-
4
TIME
47
20
2
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
-
1+3
-
1+7
-
1+7+2
9+1
1+0
-
-
4
-
8
GREENWICH MEAN TIME
10
10
1
-
-
-
-
-
-
1+0
1+0
-
-
-
4
-
8
GREENWICH MEAN TIME
1
1
1

 

 

-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
-
-
-
-
-
M
=
4
-
4
MEAN
33
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
5
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
56
-
9
-
92
56
56
-
-
-
-
-
-
-
-
-
-
M
=
5
10
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
4
-
33
15
15
-
-
-
-
-
-
-
-
-
-
T
=
2
14
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
5
16
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
20
-
4
-
47
20
20
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
8
35
6
7
8
27
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
3+5
-
-
-
2+7
M
=
4
-
4
MEAN
33
15
6
-
1
2
3
8
8
6
7
8
9
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
8
8
6
7
8
9
-
-
1+3
-
1+7
-
1+7+2
9+1
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
10
10
1
-
1
2
3
8
8
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
1
1
1
-
1
2
3
8
8
6
7
8
9

 

 

-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
-
-
-
-
-
M
=
4
-
4
MEAN
33
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
N
=
5
5
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
M
=
5
10
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
T
=
2
14
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
M
=
5
16
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
8
35
6
7
8
27
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
3+5
-
-
-
2+7
M
=
4
-
4
MEAN
33
15
6
-
1
2
3
8
8
6
7
8
9
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
8
8
6
7
8
9
-
-
1+3
-
1+7
-
1+7+2
9+1
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
10
10
1
-
1
2
3
8
8
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
1
1
1
-
1
2
3
8
8
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
-
-
-
-
-
M
=
4
-
4
MEAN
33
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
T
=
2
14
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
M
=
5
10
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
M
=
5
16
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
N
=
5
5
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GREENWICH MEAN TIME
-
-
-
-
1
2
3
8
35
6
7
8
27
G
=
7
-
9
GREENWICH
92
56
2
-
-
-
-
-
3+5
-
-
-
2+7
M
=
4
-
4
MEAN
33
15
6
-
1
2
3
8
8
6
7
8
9
T
=
2
-
4
TIME
47
20
2
-
-
-
-
-
-
-
-
-
-
-
-
13
-
17
GREENWICH MEAN TIME
172
91
10
-
1
2
3
8
8
6
7
8
9
-
-
1+3
-
1+7
-
1+7+2
9+1
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
10
10
1
-
1
2
3
8
8
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
8
GREENWICH MEAN TIME
1
1
1
-
1
2
3
8
8
6
7
8
9

 

GREENWICH MEAN TIME

 

:prime meridian

Alternative Title

Greenwich Mean Time is the mean solar time

 

 

-
-
-
-
-
PRIME MERIDIAN
-
-
-
P
=
7
-
5
PRIME
61
34
7
M
=
4
-
8
MERIDIAN
73
46
1
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
-
1+1
-
1+3
-
1+3+4
8+0
-
-
-
2
-
4
PRIME MERIDIAN
8
8
8

 

 

-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
5
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
34
-
5
-
61
34
34
-
-
-
-
-
-
-
-
-
-
M
=
5
6
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
5
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
11
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
46
-
8
-
73
46
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
12
15
6
7
8
45
-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
-
-
-
1+2
1+5
-
-
-
4+5
P
=
7
-
5
PRIME
61
34
7
-
1
2
3
3
6
6
7
8
9
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
3
6
6
7
8
9
-
-
1+1
-
1+3
-
1+3+4
8+0
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
4
PRIME MERIDIAN
8
8
8
-
1
2
3
3
6
6
7
8
9

 

 

-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
1
1
P
16
7
7
-
-
2
3
-
-
6
7
7
-
R
=
9
2
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
M
=
5
4
1
M
13
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
M
=
5
6
1
M
13
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
8
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
9
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
D
=
5
10
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
I
=
9
11
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
A
=
1
12
1
A
1
1
1
-
1
2
3
-
-
6
-
8
-
N
=
5
13
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
12
15
6
7
8
45
-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
-
-
-
1+2
1+5
-
-
-
4+5
P
=
7
-
5
PRIME
61
34
7
-
1
2
3
3
6
6
7
8
9
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
3
6
6
7
8
9
-
-
1+1
-
1+3
-
1+3+4
8+0
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
4
PRIME MERIDIAN
8
8
8
-
1
2
3
3
6
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
2
3
-
-
6
-
8
-
M
=
5
4
1
M
13
4
4
-
-
2
3
4
-
6
-
8
-
M
=
5
6
1
M
13
4
4
-
-
2
3
4
-
6
-
8
-
D
=
5
10
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
13
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
2
3
-
-
6
7
7
-
R
=
9
2
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
8
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
9
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
11
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
12
15
6
7
8
45
-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
-
-
-
1+2
1+5
-
-
-
4+5
P
=
7
-
5
PRIME
61
34
7
-
1
2
3
3
6
6
7
8
9
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
2
3
3
6
6
7
8
9
-
-
1+1
-
1+3
-
1+3+4
8+0
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
4
PRIME MERIDIAN
8
8
8
-
1
2
3
3
6
6
7
8
9

 

 

-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
1
4
5
7
9
P
=
7
-
5
PRIME
61
34
7
-
-
-
-
-
-
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
4
5
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
M
=
5
4
1
M
13
4
4
-
-
4
-
-
-
M
=
5
6
1
M
13
4
4
-
-
4
-
-
-
D
=
5
10
1
D
4
4
4
-
-
4
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
5
-
-
E
=
5
7
1
E
5
5
5
-
-
-
5
-
-
N
=
5
13
1
N
14
5
5
-
-
-
5
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
7
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
9
R
=
9
8
1
R
18
9
9
-
-
-
-
-
9
I
=
9
9
1
I
9
9
9
-
-
-
-
-
9
I
=
9
11
1
I
9
9
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
1
12
15
7
45
-
-
-
-
-
PRIME MERIDIAN
-
-
-
-
-
1+2
1+5
-
4+5
P
=
7
-
5
PRIME
61
34
7
-
1
3
6
7
9
M
=
4
-
8
MERIDIAN
73
46
1
-
-
-
-
-
-
-
-
11
-
13
PRIME MERIDIAN
134
80
8
-
1
3
6
7
9
-
-
1+1
-
1+3
-
1+3+4
8+0
-
-
-
-
-
-
-
-
-
2
-
4
PRIME MERIDIAN
8
8
8
-
1
3
6
7
9

 

 

EARTH HEART EARTH

THE

HEART OF EARTH

 

The line in Greenwich represents the historic Prime Meridian of the World - Longitude 0º. Every place on Earth was measured in terms of its distance east or west from this line. The line itself divided the eastern and western hemispheres of the Earth - just as the Equator divides the northern and southern hemispheres.

Prime meridian (Greenwich) - Wikipedia
https://en.wikipedia.org › wiki › Prime_meridian_(Gree...

The prime meridian is a geographical reference line that passes through the Royal Observatory, Greenwich, in London, England. ... It was first established by Sir ...

?History · ?Meridian today

The prime meridian is a geographical reference line that passes through the Royal Observatory, Greenwich, in London, England.[1] It was first established by Sir George Airy in 1851, and by 1884, over two-thirds of all ships and tonnage used it as the reference meridian on their charts and maps. In October of that year, at the behest of US President Chester A. Arthur, 41 delegates from 25 nations met in Washington, D.C., United States, for the International Meridian Conference. This conference selected the meridian passing through Greenwich as the official prime meridian due to its popularity.[note 1][2] However, France abstained from the vote, and French maps continued to use the Paris meridian for several decades. In the 18th century, London lexicographer Malachy Postlethwayt published his African maps showing the "Meridian of London" intersecting the Equator a few degrees west of the later meridian and Accra, Ghana.[3]
Laser projected from the Royal Observatory in Greenwich, marking the Prime meridian.
The plane of the prime meridian is parallel to the local gravity vector at the Airy transit circle (

51°28'40.1"N 0°0'5.3"W)[4] of the Greenwich observatory. The prime meridian was therefore long symbolised by a brass strip in the courtyard, now replaced by stainless steel, and since 16 December 1999, it has been marked by a powerful green laser shining north across the London night sky.

Global Positioning System (GPS) receivers show that the marking strip for the prime meridian at Greenwich is not exactly at zero degrees, zero minutes, and zero seconds but at approximately 5.3 seconds of arc to the west of the meridian (meaning that the meridian appears to be 102.478 metres east). In the past, this offset has been attributed to the establishment of reference meridians for space-based location systems such as WGS 84 (which GPS relies on) or that errors gradually crept into the International Time Bureau timekeeping process. The actual reason for the discrepancy is that the difference between precise GNSS coordinates and astronomically determined coordinates everywhere remains a localized gravity effect due to vertical deflection; thus, no systematic rotation of global longitudes occurred between the former astronomical system and the current geodetic system.[5]

 

Stand on the Prime Meridian Line | Royal Museums Greenwich
https://www.rmg.co.uk › royal-observatory › attractions

Since the late 19th century, the Prime Meridian at Greenwich has divided the eastern and western hemispheres of the earth - just as the equator divides the ...

 

prime meridian | National Geographic Society
https://www.nationalgeographic.org › encyclopedia › p...

16 Feb 2011 — The prime meridian is the line of 0 longitude, the starting point for measuring distance both east and west around the Earth. The prime meridian is ...
prime meridian

Encyclopedic entry. The prime meridian is the line of 0° longitude, the starting point for measuring distance both east and west around the Earth. The prime meridian is arbitrary, meaning it could be chosen to be anywhere.

The prime meridian is the line of 0 longitude, the starting point for measuring distance both east and west around the Earth.

The prime meridian is arbitrary, meaning it could be chosen to be anywhere. Any line of longitude (a meridian) can serve as the 0 longitude line. However, there is an international agreement that the meridian that runs through Greenwich, England, is considered the official prime meridian.

Governments did not always agree that the Greenwich meridian was the prime meridian, making navigation over long distances very difficult. Different countries published maps and charts with longitude based on the meridian passing through their capital city. France would publish maps with 0 longitude running through Paris. Cartographers in China would publish maps with 0 longitude running through Beijing. Even different parts of the same country published materials based on local meridians.

Finally, at an international convention called by U.S. President Chester Arthur in 1884, representatives from 25 countries agreed to pick a single, standard meridian. They chose the meridian passing through the Royal Observatory in Greenwich, England. The Greenwich Meridian became the international standard for the prime meridian.

UTCThe prime meridian also sets Coordinated Universal Time (UTC). UTC never changes for daylight savings or anything else. Just as the prime meridian is the standard for longitude, UTC is the standard for time. All countries and regions measure their time zones according to UTC.

There are 24 time zones in the world. If an event happens at 11:00 a.m. in Houston, Texas, it would be reported at 12 p.m. in Orlando, Florida; 4:00 p.m. in Morocco; 9:00 p.m. in Kolkata, India; and 6:00 a.m. in Honolulu, Hawaii. The event happened at 4:00 p.m. UTC.

The prime meridian also helps establish the International Date Line. The Earth's longitude measures 360, so the halfway point from the prime meridian is the 180 longitude line. The meridian at 180 longitude is commonly known as the International Date Line. As you pass the International Date Line, you either add a day (going west) or subtract a day (going east.)

Hemispheres

The prime meridian and the International Date Line create a circle that divides the Earth into the eastern and western hemispheres. This is similar to the way the Equator serves as the 0 latitude line and divides the Earth into the northern and southern hemispheres.

The eastern hemisphere is east of the prime meridian and west of the International Date Line. Most of Earths landmasses, including all of Asia and Australia, and most of Africa, are part of the eastern hemisphere.

The western hemisphere is west of the prime meridian and east of the International Date Line. The Americas, the western part of the British Isles (including Ireland and Wales), and the northwestern part of Africa are landmasses in the western hemisphere.

prime meridian
The Royal Observatory, which identified the prime meridian in 1884, is no longer a working scientific facility. It is maintained as a tourist attraction.
Photograph by Bruce Dale

Laser Meridian
Today, the prime meridian is marked by a laser beam that shoots out northward from the Royal Observatory in Greenwich, England.

Planetary Prime Meridians
The Earth is not the only planet with a prime meridian. Scientists use craters or other geographic features to mark prime meridians on other planets and celestial bodies. The prime meridian of Mars runs through a crater named Airy-0. The prime meridian of the Earth's moon runs near a crater named Bruce.

