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Evokation
  
 
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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,.."

 

 

MARIO AND THE MAGICIANS

THOMAS MANN

1875 - 1955

18

THE

TABLES OF THE LAW

Page 289

"...WITH A HANDFUL OF THESE SIGNS ALL THE WORDS

OF ALL THE LANGUAGES OF ALL THE PEOPLE

COULD, IF NEED BE, BE WRITTEN,..."

 

 

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."

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE 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

AT THE THROW OF THE NINTH RAM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

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."

 

 

 

A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

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

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

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

 

 

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
-
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
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
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
+
=
28
2+8
=
10
1+0
1
-
1
2
3
4
5
6
7
-
-
+
=
28
2+8
=
10
1+0
1
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
9
A
B
C
D
E
F
G
H
I
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
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
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
-
+
=
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
9
+
=
9
occurs
x
1
=
9
9
A
B
C
D
E
F
G
H
I
-
-
45
-
-
9
-
45
-
1
2
3
4
5
6
7
8
9
-
-
4+5
-
-
-
-
4+5
9
A
B
C
D
E
F
G
H
I
-
-
9
-
-
9
-
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
9
A
B
C
D
E
F
G
H
I
-
-
9
-
-
9
-
9

 

 

9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
-
-
-
-
5
6
-
-
-
+
=
11
1+1
=
2
=
2
-
-
-
-
-
14
15
-
-
-
+
=
29
2+9
=
11
1+1
2
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
1
2
3
4
-
-
7
8
9
+
=
34
3+4
=
7
=
7
-
10
11
12
13
-
-
16
17
18
+
=
97
9+7
=
16
1+6
7
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
10
11
12
13
14
15
16
17
18
+
=
126
1+2+6
=
9
=
9
-
1
2
3
4
5
6
7
8
9
+
=
45
4+5
=
9
=
9
9
J
K
L
M
N
O
P
Q
R
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
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
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
-
+
=
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
9
+
=
9
occurs
x
1
=
9
9
J
K
L
M
N
O
P
Q
R
-
-
45
-
-
9
-
45
-
10
11
12
13
14
15
16
17
18
-
-
4+5
-
-
-
-
4+5
9
J
K
L
M
N
O
P
Q
R
-
-
9
-
-
9
-
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
9
J
K
L
M
N
O
P
Q
R
-
-
9
-
-
9
-
9

 

 

8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
1
-
-
-
-
6
-
8
+
=
15
1+5
=
6
=
6
-
19
-
-
-
-
24
-
26
+
=
69
6+9
=
15
1+5
6
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
2
3
4
5
-
7
-
+
=
21
2+1
=
3
=
3
-
-
20
21
22
23
-
25
-
+
=
111
1+1+1
=
3
=
3
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
19
20
21
22
23
24
25
26
+
=
180
1+8+0
=
9
=
9
-
1
2
3
4
5
6
7
8
+
=
36
3+6
=
9
=
9
8
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
1
=
1
-
-
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
occurs
x
1
=
6
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
1
=
7
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
1
=
8
8
S
T
U
V
W
X
Y
Z
-
-
36
-
-
8
-
36
-
1
2
3
4
5
6
7
8
-
-
3+6
-
-
-
-
3+6
8
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
19
20
21
22
23
24
25
26
-
-
-
-
-
-
-
-
8
S
T
U
V
W
X
Y
Z
-
-
9
-
-
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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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 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"

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

"'Into the Comet' and 'The Nine Billion Names of God' both involve computers and the troubles they may cause us. While writing this preface, I had occasion to call upon my own HP 9100A computer, Hal Junior, to answer an interesting question. Looking at my records, I find that I have now written just about one hundred short stories. This volume contains eighteen of them: therefore, how many possible 18-story collections will I be able to put together? The answer ­as I am sure will be instantly obvious to you - is 100 x 99. . . x 84 x 83 divided by 18 x 17 x 16 ... x .2 x 1. This is an impressive number - Hal Junior tells me that it is approximately 20,772,733,124,605,000,000.