 

 

A
=
1
6
AUTUMN
90
18
9
S
=
1
6
SUMMER
89
26
8
W
=
5
6
WINTER
89
35
8
S
=
1
6
SPRING
83
38
2
-
-
8
24
Add to Reduce
351
117
27
-
-
-
2+4
Reduce to Deduce
3+5+1
1+1+7
2+7
-
-
8
6
Essence of Number
9
9
9

 

 

-
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
5
+
1
-
-
-
-
-
+
-
9
5
-
-
-
+
1
-
-
9
5
-
+
=
35
3+5
=
8
=
8
=
8
-
-
-
-
-
-
-
14
+
19
-
-
-
-
-
+
-
9
14
-
-
-
+
19
-
-
9
14
-
+
=
98
9+8
=
17
1+7
8
=
8
-
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
1
3
2
3
4
-
+
-
3
4
4
5
9
+
5
-
-
2
5
9
+
-
7
9
-
-
7
+
=
82
8+2
=
10
1+0
1
=
1
-
-
1
21
20
21
13
-
+
-
21
13
13
5
18
+
23
-
-
20
5
18
+
-
16
18
-
-
7
+
=
253
2+5+3
=
10
1+0
1
=
1
-
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
1
21
20
21
13
14
+
19
21
13
13
5
18
+
23
9
14
20
5
18
+
19
16
18
9
14
7
+
=
351
3+5+1
=
9
=
9
=
9
-
-
1
3
2
3
4
5
+
1
3
4
4
5
9
+
5
9
5
2
5
9
+
1
7
9
9
5
7
+
=
117
1+1+7
=
9
=
9
=
9
-
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
4
-
-
-
-
4
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
5
-
5
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
-
9
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
14
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
31
-
-
24
-
117
-
36
1+4
2+4
-
-
-
--
-
-
-
--
-
-
-
-
9
-
--
9
-
-
-
9
-
--
-
9
9
-
-
-
-
3+1
-
-
2+4
-
1+1+7
-
3+6
5
6
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9
-
-
1
3
2
3
4
5
+
1
3
4
4
5
9
+
5
9
5
2
5
9
+
1
7
9
9
5
7
-
-
-
-
-
-
-
-
-
-
5
6
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9

 

 

4
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
+
1
-
-
-
-
-
+
-
9
5
-
-
-
+
1
-
-
9
5
-
+
=
35
3+5
=
8
=
8
=
8
-
-
-
-
-
-
14
+
19
-
-
-
-
-
+
-
9
14
-
-
-
+
19
-
-
9
14
-
+
=
98
9+8
=
17
1+7
8
=
8
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
1
3
2
3
4
-
+
-
3
4
4
5
9
+
5
-
-
2
5
9
+
-
7
9
-
-
7
+
=
82
8+2
=
10
1+0
1
=
1
-
1
21
20
21
13
-
+
-
21
13
13
5
18
+
23
-
-
20
5
18
+
-
16
18
-
-
7
+
=
253
2+5+3
=
10
1+0
1
=
1
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
1
21
20
21
13
14
+
19
21
13
13
5
18
+
23
9
14
20
5
18
+
19
16
18
9
14
7
+
=
351
3+5+1
=
9
=
9
=
9
-
1
3
2
3
4
5
+
1
3
4
4
5
9
+
5
9
5
2
5
9
+
1
7
9
9
5
7
+
=
117
1+1+7
=
9
=
9
=
9
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
4
-
-
-
-
4
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
5
-
5
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
-
9
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
24
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
31
-
-
24
-
117
-
36
2+4
-
-
-
--
-
-
-
--
-
-
-
-
9
-
--
9
-
-
-
9
-
--
-
9
9
-
-
-
-
3+1
-
-
2+4
-
1+1+7
-
3+6
6
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9
-
1
3
2
3
4
5
+
1
3
4
4
5
9
+
5
9
5
2
5
9
+
1
7
9
9
5
7
-
-
-
-
-
-
-
-
-
-
6
A
U
T
U
M
N
-
S
U
M
M
E
R
-
W
I
N
T
E
R
-
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9

 

 

4
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
1
-
-
-
-
-
-
9
5
-
-
-
1
-
-
9
5
-
+
=
35
3+5
=
8
=
8
=
8
-
-
-
-
-
-
14
19
-
-
-
-
-
-
9
14
-
-
-
19
-
-
9
14
-
+
=
98
9+8
=
17
1+7
8
=
8
24
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
1
3
2
3
4
-
-
3
4
4
5
9
5
-
-
2
5
9
-
7
9
-
-
7
+
=
82
8+2
=
10
1+0
1
=
1
-
1
21
20
21
13
-
-
21
13
13
5
18
23
-
-
20
5
18
-
16
18
-
-
7
+
=
253
2+5+3
=
10
1+0
1
=
1
24
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
-
-
-
--
-
-
-
-
-
1
21
20
21
13
14
19
21
13
13
5
18
23
9
14
20
5
18
19
16
18
9
14
7
+
=
351
3+5+1
=
9
=
9
=
9
-
1
3
2
3
4
5
1
3
4
4
5
9
5
9
5
2
5
9
1
7
9
9
5
7
+
=
117
1+1+7
=
9
=
9
=
9
24
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
4
-
-
-
4
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
5
-
-
-
-
5
-
5
-
5
-
5
-
-
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
9
-
-
9
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
24
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
31
-
-
24
-
117
-
36
2+4
-
-
-
--
-
-
--
-
-
-
-
9
--
9
-
-
-
9
--
-
9
9
-
-
-
-
3+1
-
-
2+4
-
1+1+7
-
3+6
6
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9
-
1
3
2
3
4
5
1
3
4
4
5
9
5
9
5
2
5
9
1
7
9
9
5
7
-
-
-
-
-
-
-
-
-
-
6
A
U
T
U
M
N
S
U
M
M
E
R
W
I
N
T
E
R
S
P
R
I
N
G
-
-
4
-
-
6
-
9
-
9

 

 

AUTUMN ATUM AUTUMN

 

 

T
=
2
-
6
TWENTY
107
26
8
F
=
6
-
4
FOUR
60
24
6
H
=
8
-
5
HOURS
81
27
9
I
=
9
-
2
IN
23
14
5
A
=
1
-
1
A
1
1
1
D
=
4
-
3
DAY
30
12
3
-
-
30
Q
21
Add to Reduce
302
104
32
-
-
2+0
-
2+1
Reduce to Deduce
3+0+2
1+0+4
3+2
-
-
8
-
3
Essence of Number
5
5
5

 

 

M
=
4
-
6
MINUTE
82
28
1
-
1
H
=
8
-
4
HOUR
62
26
8
-
8
D
=
4
-
3
DAY
30
12
3
-
3
S
=
1
-
6
SECOND
60
33
6
-
6
-
-
17
Q
19
First Total
234
99
18
Q
18
-
-
1+7
-
1+9
Add to Reduce
2+3+4
9+9
1+8
-
1+8
-
-
8
-
10
Second Total
9
18
9
-
9
-
-
-
-
1+0
Reduce to Deduce
-
1+8
-
-
-
-
-
8
-
1
Essence of Number
9
9
9
-
9

 

 

-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MINUTE
82
28
1
-
1
-
-
-
-
-
-
-
-
-
H
=
8
-
4
HOUR
62
26
8
-
8
-
-
-
-
-
-
-
-
-
D
=
4
-
3
DAY
30
12
3
-
3
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SECOND
60
33
6
-
6
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
MINUTE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
-
2
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
-
-
28
-
6
MINUTE
82
28
28
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HOUR
-
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
-
8
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
-
9
-
-
26
-
4
HOUR
62
26
26
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
DAY
-
-
-
-
-
-
-
-
-
-
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
-
1
-
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
-
7
-
-
-
-
12
-
3
DAY
30
12
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SECOND
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
3
S
19
10
1
-
-
1
-
-
-
-
-
-
-
-
E
=
5
-
5
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
C
=
3
-
3
C
3
3
3
-
-
-
-
3
-
-
-
-
-
-
O
=
6
-
6
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
-
-
24
-
3
SECOND
60
33
24
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
-
6
MINUTE
82
28
1
-
-
2
2
9
12
20
12
7
8
18
H
=
8
-
4
HOUR
62
26
8
-
-
-
-
-
1+2
2+0
1+2
-
-
1+8
D
=
4
-
3
DAY
30
12
3
-
-
2
2
9
3
2
3
7
8
9
S
=
1
-
6
SECOND
60
33
6
-
-
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
-
2
2
9
3
2
3
7
8
9
-
-
1+7
-
1+9
Add to Reduce
2+3+4
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
Second Total
9
18
9
-
-
2
2
9
3
2
3
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
Essence of Number
9
9
5
-
-
2
2
9
3
2
3
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MINUTE
82
28
1
-
1
-
-
-
-
-
-
-
-
-
H
=
8
-
4
HOUR
62
26
8
-
8
-
-
-
-
-
-
-
-
-
D
=
4
-
3
DAY
30
12
3
-
3
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SECOND
60
33
6
-
6
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
1
M
13
4
4
-
-
-
-
-
4
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
-
2
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
-
8
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
-
9
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
A
=
1
-
1
A
1
1
1
-
-
1
-
-
-
-
-
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
-
7
-
-
S
=
1
-
3
S
19
10
1
-
-
1
-
-
-
-
-
-
-
-
E
=
5
-
5
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
C
=
3
-
3
C
3
3
3
-
-
-
-
3
-
-
-
-
-
-
O
=
6
-
6
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
-
6
MINUTE
82
28
1
-
-
2
2
9
12
20
12
7
8
18
H
=
8
-
4
HOUR
62
26
8
-
-
-
-
-
1+2
2+0
1+2
-
-
1+8
D
=
4
-
3
DAY
30
12
3
-
-
2
2
9
3
2
3
7
8
9
S
=
1
-
6
SECOND
60
33
6
-
-
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
-
2
2
9
3
2
3
7
8
9
-
-
1+7
-
1+9
Add to Reduce
2+3+4
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
Second Total
9
18
9
-
-
2
2
9
3
2
3
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
Essence of Number
9
9
5
-
-
2
2
9
3
2
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MINUTE
82
28
1
-
1
-
-
-
-
-
-
-
-
-
H
=
8
-
4
HOUR
62
26
8
-
8
-
-
-
-
-
-
-
-
-
D
=
4
-
3
DAY
30
12
3
-
3
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SECOND
60
33
6
-
6
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
-
1
-
-
-
-
-
-
-
-
S
=
1
-
3
S
19
10
1
-
-
1
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
-
2
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
-
3
-
-
-
-
-
-
C
=
3
-
3
C
3
3
3
-
-
-
-
3
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
-
4
-
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
D
=
4
-
1
D
4
4
4
-
-
-
-
-
4
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
E
=
5
-
5
E
5
5
5
-
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
O
=
6
-
6
O
15
6
6
-
-
-
-
-
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
-
6
MINUTE
82
28
1
-
-
2
2
9
12
20
12
7
8
18
H
=
8
-
4
HOUR
62
26
8
-
-
-
-
-
1+2
2+0
1+2
-
-
1+8
D
=
4
-
3
DAY
30
12
3
-
-
2
2
9
3
2
3
7
8
9
S
=
1
-
6
SECOND
60
33
6
-
-
-
-
-
-
-
-
-
-
-
-
-
17
Q
19
First Total
234
99
18
Q
-
2
2
9
3
2
3
7
8
9
-
-
1+7
-
1+9
Add to Reduce
2+3+4
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
Second Total
9
18
9
-
-
2
2
9
3
2
3
7
8
9
-
-
-
-
1+0
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
Essence of Number
9
9
5
-
-
2
2
9
3
2
3
7
8
9

 

LETTERS RE-ARRANGED IN NUMERICAL ORDER

 

 

What are 7 days in a week?

According to international standard ISO 8601,

Monday is the first day of the week. It is followed by Tuesday, Wednesday, Thursday, Friday, and Saturday. Sunday is the 7th and last day of the week.