 

 

3
THE
33
15
6
4
NINE
42
24
6
7
BILLION
73
37
1
5
NAMES
52
16
7
2
OF
21
12
3
3
GOD
26
17
8
24
-
247
121
31
2+4
-
2+4+7
1+2+1
3+1
6
-
13
4
4
-
-
1+3
-
-
6
-
4
4
4

Page 15

The Nine Billion Names of God

'This is a slightly unusual request,' said Dr Wagner, with what he hoped was commendable restraint. 'As far as I know, it's the first time anyone's been asked to supply a Tibetan monastery with an Automatic Sequence Computer. I don't wish to be inquisitive, but I should hardly have thought that your - ah - establishment had much use for such a machine. Could you explain just what you intend to do with it?'
'Gladly,' replied the lama, readjusting his silk robes and carefully putting away the slide rule he had been using far currency conversions. 'Your Mark V Computer can carry out any routine mathematical operation involving up to ten digits. However, for our work we are interested in letters, not numbers. As we wish you to modify the output circuits, the machine will be printing words, not columns of figures.'
'I don't quite understand. . .'
'This is a project on which we have been working for the last three centuries - since the lamasery was founded, in fact. It is somewhat alien to your way of thought, so I hope you will listen with an open mind while I explain it.'
'Naturally.'
'It is really quite simple. We have been compiling a list which shall contain all the possible names of God.'
'I beg your pardon?'

Page16

'We have reason to believe,' continued the lama imperturbably, 'that all such names can be written with not more than nine letters in an alphabet we have devised.'
'And you have been doing this for three centuries?'
'Yes: we expected it would take us about fifteen thousand years to complete the task.'
'Oh,' Dr Wagner looked a little dazed. 'Now I see why you wanted to hire one of our machines. But what exactly is the purpose of this project?'
The lama hesitated for a fraction of a second, and Wagner wondered if he had offended him. If so, there was no trace of annoyance in the reply.
'Call it ritual, if you like, but it's a fundamental part of our belief. All the many names of the Supreme Being - God Jehova, Allah, and so on - they are only man-made labels. There is a philosophical problem of some difficulty here, which I do not propose to discuss, but somewhere among all the possible combinations of letters that can occur are what one may call the real names of God. By systematic permutation of letters, we have been trying to list them all.'
'I see. You've been starting at AAAAAAA . . . and working up to ZZZZZZZZ . . .'
'Exactly - though we use a special alphabet of our own. Modifying the electromatic typewriters to deal with this is, of course, trivial. A rather more interesting problem is that of devising suitable circuits to eliminate ridiculous combinations. For example, no letter must occur more than three times in succession.'
,'Three? Surely you mean two.'
'Three is correct: I am afraid it would take too long to explain why, even if you understood our language.' "

Page 68

Into the Comet


"Pickett's fingers danced over the beads, sliding them up and down the wires with lightning speed. There were twelve wires in all, so that the abacus could handle numbers up to 999,999,999,999 - or could be divided into separate sections where several independent calculations could be carried out simultaneously.
'374072,' said Pickett, after an incredibly brief interval of time. 'Now see how long you take to do it, with pencil and paper.'
There was a much longer delay before Martens, who like most mathematicians was poor at arithmetic, called out '375072'. A hasty check soon confirmed that Martens had taken at least three times as long as Pickett to arrive at the wrong answer.
The atronomer's face was a study in mingled chagrin, astonishment, and curiosity.
'Where did you learn that trick?' he asked. 'I thought those things could only add and subtract.'
'Well - multiplication's only repeated addition, isn't it? All I did was to add 856 seven times in the unit column, three times in the tens column, and four times in the hundreds column. You do the same thing when you use pencil and paper. Of course, there are some short cuts, but if you think I'm fast, you should have seen my grand-uncle. He used to work in a Yokohama bank, and you couldn't see his fingers / Page 69 / when he was going at speed"

 

 

I

SAY

THREAD THAT THREAD

THREAD READ DEATH DEATH READ THREAD

THREAD R DEATH DEATH R THREAD

THREAD READ DEAR THREAD

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

Circa 1900

FOURTH EDITION

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

FOURTH EDITION

Circa 1900

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

lisle thread: lisle thread

A strong tightly twisted cotton thread (usually made of long-staple cotton) - lisle. Derived forms: lisle threads. Type of: cotton. Nearest ... www.wordwebonline.com/en/LISLETHREAD

 

 

Definition - of Lisle from Dictionary.net

Lisle thread, a hard twisted cotton thread, originally produced at Lisle. Source: Webster's Revised Unabridged Dictionary (1913) ... www.dictionary.net/lisle - 9k

 

 

CASSELL'S ENGLISH DICTIONARY

1974

Lisle thread (lil thred) [ town in France, now Lille], n, A fine, hard thread orig. made at Lille.