 

 

M
=
4
-
6
MONDAY
72
27
9
T
=
2
-
7
TUESDAY
95
32
5
W
=
5
-
9
WEDNESDAY
100
46
1
T
=
2
-
8
THURSDAY
116
44
8
F
=
6
-
6
FRIDAY
63
36
9
S
=
1
-
8
SATURDAY
109
37
1
S
=
1
-
6
SUNDAY
84
30
3
-
-
21
4
50
First Total
639
252
36
-
-
2+1
-
5+0
Add to Reduce
6+3+9
2+0+7
3+6
-
-
3
-
5
Second Total
18
9
9
-
-
-
4
-
Reduce to Deduce
1+8
-
-
-
-
3
5
5
Essence of Number
9
9
9

 

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MONDAY
72
27
9
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
TUESDAY
95
32
5
-
-
-
-
-
-
-
-
-
-
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
-
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
-
-
-
-
-
-
-
-
-
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
MONDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
6
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
27
-
6
MONDAY
72
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
TUESDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
11
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
13
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
23
-
7
TUESDAY
92
32
23
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
WEDNESDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
21
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
22
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
37
-
6
WEDNESDAY
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THURSDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
28
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
29
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
30
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
28
-
8
THURSDAY
116
44
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FRIDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
35
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
36
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
28
-
6
FRIDAY
63
36
28
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SATURDAY
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
42
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
43
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
44
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
28
-
8
SATURDAY
109
37
28
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUNDAYAY
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
48
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
49
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
50
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
21
-
6
SUNDAY
84
30
21
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
13
6
12
36
35
12
49
8
36
M
=
4
-
6
MONDAY
72
27
9
-
1+3
-
1+2
3+6
3+5
1+2
4+9
-
3+6
T
=
2
-
7
TUESDAY
95
32
5
-
4
6
3
9
8
3
13
8
9
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
1+3
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
4
6
3
9
8
3
4
8
9
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
4
6
3
9
8
3
4
8
9
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
4
6
3
9
8
3
4
8
9
-
-
2+1
-
5+0
Add to Reduce
6+3+9
2+0+7
3+6
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
18
9
9
-
4
6
3
9
8
3
4
8
9
-
-
-
4
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
5
Essence of Number
9
9
9
-
4
6
3
9
8
3
4
8
9

 

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MONDAY
72
27
9
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
TUESDAY
95
32
5
-
-
-
-
-
-
-
-
-
-
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
-
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
-
-
-
-
-
-
-
-
-
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
6
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
11
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
13
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
21
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
22
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
D
=
4
28
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
29
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
30
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
35
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
36
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
42
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
43
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
44
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
48
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
49
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
50
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
13
6
12
36
35
12
49
8
36
M
=
4
-
6
MONDAY
72
27
9
-
1+3
-
1+2
3+6
3+5
1+2
4+9
-
3+6
T
=
2
-
7
TUESDAY
95
32
5
-
4
6
3
9
8
3
13
8
9
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
1+3
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
4
6
3
9
8
3
4
8
9
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
4
6
3
9
8
3
4
8
9
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
4
6
3
9
8
3
4
8
9
-
-
2+1
-
5+0
Add to Reduce
6+3+9
2+0+7
3+6
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
18
9
9
-
4
6
3
9
8
3
4
8
9
-
-
-
4
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
5
Essence of Number
9
9
9
-
4
6
3
9
8
3
4
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
6
MONDAY
72
27
9
-
-
-
-
-
-
-
-
-
-
T
=
2
-
7
TUESDAY
95
32
5
-
-
-
-
-
-
-
-
-
-
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
-
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
-
-
-
-
-
-
-
-
-
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
21
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
29
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
A
=
1
35
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
A
=
1
43
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
49
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
11
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
28
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
34
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
42
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
48
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
6
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
13
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
22
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
36
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
44
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
30
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
13
6
12
36
35
12
49
8
36
M
=
4
-
6
MONDAY
72
27
9
-
1+3
-
1+2
3+6
3+5
1+2
4+9
-
3+6
T
=
2
-
7
TUESDAY
95
32
5
-
4
6
3
9
8
3
13
8
9
W
=
5
-
9
WEDNESDAY
100
46
1
-
-
-
-
-
-
-
1+3
-
-
T
=
2
-
8
THURSDAY
116
44
8
-
4
6
3
9
8
3
4
8
9
F
=
6
-
6
FRIDAY
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SATURDAY
109
37
1
-
4
6
3
9
8
3
4
8
9
S
=
1
-
6
SUNDAY
84
30
3
-
-
-
-
-
-
-
-
-
-
-
-
21
4
50
First Total
639
252
36
Q
4
6
3
9
8
3
4
8
9
-
-
2+1
-
5+0
Add to Reduce
6+3+9
2+0+7
3+6
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
18
9
9
-
4
6
3
9
8
3
4
8
9
-
-
-
4
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
5
Essence of Number
9
9
9
-
4
6
3
9
8
3
4
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY

 

MINUS A DAY IN THE LIFE OF

MON TUES WEDNES THURS FRI SATUR SUN

 

M
=
4
-
3
MON
42
15
6
T
=
2
-
4
TUES
65
20
2
W
=
5
-
6
WEDNES
70
34
7
T
=
2
-
5
THURS
86
32
5
F
=
6
-
3
FRI
33
24
6
S
=
1
-
5
SATUR
79
25
7
S
=
1
-
3
SUN
54
18
9
-
-
21
4
29
First Total
429
168
42
-
-
2+1
-
2+9
Add to Reduce
4+2+9
1+6+8
4+2
-
-
3
-
11
Second Total
15
15
6
-
-
-
4
1+1
Reduce to Deduce
1+5
1+5
-
-
-
3
5
2
Essence of Number
6
6
6

 

MINUS A DAY IN THE LIFE OF

MON TUES WEDNES THURS FRI SATUR SUN

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
3
MON
42
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TUES
65
20
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
-
-
-
-
-
-
-
-
-
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
MON
-
-
-
-
-
-
-
-
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
3
MON
42
15
15
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
TUES
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
11
-
7
TUES
65
20
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
WEDNES
-
-
-
-
-
-
-
-
-
-
-
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
25
-
6
WEDNES
70
34
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THURS
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
23
-
5
THURS
86
32
23
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FRI
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
28
-
3
FRI
33
24
24
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SATUR
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
16
-
5
SATUR
79
25
16
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUNY
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
9
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
12
8
35
12
7
8
36
M
=
4
-
3
MON
42
15
6
-
-
-
1+2
-
3+5
1+2
-
-
3+6
T
=
2
-
4
TUES
65
20
2
-
6
6
3
8
8
3
7
8
9
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
6
6
3
8
8
3
7
8
9
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
6
6
3
8
8
3
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
6
6
3
8
8
3
7
8
9
-
-
2+1
-
2+9
Add to Reduce
4+2+9
1+6+8
4+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
11
Second Total
15
15
6
-
6
6
3
8
8
3
7
8
9
-
-
-
4
1+1
Reduce to Deduce
1+5
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
2
Essence of Number
6
6
6
-
6
6
3
8
8
3
7
8
9

 

MON TUES WEDNES THURS FRI SATUR SUN

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
3
MON
42
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TUES
65
20
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
-
-
-
-
-
-
-
-
-
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
7
-
-
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
-
-
-
-
-
-
-
-
-
-
6
6
12
8
35
12
7
8
36
M
=
4
-
3
MON
42
15
6
-
-
-
1+2
-
3+5
1+2
-
-
3+6
T
=
2
-
4
TUES
65
20
2
-
6
6
3
8
8
3
7
8
9
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
6
6
3
8
8
3
7
8
9
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
6
6
3
8
8
3
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
6
6
3
8
8
3
7
8
9
-
-
2+1
-
2+9
Add to Reduce
4+2+9
1+6+8
4+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
11
Second Total
15
15
6
-
6
6
3
8
8
3
7
8
9
-
-
-
4
1+1
Reduce to Deduce
1+5
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
2
Essence of Number
6
6
6
-
6
6
3
8
8
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
3
MON
42
15
6
-
-
-
-
-
-
-
-
-
-
T
=
2
-
4
TUES
65
20
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
-
-
-
-
-
-
-
-
-
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
-
-
-
-
-
-
-
-
-
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
S
=
1
27
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
S
=
1
37
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
A
=
1
38
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
S
=
1
45
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
39
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
U
=
3
25
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
U
=
3
40
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
U
=
3
46
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
W
=
5
14
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
F
=
6
31
1
F
6
6
6
-
-
-
-
-
-
6
7
-
-
H
=
8
24
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
R
=
9
26
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
32
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
I
=
9
33
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
41
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
-
-
-
-
-
-
-
-
-
-
6
6
12
8
35
12
7
8
36
M
=
4
-
3
MON
42
15
6
-
-
-
1+2
-
3+5
1+2
-
-
3+6
T
=
2
-
4
TUES
65
20
2
-
6
6
3
8
8
3
7
8
9
W
=
5
-
6
WEDNES
70
34
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
THURS
86
32
5
-
6
6
3
8
8
3
7
8
9
F
=
6
-
3
FRI
33
24
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SATUR
79
25
7
-
6
6
3
8
8
3
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
-
-
-
-
-
-
-
21
4
29
First Total
429
168
42
Q
6
6
3
8
8
3
7
8
9
-
-
2+1
-
2+9
Add to Reduce
4+2+9
1+6+8
4+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
11
Second Total
15
15
6
-
6
6
3
8
8
3
7
8
9
-
-
-
4
1+1
Reduce to Deduce
1+5
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
2
Essence of Number
6
6
6
-
6
6
3
8
8
3
7
8
9

 

MON TUES WEDNES THURS FRI SATUR SUN

 

 

 

 

M
=
4
-
6
MONDAY
72
27
9
T
=
2
-
7
TUESDAY
95
23
5
W
=
5
-
9
WEDNESDAY
100
37
1
T
=
2
-
8
THURSDAY
116
35
8
F
=
6
-
6
FRIDAY
63
36
9
S
=
1
-
8
SATURDAY
109
28
1
S
=
1
-
6
SUNDAY
84
21
3
-
-
21
4
50
First Total
639
207
36
-
-
2+1
-
5+0
Add to Reduce
6+3+9
2+0+7
3+6
-
-
3
-
5
Second Total
18
9
9
-
-
-
4
-
Reduce to Deduce
1+8
-
-
-
-
3
5
5
Essence of Number
9
9
9

 

 

5
SEVEN
65
20
2
4
DAYS
49
13
4
2
IN
23
14
5
1
A
1
1
1
4
WEEK
44
17
8

 

 

5
SEVEN
65
20
2
3
DAY
30
12
3
4
WEEK
44
17
8
12
First Total
139
49
13
1+2
Add to Reduce
1+3+9
4+9
1+3
3
Second Total
13
13
4
-
Reduce to Deduce
1+3
1+3
-
3
Essence of Number
4
4
4

 

 

-`
6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
1
-`
5
-
-
-
+
=
6
-
=
6
=
6
-
-
19
-
14
-
-
-
+
=
33
3+3
=
6
=
6
-
6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
3
-
4
1
7
+
=
15
1+5
=
6
=
6
-
-
-
21
-
4
1
25
+
=
51
5+1
=
6
=
6
-
6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
19
21
14
4
1
25
+
=
84
8+4
=
12
1+2
3
-
-
1
3
5
4
1
7
+
=
21
2+1
=
3
=
3
-
6
S
U
N
D
A
Y
T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
occurs
x
2
=
2
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
--
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
25
6
S
U
N
D
A
Y
-
-
20
-
-
6
-
21
2+5
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
2+1
7
6
S
U
N
D
A
Y
-
-
2
-
-
6
-
3
-
-
1
3
5
4
1
7
T
-
-
-
-
-
-
-
7
6
S
U
N
D
A
Y
-
-
2
-
-
6
-
3

 

 

6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
1
-`
5
-
-
-
+
=
6
-
=
6
=
6
-
19
-
14
-
-
-
+
=
33
3+3
=
6
=
6
6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
3
-
4
1
7
+
=
15
1+5
=
6
=
6
-
-
21
-
4
1
25
+
=
51
5+1
=
6
=
6
6
S
U
N
D
A
Y
-
-
-
-
-
-
-
-
-
19
21
14
4
1
25
+
=
84
8+4
=
12
1+2
3
-
1
3
5
4
1
7
+
=
21
2+1
=
3
=
3
6
S
U
N
D
A
Y
T
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
occurs
x
2
=
2
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
--
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
6
S
U
N
D
A
Y
-
-
20
-
-
6
-
21
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
2+1
6
S
U
N
D
A
Y
-
-
2
-
-
6
-
3
-
1
3
5
4
1
7
T
-
-
-
-
-
-
-
6
S
U
N
D
A
Y
-
-
2
-
-
6
-
3

 

 

-`
6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
+
=
11
1+1
=
2
=
2
-
-
-
15
14
-
-
-
+
=
29
2+9
=
11
1+1
2
-
6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
4
-
-
4
1
7
+
=
16
1+6
=
7
=
7
-
-
13
-
-
4
1
25
+
=
43
4+3
=
7
=
7
-
6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
13
15
14
4
1
25
+
=
72
7+2
=
9
=
9
-
-
4
6
5
4
1
7
+
=
27
2+7
=
9
=
9
-
6
M
O
N
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
--
4
-
-
4
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
22
6
M
O
N
D
A
Y
-
-
23
-
-
6
-
27
2+2
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+7
4
6
M
O
N
D
A
Y
-
-
5
-
-
6
-
9
-
-
4
6
5
4
1
7
T
-
-
-
-
-
-
-
4
6
M
O
N
D
A
Y
-
-
5
-
-
6
-
9

 

 

6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
+
=
11
1+1
=
2
=
2
-
-
15
14
-
-
-
+
=
29
2+9
=
11
1+1
2
6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
4
-
-
4
1
7
+
=
16
1+6
=
7
=
7
-
13
-
-
4
1
25
+
=
43
4+3
=
7
=
7
6
M
O
N
D
A
Y
-
-
-
-
-
-
-
-
-
13
15
14
4
1
25
+
=
72
7+2
=
9
=
9
-
4
6
5
4
1
7
+
=
27
2+7
=
9
=
9
6
M
O
N
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
--
4
-
-
4
-
-
-
-
4
occurs
x
2
=
8
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
6
M
O
N
D
A
Y
-
-
23
-
-
6
-
27
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+7
6
M
O
N
D
A
Y
-
-
5
-
-
6
-
9
-
4
6
5
4
1
7
T
-
-
-
-
-
-
-
6
M
O
N
D
A
Y
-
-
5
-
-
6
-
9

 

 

-`
7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-`
-`
-
1
-
-
-
+
=
1
-
=
1
=
1
-
-
-
-
-
19
-
-
-
+
=
19
1+9
=
10
1+0
1
-
7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
3
3
5
-
4
1
7
+
=
22
2+2
=
4
=
4
-
-
21
21
5
-
4
1
25
+
=
76
7+6
=
13
1+3
4
-
7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
20
21
5
19
4
1
25
+
=
95
9+5
=
14
1+4
5
-
-
2
3
5
1
4
1
7
+
=
23
2+3
=
5
=
5
-
7
T
U
E
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
23
7
T
U
E
S
D
A
Y
-
-
22
-
-
7
-
23
2+3
-
-
-
-
-
-
-
-
-
-
2+2
-
-
-
-
2+3
5
7
T
U
E
S
D
A
Y
-
-
4
-
-
7
-
5
-
-
2
3
5
1
4
1
7
-
-
-
-
-
-
-
-
5
7
T
U
E
S
D
A
Y
-
-
4
-
-
7
-
5

 

 

7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-`
-`
-
1
-
-
-
+
=
1
-
=
1
=
1
-
-
-
-
19
-
-
-
+
=
19
1+9
=
10
1+0
1
7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
3
3
5
-
4
1
7
+
=
22
2+2
=
4
=
4
-
21
21
5
-
4
1
25
+
=
76
7+6
=
13
1+3
4
7
T
U
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
20
21
5
19
4
1
25
+
=
95
9+5
=
14
1+4
5
-
2
3
5
1
4
1
7
+
=
23
2+3
=
5
=
5
7
T
U
E
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
7
T
U
E
S
D
A
Y
-
-
22
-
-
7
-
23
-
-
-
-
-
-
-
-
-
-
2+2
-
-
-
-
2+3
7
T
U
E
S
D
A
Y
-
-
4
-
-
7
-
5
-
2
3
5
1
4
1
7
-
-
-
-
-
-
-
-
7
T
U
E
S
D
A
Y
-
-
4
-
-
7
-
5

 

 

-`
9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
-
14
-
19
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
5
5
4
-
5
-
4
1
7
+
=
31
3+1
=
4
=
4
=
4
-
-
23
5
4
-
5
-
4
1
25
+
=
67
6+7
=
13
1+3
4
=
4
-
9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
23
5
4
14
5
19
4
1
25
+
=
100
1+0+0
=
1
=
1
=
1
-
-
5
5
4
5
5
1
4
1
7
+
=
37
3+7
=
10
1+0
1
=
1
-
9
W
E
D
N
E
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
5
5
-
5
5
-
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
28
9
W
E
D
N
E
S
D
A
Y
-
-
17
-
-
9
-
37
-
19
2+8
-
-
-
-
-
-
-
-
-
-
-
-
1+7
-
-
-
-
3+7
-
1+9
10
9
W
E
D
N
E
S
D
A
Y
-
-
8
-
-
9
-
10
-
10
1+0
-
5
5
4
5
5
1
4
1
7
-
-
-
-
-
-
-
1+0
-
1+0
1
9
W
E
D
N
E
S
D
A
Y
-
-
8
-
-
9
-
1
-
1

 

 

9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
14
-
19
-
-
-
+
=
33
3+3
=
6
=
6
=
6
9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
5
5
4
-
5
-
4
1
7
+
=
31
3+1
=
4
=
4
=
4
-
23
5
4
-
5
-
4
1
25
+
=
67
6+7
=
13
1+3
4
=
4
9
W
E
D
N
E
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
23
5
4
14
5
19
4
1
25
+
=
100
1+0+0
=
1
=
1
=
1
-
5
5
4
5
5
1
4
1
7
+
=
37
3+7
=
10
1+0
1
=
1
9
W
E
D
N
E
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
4
-
-
-
4
-
-
-
-
4
occurs
x
2
=
8
=
8
-
5
5
-
5
5
-
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
9
W
E
D
N
E
S
D
A
Y
-
-
17
-
-
9
-
37
-
19
-
5
5
-
5
5
-
-
-
-
-
-
1+7
-
-
-
-
3+7
-
1+9
9
W
E
D
N
E
S
D
A
Y
-
-
8
-
-
9
-
10
-
10
-
5
5
4
5
5
1
4
1
7
-
-
-
-
-
-
-
1+0
-
1+0
9
W
E
D
N
E
S
D
A
Y
-
-
8
-
-
9
-
1
-
1

 

 

-
8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
-
-
+
=
9
-
=
9
=
9
-
-
-
8
-
-
19
-
-
-
+
=
27
2_7
=
9
=
9
-
8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
2
-
3
9
-
4
1
7
+
=
26
2+6
=
8
=
8
-
-
20
-
21
18
-
4
1
25
+
=
89
8+9
=
17
1+7
8
-
8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
20
8
21
18
19
4
1
25
+
=
116
1+1+6
=
8
=
8
-
-
2
8
3
9
1
4
1
7
+
=
35
3+5
=
8
=
8
-
8
T
H
U
R
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
--
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
11
8
T
H
U
R
S
D
A
Y
-
-
34
-
-
8
-
35
1+1
-
-
-
-
9
-
-
-
-
-
-
3+4
-
-
-
-
3+5
2
8
T
H
U
R
S
D
A
Y
-
-
7
-
-
8
-
8
-
-
2
8
3
9
1
4
1
7
T
-
-
-
-
-
-
-
2
8
T
H
U
R
S
D
A
Y
-
-
7
-
-
8
-
8

 

 

8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
-
8
-
-
1
-
-
-
+
=
9
-
=
9
=
9
-
-
8
-
-
19
-
-
-
+
=
27
2_7
=
9
=
9
8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
2
-
3
9
-
4
1
7
+
=
26
2+6
=
8
=
8
-
20
-
21
18
-
4
1
25
+
=
89
8+9
=
17
1+7
8
8
T
H
U
R
S
D
A
Y
-
-
-
-
-
-
-
-
-
20
8
21
18
19
4
1
25
+
=
116
1+1+6
=
8
=
8
-
2
8
3
9
1
4
1
7
+
=
35
3+5
=
8
=
8
8
T
H
U
R
S
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
--
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
8
T
H
U
R
S
D
A
Y
-
-
34
-
-
8
-
35
-
-
-
-
9
-
-
-
-
-
-
3+4
-
-
-
-
3+5
8
T
H
U
R
S
D
A
Y
-
-
7
-
-
8
-
8
-
2
8
3
9
1
4
1
7
T
-
-
-
-
-
-
-
8
T
H
U
R
S
D
A
Y
-
-
7
-
-
8
-
8

 

 

-
6
F
R
I
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
6
9
-
4
1
7
+
=
27
2+7
=
9
=
9
=
9
-
-
6
18
-
4
1
25
+
=
54
5+4
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
-
-
-
-
-
--
-
-
-
-
-
-
6
18
9
4
1
25
+
=
63
6+3
=
9
=
9
=
9
-
-
6
9
9
4
1
7
+
=
36
3+6
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
6
F
R
I
D
A
Y
-
-
27
-
-
6
-
36
-
27
1+8
-
-
9
9
-
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
9
6
F
R
I
D
A
Y
-
-
9
-
-
6
-
9
-
9
-
-
6
9
9
4
1
7
T
-
-
-
-
-
-
-
-
-
9
6
F
R
I
D
A
Y
-
-
9
-
-
6
-
9
-
9

 

 

-
6
F
R
I
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
6
9
-
4
1
7
+
=
27
2+7
=
9
=
9
=
9
-
-
6
18
-
4
1
25
+
=
54
5+4
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
6
18
9
4
1
25
+
=
63
6+3
=
9
=
9
=
9
-
-
6
9
9
4
1
7
+
=
36
3+6
=
9
=
9
=
9
-
6
F
R
I
D
A
Y
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
6
F
R
I
D
A
Y
-
-
27
-
-
6
-
36
-
27
1+8
-
-
9
9
-
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
9
6
F
R
I
D
A
Y
-
-
9
-
-
6
-
9
-
9
-
-
6
9
9
4
1
7
T
-
-
-
-
-
-
-
-
-
9
6
F
R
I
D
A
Y
-
-
9
-
-
6
-
9
-
9

 

 

-
8
S
A
T
U
R
D
A
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
-
=
1
=
1
-
-
19
-
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
-
8
S
A
T
U
R
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
1
2
3
9
4
1
7
+
=
27
2+7
=
9
=
9
-
-
-
1
20
21
18
4
1
25
+
=
90
9+0
=
9
=
9
-
8
S
A
T
U
R
D
A
Y
-
-
-
-
-
--
-
-
-
-
19
1
20
21
18
4
1
25
+
=
109
1+0+9
=
10
1+0
1
-
-
1
1
2
3
9
4
1
7
+
=
28
2+8
=
10
1+0
1
-
8
S
A
T
U
R
D
A
Y
T
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
19
8
S
A
T
U
R
D
A
Y
-
-
26
-
-
8
-
28
1+9
-
-
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
2+8
10
8
S
A
T
U
R
D
A
Y
-
-
8
-
-
8
-
10
1+0
-
1
1
2
3
9
4
1
7
-
-
-
-
-
-
-
1+0
1
8
S
A
T
U
R
D
A
Y
-
-
8
-
-
8
-
1

 

 
S
A
T
U
R
D
A
Y
-
-
-
-
-
--
-
-
-
1
-
-
-
-
-
-
-
+
=
1
-
=
1
=
1
-
19
-
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
8
S
A
T
U
R
D
A
Y
-
-
-
-
-
-
-
-
-
-
1
2
3
9
4
1
7
+
=
27
2+7
=
9
=
9
-
-
1
20
21
18
4
1
25
+
=
90
9+0
=
9
=
9
8
S
A
T
U
R
D
A
Y
-
-
-
-
-
-
-
-
-
19
1
20
21
18
4
1
25
+
=
109
1+0+9
=
10
1+0
1
-
1
1
2
3
9
4
1
7
+
=
28
2+8
=
10
1+0
1
8
S
A
T
U
R
D
A
Y
T
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
8
S
A
T
U
R
D
A
Y
-
-
26
-
-
8
-
28
-
-
-
-
-
9
-
-
-
-
-
2+6
-
-
-
-
2+8
8
S
A
T
U
R
D
A
Y
-
-
8
-
-
8
-
10
-
1
1
2
3
9
4
1
7
-
-
-
-
-
-
-
1+0
8
S
A
T
U
R
D
A
Y
-
-
8
-
-
8
-
1

 

 