 

 

L
=
3
4
LIFE
32
23
5
H
=
8
7
HANGING
60
42
6
B
=
2
2
BY
27
9
9
A
=
1
1
A
1
1
1
T
=
2
6
THREAD
56
29
2
-
-
16
20
First Total
176
104
23
-
-
1+6
2+0
Add to Reduce
1+7+6
1+0+4
2+3
Q
-
7
2
Second Total
14
5
5
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
7
2
Essence of Number
5
5
5

 

 

-
THREAD
-
-
-
1
R
18
9
9
5
DEATH
38
20
2
6
THREAD
56
29
2

 

LIFE HANGING BY A THREAD

 

-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
44
-
-
9
-
-
-
8
-
5
-
9
5
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
44
4+4
=
8
=
8
=
8
62
-
-
9
-
-
-
8
-
14
-
9
14
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
62
6+2
=
8
=
8
=
8
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
60
-
3
-
6
5
-
-
1
-
7
-
-
7
-
2
7
-
1
-
2
-
9
5
1
4
+
=
60
6+0
=
6
=
6
=
6
114
-
12
-
6
5
-
-
1
-
7
-
-
7
-
2
25
-
1
-
20
-
18
5
1
4
+
=
114
1+1+4
=
6
=
6
=
6
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
--
-
-
-
-
176
-
12
9
6
5
-
8
1
14
7
9
14
7
-
2
25
-
1
-
20
8
18
5
1
4
+
=
176
1+7+6
=
14
1+4
5
=
5
104
-
3
9
6
5
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
+
=
104
1+0+4
=
5
=
5
=
5
-
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
=
3
2
``-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
20
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
45
-
-
20
-
104
-
41
4+5
2+0
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
2+0
-
1+0+4
-
4+1
9
2
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
2
-
5
-
5
-
-
3
9
6
5
-
8
1
5
7
9
5
7
-
2
7
-
1
-
2
8
9
5
1
4
-
-
-
-
-
-
-
-
-
-
9
2
L
I
F
E
-
H
A
N
G
I
N
G
-
B
Y
-
A
-
T
H
R
E
A
D
-
-
9
-
-
2
-
5
-
5

 

 

THE TIBETAN BOOK OF THE DEAD

Or

The After Death Experience on the Bardo Plane,

according to Lama Kazi Dawa-Samdup's English Rendering

Compiled and edited Edited by W. Y. Evans-Wentz 1960

Facing Preface To The Paperback Edition

'Thou shalt understand that it is a science most profitable, and passing all other sciences, for to learn to die. For a man to know that he shall die, that is common to all men; as much as there is no man that may ever live or he hath hope or trust thereof; but thou shalt find full few that have this callning to learn to die. . . . I shall give thee the mystery of this doctrine; the which shall profit thee greatly to the beginning of ghostly health, and to a stable fundament of all virtues. '- OrologiumSapientiae.

'Against his will he dieth that hath not learned to die. Learn to die and thou shalt learn to live, for there shall none learn to live that hath not learned to die.'-Toure of all Toures: and Teacheth a Man for to Die.

The Book of the Craft of Dying (Comper's Edition).

'\Vhatever is here, that is there; what is there, the same is here. He who seeth here as different, meeteth death after death.
'By mind alone this is to be realized, and [then] there is no difference here. From death to death he goeth, who seeth as if there is dificrence here.'-Katha Upanishad, iv. 10-11 (Swami Sharvanallda's Translation)"

Facing Preface to the Second Edition

BONDAGE TO REBIRTH

"As a man's desire is, so is his destiny. For as his desire is, so is his will; and as his will is, so is his deed; and as his deed is, so is his reward, whether good or bad.
' A man acteth according to the desires to which he clingeth. After death he goeth to the next world bearing in his mind the subtle impressions of his deeds; and, after reaping there the harvest of his deeds, he returneth again to this world of action. Thus he who hath desire continueth subject to rebirth.' "

Brihadaranyaka Upanishad

FREEDOM FROM REBIRTH

'He who lacketh discrimination, whose mind is unsteady and whose heart is impure, never reacheth the goal, but is born again and again. But he who hath discrimination, whose mind is steady and whose heart is pure, reacheth the goal, and having reached it is born no more.'

Katha U panishad.
(Swami Prabhavananda's and Frederick Manchester's Translations).

Page xi

SRI KRISHNA'S REMEMBERING

'Many lives Arjuna, you and I have lived.