S
=
1
-
6
SUNDAY
84
21
3
M
=
4
-
6
MONDAY
72
27
9
T
=
2
-
7
TUESDAY
95
23
5
W
=
5
-
9
WEDNESDAY
100
37
1
T
=
2
-
8
THURSDAY
116
35
8
F
=
6
-
6
FRIDAY
63
36
9
S
=
1
-
8
SATURDAY
109
28
1
-
-
21
-
50
-
639
207
36
-
-
2+1
-
5+0
-
6+3+9
2+0+7
3+6
-
-
3
-
5
-
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
3
-
5
-
9
9
9

 

 

 

S
=
1
-
6
SUNDAY
84
21
3
M
=
4
-
6
MONDAY
72
27
9
T
=
2
-
7
TUESDAY
95
23
5
W
=
5
-
9
WEDNESDAY
100
37
1
T
=
2
-
8
THURSDAY
116
35
8
F
=
6
-
6
FRIDAY
63
36
9
S
=
1
-
8
SATURDAY
109
28
1
-
-
21
-
50
-
639
207
36
-
-
2+1
-
5+0
-
6+3+9
2+0+7
3+6
-
-
3
-
5
-
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
3
-
5
-
9
9
9

 

 

M
=
4
-
6
MONDAY
72
27
9
T
=
2
-
7
TUESDAY
95
23
5
W
=
5
-
9
WEDNESDAY
100
37
1
T
=
2
-
8
THURSDAY
116
35
8
F
=
6
-
6
FRIDAY
63
36
9
S
=
1
-
8
SATURDAY
109
28
1
S
=
1
-
6
SUNDAY
84
21
3
-
-
21
-
50
-
639
207
36
-
-
2+1
-
5+0
-
6+3+9
2+0+7
3+6
-
-
3
-
5
-
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
3
-
5
-
9
9
9

 

 

-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
1
-
5
+
=
6
-
=
6
-
6
-
-
19
-
14
+
=
33
3+3
=
6
-
6
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
=
3
-
+
=
3
-
=
3
=
3
-
-
-
21
-
+
=
21
2+1
=
3
=
3
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
19
21
14
+
=
54
5+4
=
9
=
9
-
-
1
3
5
+
=
9
-
=
9
=
9
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
36
3
S
U
N
-
-
9
-
-
3
-
9
3+6
-
1
3
5
-
-
-
-
-
-
-
-
2
3
S
U
N
-
-
9
-
-
3
-
9
-
-
1
3
5
-
-
-
-
-
-
-
-
36
3
S
U
N
-
-
9
-
-
3
-
9

 

 

3
S
U
N
-
-
-
-
-
-
-
-
-
1
-
5
+
=
6
-
=
6
-
6
-
19
-
14
+
=
33
3+3
=
6
-
6
3
S
U
N
-
-
-
-
-
-
-
-
-
=
3
-
+
=
3
-
=
3
=
3
-
-
21
-
+
=
21
2+1
=
3
=
3
3
S
U
N
-
-
-
-
-
-
-
-
-
19
21
14
+
=
54
5+4
=
9
=
9
-
1
3
5
+
=
9
-
=
9
=
9
3
S
U
N
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
5
occurs
x
1
=
5
3
S
U
N
-
-
9
-
-
3
-
9
-
1
3
5
-
-
-
-
-
-
-
-
3
S
U
N
-
-
9
-
-
3
-
9
-
1
3
5
-
-
-
-
-
-
-
-
3
S
U
N
-
-
9
-
-
3
-
9

 

 

-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
+
=
8
-
=
8
=
8
-
-
-
-
-
-
8
+
=
8
-
=
8
=
8
-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
5
1
9
2
-
+
=
17
1+7
=
8
=
8
-
`-
5
1
18
20
-
+
=
44
4+4
=
8
=
8
-
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
`-
5
1
18
20
8
+
=
52
5+2
=
7
=
7
-
-
5
1
9
2
8
+
=
25
2+5
=
7
=
7
-
5
E
A
R
T
H
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
20
5
E
A
R
T
H
-
-
25
-
-
5
-
25
2+0
-
-
-
9
-
-
-
-
2+5
-
-
-
-
2+5
2
5
E
A
R
T
H
-
-
7
-
-
5
-
7
-
-
5
1
9
2
8
-
-
-
-
-
--
-
-
2
5
E
A
R
T
H
-
-
7
-
-
5
-
7

 

EARTH HEART THERA TERAH

 

5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
-
-
-
-
8
+
=
8
-
=
8
=
8
-
-
-
-
-
8
+
=
8
-
=
8
=
8
5
E
A
R
T
H
-
-
-
-
-
--
-
-
-
5
1
9
2
-
+
=
17
1+7
=
8
=
8
`-
5
1
18
20
-
+
=
44
4+4
=
8
=
8
5
E
A
R
T
H
-
-
-
-
-
--
-
-
`-
5
1
18
20
8
+
=
52
5+2
=
7
=
7
-
5
1
9
2
8
+
=
25
2+5
=
7
=
7
5
E
A
R
T
H
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
8
-
-
8
occurs
x
1
=
8
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
5
E
A
R
T
H
-
-
25
-
-
5
-
25
-
-
-
9
-
-
-
-
2+5
-
-
-
-
2+5
5
E
A
R
T
H
-
-
7
-
-
5
-
7
-
5
1
9
2
8
-
-
-
-
-
--
-
-
5
E
A
R
T
H
-
-
7
-
-
5
-
7

 

 

-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
6
6
5
+
=
17
1+7
=
8
-
8
=
8
-
-
-
15
15
14
+
=
44
4+4
=
8
=
8
=
8
-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
-
+
=
4
-
=
4
=
4
=
4
-
`-
13
-
-
-
+
=
13
1+3
=
4
=
4
=
4
-
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
13
15
15
14
+
=
57
5+7
=
12
1+2
3
=
3
-
-
4
6
6
5
+
=
21
2+1
=
3
=
3
=
3
-
4
M
O
O
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
--
-
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
--
-
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
--
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
7
-
-
-
-
-
-
-
7
SEVEN
7
--
-
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
--
-
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
--
-
-
-
-
30
4
M
O
O
N
-
-
15
-
-
4
-
21
-
12
3+0
-
4
6
6
5
-
-
1+5
-
-
-
-
2+1
-
1+2
3
4
M
O
O
N
-
-
6
-
-
4
-
3
-
3

 

 

4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
6
6
5
+
=
17
1+7
=
8
-
8
=
8
-
-
15
15
14
+
=
44
4+4
=
8
=
8
=
8
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
4
-
-
-
+
=
4
-
=
4
=
4
=
4
`-
13
-
-
-
+
=
13
1+3
=
4
=
4
=
4
4
M
O
O
N
-
-
-
-
-
--
-
-
-
-
`-
13
15
15
14
+
=
57
5+7
=
12
1+2
3
=
3
-
4
6
6
5
+
=
21
2+1
=
3
=
3
=
3
4
M
O
O
N
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
4
M
O
O
N
-
-
15
-
-
4
-
21
-
12
-
4
6
6
5
-
-
1+5
-
-
-
-
2+1
-
1+2
4
M
O
O
N
-
-
6
-
-
4
-
3
-
3

 

 

-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
1
-
5
-
-
-
-
-
8
-
-
6
6
5
+
=
31
3+1
=
4
-
4
=
4
-
-
19
-
14
-
-
-
-
-
8
-
-
15
15
14
+
=
85
8+5
=
13
1+3
4
=
4
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
3
-
-
5
1
9
2
-
-
4
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
`-
-
21
-
-
5
1
18
20
-
-
13
-
-
-
+
=
78
7+8
=
15
1+5
6
=
6
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
19
21
14
-
5
1
18
20
8
-
13
15
15
14
+
=
163
1+6+3
=
10
1+0
1
=
1
-
-
1
3
5
-
5
1
9
2
8
-
4
6
6
5
+
=
55
5+5
=
10
1+0
1
=
1
-
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
=
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
38
-
-
12
-
55
-
37
-
1+2
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+8
-
-
1+2
-
5+5
-
3+7
7
3
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
11
-
-
3
-
10
-
10
-
-
1
3
5
-
5
1
9
2
8
-
4
6
6
5
-
-
1+1
-
-
-
-
1+0
-
1+0
7
3
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
2
-
-
3
-
1
-
1

 

 

-
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
5
9
5
-
-
1
-
-
-
5
-
-
8
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
14
9
14
-
-
19
-
-
-
14
-
-
8
-
-
-
+
=
78
7+8
=
15
1+5
6
=
6
-
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
5
4
5
-
-
2
-
9
5
5
+
=
40
4+0
=
4
-
4
=
4
-
-`
-
-
-
5
-
-
5
22
5
-
-
20
-
18
5
5
+
=
85
8+5
=
13
1+3
4
=
4
-
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
14
9
14
5
-
19
5
22
5
14
-
20
8
18
5
5
+
=
163
1+6+3
=
10
1+0
1
=
1
-
-
5
9
5
5
-
1
5
4
5
5
-
2
8
9
5
5
+
=
73
7+3
=
10
1+0
1
=
1
-
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
5
-
-
5
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
8
=
40
4+0
4
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
16
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
29
-
-
14
-
73
-
28
1+6
1+4
5
-
5
5
-
-
5
-
5
5
-
-
-
-
5
5
-
-
2+9
-
-
1+4
-
7+3
-
2+8
7
5
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
11
-
-
5
-
10
-
10
-
-
5
9
5
5
-
1
5
4
5
5
-
2
8
9
5
5
-
-
1+1
-
-
-
-
1+0
-
1+0
7
5
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
2
-
-
5
-
1
-
1

 

 

14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
5
9
5
-
-
1
-
-
-
5
-
-
8
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
14
9
14
-
-
19
-
-
-
14
-
-
8
-
-
-
+
=
78
7+8
=
15
1+5
6
=
6
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
5
4
5
-
-
2
-
9
5
5
+
=
40
4+0
=
4
-
4
=
4
-`
-
-
-
5
-
-
5
22
5
-
-
20
-
18
5
5
+
=
85
8+5
=
13
1+3
4
=
4
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
14
9
14
5
-
19
5
22
5
14
-
20
8
18
5
5
+
=
163
1+6+3
=
10
1+0
1
=
1
-
5
9
5
5
-
1
5
4
5
5
-
2
8
9
5
5
+
=
73
7+3
=
10
1+0
1
=
1
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
5
5
-
-
5
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
8
=
40
4+0
4
--
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
29
-
-
14
-
73
-
28
1+4
5
-
5
5
-
-
5
-
5
5
-
-
-
-
5
5
-
-
2+9
-
-
1+4
-
7+3
-
2+8
5
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
11
-
-
5
-
10
-
10
-
5
9
5
5
-
1
5
4
5
5
-
2
8
9
5
5
-
-
1+1
-
-
-
-
1+0
-
1+0
5
N
I
N
E
-
S
E
V
E
N
-
T
H
R
E
E
-
-
2
-
-
5
-
1
-
1

 

 

S
=
1
5
SOUND
73
19
1
T
=
2
5
TOUCH
67
22
4
T
=
2
5
TASTE
65
11
2
S
=
1
5
SMELL
61
16
7
S
=
1
5
SIGHT
63
27
9
-
-
7
25
First Total
329
95
23
-
-
-
 2+5
Add to Reduce
3+2+9
9+5
2+3
Q
-
7
7
Second Total
14
14
5
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
7
7
Essence of Number
5
5
5

 

 

-
-
-
-
-
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
S
=
1
-
5
SIGHT
63
36
9
S
=
1
-
5
SOUND
73
28
1
S
=
1
-
5
SMELL
61
25
7
T
=
2
-
5
TASTE
65
20
2
T
=
2
-
5
TOUCH
67
22
4
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
-
-
-
 2+5
-
3+2+9
1+3+1
2+3
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
14
5
5
-
-
-
-
-
-
1+4
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
5
5
5

 

 

-
-
-
-
-
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
27
-
5
SIGHT
63
36
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SOUND
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
19
-
5
SOUND
73
28
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SMELL-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
14
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
16
-
5
SMELL-
61
25
16
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
TASTE
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
11
-
5
TASTE
65
20
11
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
TOUCH
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
21
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
7
22
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
23
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
25
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
22
-
5
TOUCH
67
22
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
25
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
5
8
15
8
15
12
7
16
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
1+5
-
1+5
1+2
-
1+6
-
S
=
1
-
5
SOUND
73
28
1
-
5
8
6
8
6
3
7
7
9
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
5
8
6
8
6
3
7
7
9
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
5
8
6
8
6
3
7
7
9
-
-
-
-
 2+5
-
3+2+9
1+3+1
2+3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
14
5
5
-
5
8
6
8
6
3
7
7
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
5
5
5
-
5
8
6
8
6
3
7
7
9

 

 

-
-
-
-
-
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
14
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
21
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
7
22
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
23
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
25
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
25
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
5
8
15
8
15
12
7
16
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
1+5
-
1+5
1+2
-
1+6
-
S
=
1
-
5
SOUND
73
28
1
-
5
8
6
8
6
3
7
7
9
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
5
8
6
8
6
3
7
7
9
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
5
8
6
8
6
3
7
7
9
-
-
-
-
 2+5
-
3+2+9
1+3+1
2+3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
14
5
5
-
5
8
6
8
6
3
7
7
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
5
5
5
-
5
8
6
8
6
3
7
7
9

 

 

-
-
-
-
-
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
21
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
14
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
23
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
7
22
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
25
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
25
SOUND TOUCH TASTE SMELL SIGHT
-
-
-
-
5
8
15
8
15
12
7
16
9
S
=
1
-
5
SIGHT
63
36
9
-
-
-
1+5
-
1+5
1+2
-
1+6
-
S
=
1
-
5
SOUND
73
28
1
-
5
8
6
8
6
3
7
7
9
S
=
1
-
5
SMELL
61
25
7
-
-
-
-
-
-
-
-
-
-
T
=
2
-
5
TASTE
65
20
2
-
5
8
6
8
6
3
7
7
9
T
=
2
-
5
TOUCH
67
22
4
-
-
-
-
-
-
-
-
-
-
-
-
7
-
25
SOUND TOUCH TASTE SMELL SIGHT
329
131
23
-
5
8
6
8
6
3
7
7
9
-
-
-
-
 2+5
-
3+2+9
1+3+1
2+3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
14
5
5
-
5
8
6
8
6
3
7
7
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
SOUND TOUCH TASTE SMELL SIGHT
5
5
5
-
5
8
6
8
6
3
7
7
9

 

 

FIVE SENSES

 

-
10
F
I
V
E
-
S
E
N
S
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
1
-
5
1
-
1
+
=
17
1+7
=
8
=
8
=
8
-`
-
-
9
-
-
-
19
-
14
19
-
19
+
=
80
8+0
=
8
=
8
=
8
-
10
F
I
V
E
-
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
-
6
-
4
5
-
-
5
-
-
5
-
+
=
25
2+5
=
7
=
7
=
7
-
-
6
-
22
5
-
-
5
-
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
10
F
I
V
E
-
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
-
6
9
22
5
-
19
5
14
19
5
19
+
=
123
1+2+3
=
6
=
6
=
6
-
-
6
9
4
5
-
1
5
5
1
5
1
+
=
42
4+2
=
6
=
6
=
6
-
10
F
I
V
E
-
S
E
N
S
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
--
-
--
--
-
--
--
--
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
--
-
--
--
-
--
--
--
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
--
--
--
--
-
--
--
--
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
5
5
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
--
--
--
--
-
--
--
--
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
--
--
--
--
-
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
--
--
--
--
-
--
--
--
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
20
10
F
I
V
E
-
S
E
N
S
E
S
-
-
25
-
-
10
-
42
-
24
2+0
1+0
-
-
-
5
-
-
5
5
-
5
-
-
-
2+5
-
-
1+0
-
4+2
-
2+4
2
1
F
I
V
E
-
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6
-
-
6
9
4
5
-
1
5
5
1
5
1
-
-
-
-
-
-
-
-
-
-
2
1
F
I
V
E
-
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6

 

 

10
F
I
V
E
-
S
E
N
S
E
S
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
1
-
5
1
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
9
-
-
-
19
-
14
19
-
19
+
=
80
8+0
=
8
=
8
=
8
10
F
I
V
E
-
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
6
-
4
5
-
-
5
-
-
5
-
+
=
25
2+5
=
7
=
7
=
7
-
6
-
22
5
-
-
5
-
-
5
-
+
=
43
4+3
=
7
=
7
=
7
10
F
I
V
E
-
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
6
9
22
5
-
19
5
14
19
5
19
+
=
123
1+2+3
=
6
=
6
=
6
-
6
9
4
5
-
1
5
5
1
5
1
+
=
42
4+2
=
6
=
6
=
6
10
F
I
V
E
-
S
E
N
S
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
4
--
--
--
--
-
--
--
--
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
5
5
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
6
-
-
--
--
--
--
-
--
--
--
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
F
I
V
E
-
S
E
N
S
E
S
-
-
25
-
-
10
-
42
-
24
1+0
-
-
-
5
-
-
5
5
-
5
-
-
-
2+5
-
-
1+0
-
4+2
-
2+4
1
F
I
V
E
-
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6
-
6
9
4
5
-
1
5
5
1
5
1
-
-
-
-
-
-
-
-
-
-
1
F
I
V
E
-
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6

 

 

FIVE SENSES

 

-
10
F
I
V
E
S
E
N
S
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
1
-
5
1
-
1
+
=
17
1+7
=
8
=
8
=
8
-`
-
-
9
-
-
19
-
14
19
-
19
+
=
80
8+0
=
8
=
8
=
8
-
10
F
I
V
E
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
-
6
-
4
5
-
5
-
-
5
-
+
=
25
2+5
=
7
=
7
=
7
-
-
6
-
22
5
-
5
-
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
10
F
I
V
E
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
-
6
9
22
5
19
5
14
19
5
19
+
=
123
1+2+3
=
6
=
6
=
6
-
-
6
9
4
5
1
5
5
1
5
1
+
=
42
4+2
=
6
=
6
=
6
-
10
F
I
V
E
S
E
N
S
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
--
--
--
-
--
--
--
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
--
--
--
-
--
--
--
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
--
--
--
-
--
--
--
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
5
5
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
--
--
--
-
--
--
--
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
--
--
--
-
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
--
--
--
-
--
--
--
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
20
10
F
I
V
E
S
E
N
S
E
S
-
-
25
-
-
10
-
42
-
24
2+0
1+0
-
-
-
5
-
5
5
-
5
-
-
-
2+5
-
-
1+0
-
4+2
-
2+4
2
1
F
I
V
E
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6
-
-
6
9
4
5
1
5
5
1
5
1
-
-
-
-
-
-
-
-
-
-
2
1
F
I
V
E
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6

 

 

10
F
I
V
E
S
E
N
S
E
S
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
1
-
5
1
-
1
+
=
17
1+7
=
8
=
8
=
8
-
-
9
-
-
19
-
14
19
-
19
+
=
80
8+0
=
8
=
8
=
8
10
F
I
V
E
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
6
-
4
5
-
5
-
-
5
-
+
=
25
2+5
=
7
=
7
=
7
-
6
-
22
5
-
5
-
-
5
-
+
=
43
4+3
=
7
=
7
=
7
10
F
I
V
E
S
E
N
S
E
S
-
-
--
-
-
-
-
-
-
-
-
6
9
22
5
19
5
14
19
5
19
+
=
123
1+2+3
=
6
=
6
=
6
-
6
9
4
5
1
5
5
1
5
1
+
=
42
4+2
=
6
=
6
=
6
10
F
I
V
E
S
E
N
S
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
4
--
--
--
-
--
--
--
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
5
5
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
6
-
-
--
--
--
-
--
--
--
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
F
I
V
E
S
E
N
S
E
S
-
-
25
-
-
10
-
42
-
24
1+0
-
-
-
5
-
5
5
-
5
-
-
-
2+5
-
-
1+0
-
4+2
-
2+4
1
F
I
V
E
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6
-
6
9
4
5
1
5
5
1
5
1
-
-
-
-
-
-
-
-
-
-
1
F
I
V
E
S
E
N
S
E
S
-
-
7
-
-
1
-
6
-
6

 

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
-
61
25
25
-
-
-
-
-
-
-
-
-
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
32
-
-
-
77
32
32
-
1
2
3
4
10
12
7
8
12
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+2
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
1
2
3
4
10
12
7
8
18
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+8
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 
-
-
11
ATOMIC POWER
163
64
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
W
=
5
9
1
W
23
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
P
=
7
7
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
1
2
3
4
10
12
7
8
18
-
-
-
-
11
ATOMIC POWER
-
-
-
-
-
-
-
-
1+0
1+2
-
-
1+8
A
=
1
-
6
ATOMIC
61
25
7
-
1
2
3
4
1
3
7
8
9
P
=
7
-
5
POWER
77
32
5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
11
ATOMIC POWER
138
57
12
-
1
2
3
4
1
3
7
8
9
-
-
-
-
1+1
-
1+3+8
5+7
1+2
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
12
12
3
-
1
2
3
4
1
3
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
2
ATOMIC POWER
3
3
3
-
1
2
3
4
1
3
7
8
9

 

 

ATOMIC ENERGY

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
ATOMIC
61
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ENERGY
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
38
-
-
ENERGY
74
38
38
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
15
6
14
8
18
-
-
-
-
-
ATOMIC ENERGY
-
-
-
-
-
-
-
-
1+5
-
1+4
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
1
2
3
4
6
6
5
8
9
E
=
5
Q
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC ENERGY
135
63
9
-
1
2
3
4
6
6
5
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC ENERGY
9
9
9
-
1
2
3
4
6
6
5
8
9

 

LETTERS REARRANGED NUMERICALLY

 

ATOMIC NUMBERS

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
-
ATOMIC
61
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
29
-
7
NUMBERS
92
38
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
7
8
9
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

LETTERS REARRANGED NUMERICALLY

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
7
8
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
7
8
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
7
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
7
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
7
8
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
7
8
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
-
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
7
8
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
7
8
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
7
8
9

 

 

-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
1
2
3
4
5
6
9
K
=
2
Q
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
E
=
5
Q
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
Q
Q
7
Q
13
ATOMIC NUMBERS
153
63
9
-
1
2
3
4
5
6
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
1
2
3
4
5
6
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
2
2
1
T
20
2
2
-
-
2
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
U
=
3
8
1
U
21
3
3
-
-
-
3
-
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
I
=
9
5
1
I
18
9
9
-
-
-
-
-
-
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
4
6
8
10
6
18
-
-
-
-
-
ATOMIC NUMBERS
-
-
-
-
-
-
-
-
1+0
-
1+8
A
=
1
Q
6
ATOMIC
61
25
7
-
2
4
6
8
1
6
9
E
=
5
Q
6
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
Q
Q
6
Q
12
ATOMIC NUMBERS
153
63
9
-
2
4
6
88
1
6
9
-
-
-
-
1+5
-
1+3+5
6+3
-
-
-
-
-
-
-
-
-
Q
Q
6
Q
6
ATOMIC NUMBERS
9
9
9
-
2
4
6
8
1
6
9

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
3
GOD
26
26
8
P
=
7
-
8
PARTICLE
84
39
3
-
-
16
-
14
Add to Reduce
143
80
17
-
-
1+6
-
1+4
Reduce to Deduce
1+4+3
8+0
1+7
-
-
7
-
5
Essence of Number
8
8
8

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
3
GOD
26
26
8
P
=
7
-
9
PARTICLES
103
40
4
-
-
16
-
15
Add to Reduce
162
81
18
-
-
1+6
-
1+5
Reduce to Deduce
1+6+2
8+1
1+8
-
-
7
-
6
Essence of Number
9
9
9

 

 

Higgs boson - Wikipedia
https://en.wikipedia.org/wiki/Higgs_boson

The Higgs boson is an elementary particle in the Standard Model of particle physics. First suspected to exist in the 1960s, it is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory. Unlike other known fields such as the electromagnetic field, it has a non-zero constant ...