I remember them all but thou dost not.'

Bhagavad Gita, iv, 5., iv, 5.

Page xx

"......... Denison........."

 

 

INCARNATION

THE DEAD RETURN

Daniel Easterman 1998

Page 99

"........David........."

Page 3

"The old man's name was Dennison"

 

 

THE

PATH OF PTAH

THE SELF CRUCIFIXION OF THE CRUCIFIXION OF THE SELF

THE

VIRGIN BIRTH IS TO BE REBORN OF WATER

AND

SPIRIT GODS HOLY SPIRIT

AFTER

HAVING ENDURED

THE DEATH OF THE

I ME EGO SELF I SELF EGO ME I

WEIGHED IN THE BALANCE AND NOT FOUND WANTING

EVOLVE THEE THAT THOU OF LOVE LOVE LOVE OF THOU THAT THEE EVOLVE

ISISIS

THE RESURRECTION AND THE LIFE

UNLESS THAT HE AZIN SHE THAT IS THEE

IZ

BORN AGAIN AGAIN BORN

THOU CANST NOT ENTER THE KINGDOM OF EVEN

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

2
IS
28
10
1
9
UNIVERSAL
121
40
4
4
MIND
40
22
4
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

9
UNIVERSAL
121
40
4
4
MIND
40
22
4
2
IS
28
10
1
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

E
=
5
-
2
EX
11
2
2
U
=
3
-
6
UMBRIS
82
28
1
E
=
5
-
2
ET
25
7
7
I
=
9
-
10
IMAGINIBUS
104
50
5
I
=
9
-
2
IN
23
14
5
V
=
4
-
9
VERITATEM
113
41
5
-
-
35
-
31
First Total
358
142
25
-
-
3+5
-
3+1
Add to Reduce
3+5+8
1+4+2
2+5
-
-
8
-
4
Second Total
16
7
7
-
-
-
-
-
Reduce to Deduce
1+6
-
-
-
-
8
-
4
Essence of Number
7
7
7

 

 

O
=
6
-
3
OUT
56
11
2
O
=
6
-
2
OF
21
12
3
S
=
1
-
7
SHADOWS
89
26
8
A
=
1
-
3
AND
82
28
1
P
=
7
-
9
PHANTASMS
111
30
3
I
=
9
-
4
INTO
58
22
4
T
=
2
-
5
TRUTH
87
24
6
-
-
32
-
33
Add to Reduce
441
135
27
-
-
3+2
-
3+3
Reduce to Deduce
4+4+1
1+3+5
2+7
-
-
5
-
6
Essence of Number
9
9
9

 

 

WE ARE THE DEAD SHORT TIME AGO WE LIVED FELT DAWN SAW SUNSET GLOW

LOVED AND WERE LOVED AND NOW

?

 

 

Search ResultsKafka's Before the Law
9 Nov 2003 ... Kafka's Before the Law. A Review. This story is actually contained in a larger work, but it has been published alone as a work of fiction. ... www.geocities.com/Athens/Parthenon/3761/Before_the_Law.htm

 

Kafka’s Before the Law

A Review

This story is actually contained in a larger work, but it has been published alone as a work of fiction.

In the segment entitled Before the Law, K, Kafka’s recurrent protagonist is talking with a priest.  He relates a story about a man that comes to a great door seeking the Law.  Before it is a gatekeeper that tells him he can’t be allowed to enter at that moment.  The man seeking the Law is perplexed, but intentional, so he waits, and waits and waits for the entirety of his life to be permitted to access the Law.  The gatekeeper also waits and allows the man to continue waiting, but not letting him pass through the gate.  As the man is dying, he wonders why he was the only person seeking the Law.  The gatekeeper tells him, that the gate he guards was only meant for him and since he is dying, he, the gatekeeper is going to close it.

K then engages the priest that has related this tale to him, in an analytic argument about the meaning of the story.

The arguments are piercing and full of moral implications.  Kafka is showing us how an allegory can have profound meaning.  It is unavoidable that the reader will not apply the experience of the man and gatekeeper to his personal life.  Don’t we all seek some Law, some way to understand our existence?  Are we not barred in this struggle to understand by a gatekeeper, in the form of fear, doubt and confusion?  The gatekeeper as allegory goes even further.  He explains that there are deeper realms, that even he (meaning the gatekeeper himself) can’t know, and the man will not be permitted to reach them.  Again, the analytic portion of Before the Law reflects upon this notion.  The priest explains that the gatekeeper could be deceived.  Are not we deceived about our life’s meaning and substance?  Before the Law is a clear narrative of human life.  We come to a point in our lives in which we seek purpose and order, yet we are obstructed from this by own minds (our gatekeepers if you will). We want health, while declining in well being, we want youth, while growing ever aged, we need love, yet never finding it.  We seek a reason, a Law if you will, that will help us, and thus we seek it, but discover our path is obscured by ourselves!  Here is the allegory of the story.  Kafka does this with such incredible power, you can’t stop reading it.

Kafka makes a strange allegorical tale, in which we can see the senselessness of being in the human condition.  K is seeking understanding of himself in the larger work.He has irrational fears. He fears high winds and feels a sense of forboding without cause. He actually enters the church for shelter before engaging the priest.  In this work, you are K, and the priest is your alter ego.  He provides you with many different interpretations of why the man sought the Law.  Yet, none suffice, for you must understand yourself why you seek the Law.  As a final word, Kafka has K declare that the Law is not real, it is a lie. He is razor-edge close to an existential conclusion with this declaration. It adds irony to allegory to have K, make this statement to a priest, whom is trying to explain the meaning of the tale.

 

 

YEA

THOUGH I WALK THROUGH

THE VALLEY OF THE SHADOW OF DEATH I WILL FEAR NO EVIL FOR THOU ART

WITH ME ALWAYS WITH ME

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Y
=
7
-
3
YEA
31
13
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
6
THOUGH
79
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
4
WALK
47
11
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
V
=
4
-
6
VALLEY
77
23
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
6
SHADOW
70
25
7
-
-
-
-
-
-
-
7
-
-
O
=
6
-
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
D
=
4
-
5
DEATH
38
20
2
-
-
2
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
4
WILL
56
20
2
-
-
2
-
-
-
-
-
-
-
F
=
6
-
4
FEAR
30
21
3
-
-
-
3
-
-
-
-
-
-
N
=
5
-
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
E
=
5
-
4
EVIL
48
21
3
-
-
-
3
-
-
-
-
-
-
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
4
THOU
64
19
1
-
1
-
-
-
-
-
-
-
-
A
=
1
-
3
ART
39
12
3
-
-
-
3
-
-
-
-
-
-
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
2
ME
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
6
ALWAYS
81
18
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
2
ME
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
108
-
91
First Total
1107
450
126
-
1
8
18
4
5
24
21
8
45
-
-
1+0+8
-
9+1
Add to Reduce
1+1+0+7
4+5+0
1+2+6
-
-
-
1+8
-
-
2+4
2+1
-
4+5
-
-
9
-
10
Second Total
9
9
9
-
1
8
9
4
5
6
3
8
9
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
Essence of Number
9
9
9
-
1
8
9
4
5
6
3
8
9

 

 

THROUGH

DEATHS

DARK

VEIL I FEAR NO EVIL

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
-
-
-
-
-
T
=
2
-
4
THOU
64
19
1
-
1
-
-
-
-
-
-
-
-
A
=
1
-
3
ART
39
12
3
-
-
-
3
-
-
-
-
-
-
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
2
ME
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
6
ALWAYS
81
18
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
M
=
4
-
2
ME
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
108
-
91
First Total
379
136
46
-
1
2
6
4
5
12
7
8
27
-
-
1+0+8
-
9+1
Add to Reduce
3+7+9
1+3+6
4+6
-
-
-
-
-
-
1+2
-
-
2+7
-
-
9
-
10
Second Total
19
10
10
-
1
2
6
4
5
3
7
8
9
-
-
-
-
1+0
Reduce to Deduce
1+9
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
Third Total
10
1
1
-
1
2
6
4
5
3
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
Essence of Number
1
1
1
-
1
2
6
4
5
3
7
8
9

 

 

 

 