Higgs boson
Subatomic particle

The Higgs boson is an elementary particle in the Standard Model of particle physics. First suspected to exist in the 1960s, it is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory. Wikipedia

Composition: Elementary particle

Classification: Boson

Symbol: H°

Mass: 125.09±0.21 (stat.)±0.11 (syst.) GeV/c² (CMS+ATLAS)

Electric charge: 0 e

Discovered: Large Hadron Collider (2011–2013)

Mean lifetime: 1.56×10-22 s (predicted)

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
5
HIGGS
50
41
5
B
=
2
-
5
BOSON
65
29
2
-
-
12
-
13
First Total
148
85
13
-
-
1+2
-
1+3
Add to Reduce
1+4+8
8+5
1+3
-
-
3
-
4
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
3
-
4
Essence of Number
4
4
4

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
THE
-
-
-
-
-
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
15
-
3
THE
33
15
15
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
HIGGS
-
-
-
-
-
-
3
4
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
-
-
32
-
5
HIGGS
50
41
32
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
BOSON
-
-
-
-
-
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
20
-
5
BOSON
65
29
20
-
-
-
3
4
-
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

LETTERS RE-ARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
1
3
5
7
9

 

 

H
=
8
-
5
HIGGS
50
32
5
B
=
2
-
5
BOSON
65
20
2
P
=
7
-
8
PARTICLE
84
39
3
-
-
17
-
18
First Total
199
91
10
-
-
1+7
-
1+8
Add to Reduce
1+9+9
9+1
1+0
-
-
8
-
18
Second Total
10
10
1
-
-
-
-
1+8
Reduce to Deduce
1+0
1+0
-
-
-
8
-
9
Essence of Number
1
1
1

 

 

-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
8
-
-
-
15
-
-
14
+
=
37
3+7
=
10
1+0
1
=
1
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
7
4
9
-
7
5
-
+
=
32
3+2
=
5
-
5
=
5
-
-
-
25
4
18
-
7
5
-
+
=
59
5+9
=
14
1+4
5
=
5
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
8
25
4
18
15
7
5
14
+
=
96
9+6
=
15
1+5
6
=
6
-
-
8
7
3
9
6
7
5
5
+
=
51
5+1
=
6
-
6
=
6
-
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
7
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
6
8
H
Y
D
R
O
G
E
N
-
-
39
-
-
8
-
51
-
33
-
-
-
-
-
9
-
-
-
-
-
-
3+9
-
-
-
-
5+1
-
3+3
6
8
H
Y
D
R
O
G
E
N
-
-
12
-
-
8
-
6
-
6
-
-
8
7
3
9
6
7
5
5
-
-
1+2
-
-
-
-
-
-
-
6
8
H
Y
D
R
O
G
E
N
-
-
3
-
-
8
-
6
-
6

 

 

8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
6
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
8
-
-
-
15
-
-
14
+
=
37
3+7
=
10
1+0
1
=
1
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
7
4
9
-
7
5
-
+
=
32
3+2
=
5
-
5
=
5
-
-
25
4
18
-
7
5
-
+
=
59
5+9
=
14
1+4
5
=
5
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
8
25
4
18
15
7
5
14
+
=
96
9+6
=
15
1+5
6
=
6
-
8
7
3
9
6
7
5
5
+
=
51
5+1
=
6
-
6
=
6
8
H
Y
D
R
O
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
8
H
Y
D
R
O
G
E
N
-
-
39
-
-
8
-
51
-
33
-
-
-
-
9
-
-
-
-
-
-
3+9
-
-
-
-
5+1
-
3+3
8
H
Y
D
R
O
G
E
N
-
-
12
-
-
8
-
6
-
6
-
8
7
3
9
6
7
5
5
-
-
1+2
-
-
-
-
-
-
-
8
H
Y
D
R
O
G
E
N
-
-
3
-
-
8
-
6
-
6

 

The hydrogen line, 21-centimeter line, is the electromagnetic radiation spectral line

 

-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
H
=
8
-
8
HYDROGEN
96
51
6
L
=
3
-
4
LINE
40
22
4
T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
I
=
9
-
2
IS
28
10
1
T
=
2
-
3
THE
33
15
6
E
=
5
-
15
ELECTROMAGNETIC
150
69
6
R
=
9
-
9
RADIATION
91
46
1
S
=
1
-
8
SPECTRAL
94
31
4
L
=
3
-
4
LINE
40
22
4
-
-
50
-
79
First Total
898
394
52
-
-
5+0
-
7+9
Add to Reduce
8+9+9
3+9+4
5+2
-
-
5
-
16
Second Total
25
16
7
-
-
-
-
1+6
Reduce to Deduce
2+5
1+6
-
-
-
5
-
7
Essence of Number
7
7
7

 

 

Hydrogen line - Wikipedia

https://en.wikipedia.org › wiki › Hydrogen_line
The hydrogen line, 21-centimeter line, or H I line is the electromagnetic radiation spectral line ... This wavelength falls within the microwave region of the electromagnetic spectrum, and it is ... Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the ...

 

21-centimeter line, or H I line is the electromagnetic radiation spectral line

 

-
-
-
-
-
-
-
-
-
T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
-
-
8
-
23
First Total
293
113
14
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
8
-
5
Second Total
14
5
5
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
8
-
5
Essence of Number
5
5
5

 

The hydrogen line, 21-centimeter line, or H I line[1] is the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1,420,405,751.7667±0.0009 Hz,[2][3] which is equivalent to the vacuum wavelength of 21.1061140542 cm in free space. This wavelength falls within the microwave region of the electromagnetic spectrum, and it is observed frequently in radio astronomy because those radio waves can penetrate the large clouds of interstellar cosmic dust that are opaque to visible light. This line is also the theoretical basis of hydrogen maser.

The microwaves of the hydrogen line come from the atomic transition of an electron between the two hyperfine levels of the hydrogen 1 s ground state that have an energy difference of ˜ 5.87433 µeV [9.411708×10-25 J].[4] It is called the spin-flip transition. The frequency, ?, of the quanta that are emitted by this transition between two different energy levels is given by the Planck–Einstein relation E = h?. According to that relation, the photon energy of a 1,420,405,751.7667 Hz photon is ˜ 5.87433 µeV [9.411708×10-25 J]. The constant of proportionality, h, is known as the Planck constant.
Further information: Hyperfine structure

The ground state of neutral hydrogen consists of an electron bound to a proton. Both the electron and the proton have intrinsic magnetic dipole moments ascribed to their spin, whose interaction results in a slight increase in energy when the spins are parallel, and a decrease when antiparallel. The fact that only parallel and antiparallel states are allowed is a result of the quantum mechanical discretization of the total angular momentum of the system. When the spins are parallel, the magnetic dipole moments are antiparallel (because the electron and proton have opposite charge), thus one would expect this configuration to actually have lower energy just as two magnets will align so that the north pole of one is closest to the south pole of the other. This logic fails here because the wave functions of the electron and the proton overlap; that is, the electron is not spatially displaced from the proton, but encompasses it. The magnetic dipole moments are therefore best thought of as tiny current loops. As parallel currents attract, the parallel magnetic dipole moments (i.e., antiparallel spins) have lower energy.[5] The transition has an energy difference of 5.87433 µeV that when applied in the Planck equation gives:
? = 1 ? · c = h E · c = 4.1357 · 10 - 15 eV s 5.874 33 · 10 - 6 eV · 2.9979 · 10 8 m s - 1 = 0.211 06 m = 21.106 cm {\displaystyle \lambda ={\frac {1}{\nu }}\cdot c={\frac {h}{E}}\cdot c={\frac {4.1357\cdot 10^{-15}\;{\text{eV}}\;{\text{s}}}{5.874\,33\cdot 10^{-6}\;{\text{eV}}}}\cdot 2.9979\cdot 10^{8}\;{\text{m}}\;{\text{s}}^{-1}=0.211\,06\;{\text{m}}=21.106\;{\text{cm}}} {\displaystyle \lambda ={\frac {1}{\nu }}\cdot c={\frac {h}{E}}\cdot c={\frac {4.1357\cdot 10^{-15}\;{\text{eV}}\;{\text{s}}}{5.874\,33\cdot 10^{-6}\;{\text{eV}}}}\cdot 2.9979\cdot 10^{8}\;{\text{m}}\;{\text{s}}^{-1}=0.211\,06\;{\text{m}}=21.106\;{\text{cm}}}
where h is the Planck constant and c is the speed of light.

This transition is highly forbidden with an extremely small transition rate of 2.9×10-15 s-1,[6] and a mean lifetime of the excited state of around 10 million years. A spontaneous occurrence of the transition is unlikely to be seen in a laboratory on Earth, but it can be artificially induced using a hydrogen maser. It is commonly observed in astronomical settings such as hydrogen clouds in our galaxy and others. Owing to its long lifetime, the line has an extremely small natural width, so most broadening is due to Doppler shifts caused by bulk motion or nonzero temperature of the emitting regions.

Discovery?[edit]

During the 1930s, it was noticed that there was a radio 'hiss' that varied on a daily cycle and appeared to be extraterrestrial in origin. After initial suggestions that this was due to the Sun, it was observed that the radio waves seemed to propagate from the centre of the Galaxy. These discoveries were published in 1940 and were noted by Jan Oort who knew that significant advances could be made in astronomy if there were emission lines in the radio part of the spectrum. He referred this to Hendrik van de Hulst who, in 1944, predicted that neutral hydrogen could produce radiation at a frequency of 1420.4058 MHz due to two closely spaced energy levels in the ground state of the hydrogen atom.

The 21 cm line (1420.4 MHz) was first detected in 1951 by Ewen and Purcell at Harvard University,[7] and published after their data was corroborated by Dutch astronomers Muller and Oort,[8] and by Christiansen and Hindman in Australia. After 1952 the first maps of the neutral hydrogen in the Galaxy were made, and revealed for the first time the spiral structure of the Milky Way.
Uses?[edit]

In radio astronomy?[edit]

The 21 cm spectral line appears within the radio spectrum (in the L band of the UHF band of the microwave window to be exact). Electromagnetic energy in this range can easily pass through the Earth's atmosphere and be observed from the Earth with little interference.

Assuming that the hydrogen atoms are uniformly distributed throughout the galaxy, each line of sight through the galaxy will reveal a hydrogen line. The only difference between each of these lines is the doppler shift that each of these lines has. Hence, one can calculate the relative speed of each arm of our galaxy. The rotation curve of our galaxy has been calculated using the 21 cm hydrogen line. It is then possible to use the plot of the rotation curve and the velocity to determine the distance to a certain point within the galaxy.

Hydrogen line observations have also been used indirectly to calculate the mass of galaxies, to put limits on any changes over time of the universal gravitational constant and to study the dynamics of individual galaxies.

In cosmology?[edit]

The line is of great interest in Big Bang cosmology because it is the only known way to probe the "dark ages" from recombination to reionization. Including the redshift, this line will be observed at frequencies from 200 MHz to about 9 MHz on Earth. It potentially has two applications. First, by mapping the intensity of redshifted 21 centimeter radiation it can, in principle, provide a very precise picture of the matter power spectrum in the period after recombination. Second, it can provide a picture of how the universe was reionized, as neutral hydrogen which has been ionized by radiation from stars or quasars will appear as holes in the 21 cm background.

However, 21 cm observations are very difficult to make. Ground-based experiments to observe the faint signal are plagued by interference from television transmitters and the ionosphere, so they must be made from very secluded sites with care taken to eliminate interference. Space based experiments, even on the far side of the Moon (where they would be sheltered from interference from terrestrial radio signals), have been proposed to compensate for this. Little is known about other effects, such as synchrotron emission and free–free emission on the galaxy. Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the next great frontier in observational cosmology, after the cosmic microwave background polarization.

Relevance to the search for non-human intelligent life?[edit]


The hyperfine transition of hydrogen, as depicted on the Pioneer and Voyager spacecraft.
The Pioneer plaque, attached to the Pioneer 10 and Pioneer 11 spacecraft, portrays the hyperfine transition of neutral hydrogen and used the wavelength as a standard scale of measurement. For example, the height of the woman in the image is displayed as eight times 21 cm, or 168 cm. Similarly the frequency of the hydrogen spin-flip transition was used for a unit of time in a map to Earth included on the Pioneer plaques and also the Voyager 1 and Voyager 2 probes. On this map, the position of the Sun is portrayed relative to 14 pulsars whose rotation period circa 1977 is given as a multiple of the frequency of the hydrogen spin-flip transition. It is theorized by the plaque's creators that an advanced civilization would then be able to use the locations of these pulsars to locate the Solar System at the time the spacecraft were launched.