-
5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
-
-
6
-
-
-
+
=
6
-
=
6
=
6
-
-
-
15
-
-
-
+
=
15
1+5
=
6
=
6
-
5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
-
5
-
9
3
4
+
=
21
2+1
=
3
=
3
-
-
23
-
18
12
4
+
=
57
5+7
=
12
1+2
3
-
5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
-
23
15
18
12
4
+
=
72
7+2
=
9
=
9
-
-
5
6
9
3
4
+
=
27
2+7
=
9
=
9
-
5
W
O
R
L
D
T
-
-
-
-
-
-
-
1
-
-
3
-
3
3
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
3
-
2
TWO
2
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
---
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
---
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
3
-
3
3
3
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
18
5
W
O
R
L
D
-
-
27
-
-
5
-
27
1+8
-
-
-
9
-
-
-
-
2+7
-
-
-
-
2+7
9
5
W
O
R
L
D
-
-
9
-
-
5
-
9
-
-
5
6
9
3
4
T
-
-
-
-
-
-
-
9
5
W
O
R
L
D
-
-
9
-
-
5
-
9

 

W LORD WORD L WORD LORD W

 

5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
-
6
-
-
-
+
=
6
-
=
6
=
6
-
-
15
-
-
-
+
=
15
1+5
=
6
=
6
5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
5
-
9
3
4
+
=
21
2+1
=
3
=
3
-
23
-
18
12
4
+
=
57
5+7
=
12
1+2
3
5
W
O
R
L
D
-
-
-
3
-
-
3
-
-
23
15
18
12
4
+
=
72
7+2
=
9
=
9
-
5
6
9
3
4
+
=
27
2+7
=
9
=
9
5
W
O
R
L
D
T
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
5
W
O
R
L
D
-
-
27
-
-
5
-
27
-
-
-
9
-
-
-
-
2+7
-
-
-
-
2+7
5
W
O
R
L
D
-
-
9
-
-
5
-
9
-
5
6
9
3
4
T
-
-
-
-
-
-
-
5
W
O
R
L
D
-
-
9
-
-
5
-
9

 

 

-
4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
-
-
-
-
9
-
+
=
9
-
=
9
=
9
-
4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
7
1
-
1
+
=
9
-
=
9
=
9
-
-
7
1
-
1
+
=
9
-
=
9
=
9
-
4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
7
1
9
1
+
=
18
1+8
=
9
=
9
-
-
7
1
9
1
+
=
18
1+8
=
9
=
9
-
4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
-
4
FOUR
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
28
4
G
A
I
A
-
-
17
-
-
4
-
18
2+8
-
-
-
9
-
-
-
1+7
-
-
-
-
1+8
10
4
G
A
I
A
-
-
8
-
-
4
-
9
1+0
-
7
1
9
1
-
-
-
-
-
--
-
-
1
4
G
A
I
A
-
-
8
-
-
4
-
9

 

 

4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
-
-
-
9
-
+
=
9
-
=
9
=
9
4
G
A
I
A
-
-
-
-
-
-
-
-
-
7
1
-
1
+
=
9
-
=
9
=
9
-
7
1
-
1
+
=
9
-
=
9
=
9
4
G
A
I
A
-
-
-
-
-
-
-
-
-
7
1
9
1
+
=
18
1+8
=
9
=
9
-
7
1
9
1
+
=
18
1+8
=
9
=
9
4
G
A
I
A
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
9
-
-
-
9
occurs
x
1
=
9
4
G
A
I
A
-
-
17
-
-
4
-
18
-
-
-
9
-
-
-
1+7
-
-
-
-
1+8
4
G
A
I
A
-
-
8
-
-
4
-
9
-
7
1
9
1
-
-
-
-
-
--
-
-
4
G
A
I
A
-
-
8
-
-
4
-
9

 

 

-
3
T
A
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
T
A
O
-
-
-
-
-
--
-
-
-
-
2
1
-
+
=
3
-
=
3
=
3
-
-
20
1
-
+
=
21
2+1
=
3
=
3
-
3
T
A
O
-
-
-
--
-
--
-
-
-
-
20
1
15
+
=
36
3+6
=
9
=
9
-
-
2
1
6
+
=
9
-
=
9
=
9
-
3
T
A
O
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
--
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
36
3
T
A
O
-
-
9
-
-
3
-
9
3+6
-
2
1
6
-
-
-
-
-
-
-
-
9
3
T
A
O
-
-
9
-
-
3
-
9
-
-
2
1
6
-
-
-
-
-
-
-
-
9
3
T
A
O
-
-
9
-
-
8
-
9

 

 