The 21 cm hydrogen line is considered a favorable frequency by the SETI program in their search for signals from potential extraterrestrial civilizations. In 1959, Italian physicist Giuseppe Cocconi and American physicist Philip Morrison published "Searching for Interstellar Communications", a paper proposing the 21 cm hydrogen line and the potential of microwaves in the search for interstellar communications. According to George Basalla, the paper by Cocconi and Morrison "provided a reasonable theoretical basis" for the then-nascent SETI program.[9] Similarly, Pyotr Makovetsky proposed SETI use a frequency which is equal to either
p × 1420.40575177 MHz = 4.46233627 GHz
or
2p × 1420.40575177 MHz = 8.92467255 GHz
Since p is an irrational number, such a frequency could not possibly be produced in a natural way as a harmonic, and would clearly signify its artificial origin. Such a signal would not be overwhelmed by the H I line itself, or by any of its harmonics.[10]

A suggested modification to the mentioned idea is to search on currently unused Sky or other satellite LNB frequencies, as it is possible that with enough synchronized receivers AI inference techniques could be used. In this case, the target frequency would be in the 13 GHz band (13.37–13.39 GHz), derived from 3pH, but there may be merit in searching on other unused bands within the transition areas not normally used, with the PCB also including an onboard reference clock derived from Droitwich or MSF.[citation needed]

See also?[edit]
Chronology of the universe
Dark Ages Radio Explorer
H-alpha, the visible red spectral line with wavelength of 6562.8 ångstroms
Hydrogen spectral series
Rydberg formula
Balmer series
Schelling point
Timeline of the Big Bang

https://en.wikipedia.org › wiki › Hydrogen_line
The hydrogen line, 21-centimeter line, or H I line is the electromagnetic radiation spectral line ... This wavelength falls within the microwave region of the electromagnetic spectrum, and it is ... Despite these problems, 21 cm observations, along with space-based gravitational wave observations, are generally viewed as the ...

21-cm Line Radiation
In 1944 Hendrik van de Hulst predicted that the cold atomic hydrogen (H I) gas should emit a particular wavelength of radio energy from a slight energy change in the hydrogen atoms. The wavelength is 21.1 centimeters (frequency = 1420.4 MHz) so this radiation is called 21-cm line radiation.28 May 2019

 

T
=
2
-
9
TWENTYONE
141
42
6
C
=
3
-
10
CENTIMETER
112
49
4
L
=
3
-
4
LINE
40
22
4
I
=
9
-
2
IS
28
10
1
T
=
2
-
3
THE
33
15
6
E
=
5
-
15
ELECTROMAGNETIC
150
69
6
R
=
9
-
9
RADIATION
91
46
1
S
=
1
-
8
SPECTRAL
94
31
4
L
=
3
-
4
LINE
40
22
4
-
-
37
-
64
First Total
729
306
36
-
-
3+7
-
6+4
Add to Reduce
7+2+9
3+0+6
3+6
-
-
10
-
10
Second Total
18
9
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
-
-
-
-
1
-
1
Essence of Number
9
9
9

 

 

TWENTY ONE CENTIMETER LINE

21-centimeter line, or H I line is the electromagnetic radiation spectral line

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
2
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
6
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
42
-
9
-
141
42
42
-
-
-
-
-
-
-
-
-
-
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
15
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
17
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
40
-
10
-
112
49
40
-
-
-
-
-
-
-
-
-
-
L
=
3
10
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
22
-
4
-
40
22
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

T
=
2
-
9
TWENTYONE
141
42
6
-
1
2
3
4
5
6
7
8
9
C
=
3
-
10
CENTIMETER
112
49
4
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
-
-
-
-
-
-
-
-5
-
23
First Total
293
113
14
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
T
=
2
17
1
T
20
2
2
-
1
2
-
-
-
-
-
8
-
C
=
3
10
1
C
3
3
3
-
1
-
3
-
-
-
-
8
-
L
=
3
10
1
L
12
3
3
-
1
-
3
-
-
-
-
8
-
M
=
4
15
1
M
13
4
4
-
1
-
-
4
-
-
-
8
-
W
=
5
2
1
W
23
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
4
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
9
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
16
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
1
-
-
-
5
-
-
8
-
O
=
6
7
1
O
15
6
6
-
1
-
-
-
-
6
-
8
-
Y
=
7
6
1
Y
25
7
7
-
1
-
-
-
-
-
7
8
-
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
R
=
9
19
1
R
18
9
9
-
1
-
-
-
-
-
-
8
9
I
=
9
14
1
I
9
9
9
-
1
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
1
8
6
4
55
6
7
8
27
T
=
2
-
9
TWENTYONE
141
42
6
-
-
-
-
-
5+5
-
-
-
2+7
C
=
3
-
10
CENTIMETER
112
49
4
-
1
8
6
4
10
6
7
8
9
L
=
3
-
4
LINE
40
22
4
-
-
-
-
-
1+0
-
-
-
-
-
-
8
-
23
First Total
293
113
14
-
1
8
6
4
1
6
7
8
9
-
-
-
-
2+3
Add to Reduce
2+9+3
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Second Total
14
5
5
-
1
8
6
4
1
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
Essence of Number
5
5
5
-
1
8
6
4
1
6
7
8
9

 

TWENTY ONE CENTIMETER LINE

 

 

BREATHE ON ME BREATH OF GOD

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
1
2
3
4
10
12
14
8
9
-
-
3+6
-
-
-
9+0
3+6
3+6
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
9
-
6
OXYGEN
9
9
9
-
1
2
3
4
1
3
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

 

E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

E
=
5
-
-
ENERGY
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+Y
32
14
5
E
=
5
-
6
ENERGY
74
38
29
-
-
-
-
-
-
7+4
3+8
2+9
E
=
5
4
6
ENERGY
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
6
ENERGY
2
2
2

 


E
=
5
-
-
ENERGY
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+Y
32
14
5
E
=
5
-
6
ENERGY
74
38
29
-
-
-
-
-
-
7+4
3+8
2+9
E
=
5
4
6
ENERGY
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
6
ENERGY
2
2
2

 


6
ENERGY
74
38
2
8
ENERGIES
82
46
1
9
ENERGISED
86
50
5

 

 

Everything Is Energy and Science Has Proved It – Here Is How ...
https://www.learning-mind.com › Food for thought

14 Sep 2018 - Many spiritual traditions have viewed everything in the universe as part of an interconnected web of energy. ... Basically, there was a widespread belief that everything is energy or at least that a consciousness flows through everything. ... Quantum physics proves that solid matter does ...

“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet. Everything we call real is made of things that cannot be regarded as real.”

– Niels Bohr

 

energy' related words: work vitality electricity [598 more]
relatedwords.org › relatedto › energy

Words Related to energy According to the algorithm that drives this word similarity engine, the top 5 related words for "energy" are: kinetic energy, work, radiant energy, vitality, and electricity.

 

Energy is from energos, an ancient Greek word that means "active or working.

 

E
=
5
-
-
ENERGOS
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G
7
7
7
-
-
-
-
1
O
15
6
6
-
-
-
-
1
S
19
10
1
E
=
5
-
7
ENERGOS
83
47
38
-
-
-
-
-
-
8+3
4+7
3+8
E
=
5
4
7
ENERGOS
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
7
ENERGOS
2
2
2

 

Energy is from energos, an ancient Greek word that means "active or working.

 

E
=
5
-
-
ENERGOS
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+O+S
41
14
5
E
=
5
-
7
ENERGOS
83
47
38
-
-
-
-
-
-
8+3
4+7
3+8
E
=
5
4
7
ENERGOS
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
7
ENERGOS
2
2
2

 

" The word "energy" was first used in the scientific sense of mechanical or electrical energy in the 1800s.

ENERGY ENERGIES ENERGISE ENERGISES ENERGISED ENERGISING

 

E
=
5
-
6
ENERGY
74
38
2
E
=
5
-
8
ENERGIES
82
46
1
E
=
5
-
8
ENERGISE
82
46
1
E
=
5
-
9
ENERGISES
101
38
2
E
=
5
-
9
ENERGISED
86
50
5
E
=
5
-
10
ENERGISING
107
62
8
-
-
30
-
50
First Total
532
280
19
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
3
-
5
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
3
-
5
Essence of Number
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
-
-
38
-
6
-
74
38
38
-
-
-
-
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
-
-
46
-
8
-
82
55
46
-
-
-
-
-
-
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
-
-
46
-
8
-
82
55
46
-
-
-
-
-
-
-
-
-
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
-
-
47
-
9
-
101
65
47
-
-
-
-
-
-
-
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
-
-
50
-
9
-
86
59
50
-
-
-
-
-
-
-
-
-
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
-
-
50
-
10
-
107
71
62
-
-
-
-
-
-
-
-
-
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

ENERGYENERGIESENERGISEENERGISESENERGISEDENERGISING

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
-
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGISE
82
55
1
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
-
-
-
-
-
-
-
-
-
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
14
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
21
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
31
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
29
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
38
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
S
=
1
47
1
S
19
10
1
-
1
2
3
-
-
6
-
8
-
D
=
4
40
1
D
4
4
4
-
-
2
3
4
-
6
-
8
-
E
=
5
1
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
2
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
3
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
7
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
8
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
9
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
13
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
15
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
16
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
22
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
23
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
24
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
25
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
30
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
32
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
33
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
34
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
39
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
41
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
42
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
E
=
5
43
1
E
5
5
5
-
-
2
3
-
5
6
-
8
-
N
=
5
49
1
N
14
5
5
-
-
2
3
-
5
6
-
8
-
G
=
7
5
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
Y
=
7
6
1
Y
25
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
11
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
19
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
27
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
36
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
45
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
G
=
7
50
1
G
7
7
7
-
-
2
3
-
-
6
7
8
-
R
=
9
10
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
12
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
18
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
4
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
20
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
26
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
28
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
35
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
37
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
R
=
9
44
1
R
18
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
46
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
I
=
9
48
1
I
9
9
9
-
-
2
3
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
E
=
5
-
6
ENERGY
74
38
2
-
6
2
3
4
115
6
56
8
108
E
=
5
-
8
ENERGIES
82
55
1
-
-
-
-
-
1+1+5
-
5+6
-
1+0+8
E
=
5
-
8
ENERGISE
82
55
1
-
6
2
3
4
7
6
11
8
9
E
=
5
-
9
ENERGISES
101
65
2
-
-
-
-
-
-
-
1+1
-
-
E
=
5
-
9
ENERGISED
86
59
5
-
6
2
3
4
7
6
2
8
9
E
=
5
-
10
ENERGISING
107
71
8
-
-
-
-
-
-
-
-
-
-
-
-
30
-
50
First Total
532
343
19
-
6
2
3
4
7
6
2
8
9
-
-
3+0
-
5+0
Add to Reduce
2+3+5
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Second Total
10
10
1
-
6
2
3
4
7
6
2
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
Essence of Number
1
1
1
-
6
2
3
4
7
6
2
8
9

 

 

SOUL SO U LIVE
SOUL SO U LEARN
SOUL SO U LOVE

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
P
=
7
-
1
P
16
7
7
-
-
-
-
-
-
-
7
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
9
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
9
-
-
1+0
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
9

 

 

-
-
-
-
11

GLORIA IN EXCELSIS
-
-
-
G
=
7
-
6
GLORIA
62
35
8
I
=
9
-
2
IN
23
14
5
E
=
5
-
8
EXCELSIS
96
33
6
-
-
21
-
16

GLORIA IN EXCELSIS
181
82
19
-
-
2+1
-
1+6
-
1+8+1
8+2
1+9
-
-
3
-
7

GLORIA IN EXCELSIS
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
-
-
3
-
72

GLORIA IN EXCELSIS
1
1
1

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
S
=
1
-
7
SOLVING
98
44
8
P
=
7
-
8
PROBLEMS
100
46
1
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
-
-
-
-
-
1+0
-
-
-
-
8
-
6

SOLVING PROBLEMS
1
9
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SOLVING
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 

-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
7
SOLVING
98
44
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
-
-
-
-
-
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
15

SOLVING PROBLEMS
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
7
SOLVING
98
44
8
-
2
2
6
8
10
12
14
8
18
P
=
7
-
8
PROBLEMS
100
46
1
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
8
-
15

SOLVING PROBLEMS
198
90
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
1+5
-
1+9+8
9+0
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
6

SOLVING PROBLEMS
9
9
9
-
2
2
6
8
1
3
5
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

 

ABCDEFGHIJKLMNOPQRSTUVWXYZ WELCOME

HERO

WELCOME ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

 

THE CLOCKS ALL SAY THE HOURS OF HORUS HAVE ARRIVED UPON US

AND THE DICE ALL READ A FIVE

LIVING FORM FROM OUT THE IN OF GODS LIVING FORM

 

 

 

 

 

 

 
 
Top
  
 
Evokation
  
Previous Page
Index
 Next Page