3
T
A
O
-
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
T
A
O
-
-
-
-
-
--
-
-
-
2
1
-
+
=
3
-
=
3
=
3
-
20
1
-
+
=
21
2+1
=
3
=
3
3
T
A
O
-
-
-
--
-
--
-
-
-
20
1
15
+
=
36
3+6
=
9
=
9
-
2
1
6
+
=
9
-
=
9
=
9
3
T
A
O
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
-
2
occurs
x
1
=
2
--
-
-
6
-
-
6
occurs
x
1
=
6
3
T
A
O
-
-
9
-
-
3
-
9
-
2
1
6
-
-
-
-
-
-
-
-
3
T
A
O
-
-
9
-
-
3
-
9
-
2
1
6
-
-
-
-
-
-
-
-
3
T
A
O
-
-
9
-
-
8
-
9

 

 

THE SOLAR SYSTEM
UNIVERSE
THE CONSTELLATIONS
SUN
SUN EARTH MOON
SUN
MOON
EARTH
MERCURY
VENUS
SATURN
URANUS
MARS
NEPTUNE
PLUTO
JUPITER
NIBIRU
WORLD
GAIA
TAO

 

 

-
-
-
-
-
THE SOLAR SYSTEM
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
5
SOLAR
65
20
2
S
=
1
-
6
SYSTEM
101
20
2
-
-
4
-
14
THE SOLAR SYSTEM
199
55
10
-
-
-
-
1+4
-
1+9+9
5+5
1+0
-
-
5
-
5
THE SOLAR SYSTEM
19
10
1
-
-
-
-
-
-
1+9
1+0
-
-
-
5
-
5
THE SOLAR SYSTEM
10
1
1
-
-
-
-
-
-
1+0
-
-
-
-
5
-
5
THE SOLAR SYSTEM
1
1
1

 

 

-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
1
6
-
-
-
-
1
-
1
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
8
-
-
19
15
-
-
-
-
19
-
19
-
-
-
+
=
80
8+0
=
8
=
8
=
8
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
-
3
1
9
-
-
7
-
2
5
4
+
=
38
3+8
=
11
1+1
2
=
2
-
-
20
-
5
-
-
-
12
1
18
-
-
25
-
20
5
13
+
=
119
1+1+9
=
11
1+1
2
=
2
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
19
15
12
1
18
-
19
25
19
20
5
13
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
2
8
5
-
1
6
3
1
9
-
1
7
1
2
5
4
+
=
55
5+5
=
10
1+0
1
=
1
-
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
-
-
1
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
45
14
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
45
-
-
14
-
55
-
46
4+5
1+4
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
4+5
-
-
1+4
-
5+5
-
4+6
9
5
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
9
-
-
5
-
10
-
10
-
-
2
8
5
-
1
6
3
1
9
-
1
7
1
2
5
4
-
-
-
-
-
-
-
1+0
-
1+0
9
5
T
H
E
-
S
O
L
A
R
-
S
Y
S
T
E
M
-
-
9
-
-
5
-
1
-
1

 

 

-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
6
-
-
-
1
-
1
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
8
-
19
15
-
-
-
19
-
19
-
-
-
+
=
80
8+0
=
8
=
8
=
8
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
3
1
9
-
7
-
2
5
4
+
=
38
3+8
=
11
1+1
2
=
2
-
-
20
-
5
-
-
12
1
18
-
25
-
20
5
13
+
=
119
1+1+9
=
11
1+1
2
=
2
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
19
15
12
1
18
19
25
19
20
5
13
+
=
199
1+9+9
=
19
1+9
10
1+0
1
-
-
2
8
5
1
6
3
1
9
1
7
1
2
5
4
+
=
55
5+5
=
10
1+0
1
=
1
-
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
-
1
-
1
-
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
--
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
45
14
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
45
-
-
14
-
55
-
46
4+5
1+4
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
4+5
-
-
1+4
-
5+5
-
4+6
9
5
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
9
-
-
5
-
10
-
10
-
-
2
8
5
1
6
3
1
9
1
7
1
2
5
4
-
-
-
-
-
-
-
1+0
-
1+0
9
5
T
H
E
S
O
L
A
R
S
Y
S
T
E
M
-
-
9
-
-
5
-
1
-
1

 

 

-
-
-
-
-
THE SOLAR SYSTEM
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
5
SOLAR
65
20
2
S
=
1
-
6
SYSTEM
101
38
2
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
-
-
-
1+4
-
1+9+9
7+3
1+0
-
-
4
-
5
THE SOLAR SYSTEM
19
10
1
-
-
-
-
-
-
1+9
1+0
-
-
-
4
-
5
THE SOLAR SYSTEM
10
1
1
-
-
-
-
-
-
1+0
-
-
-
-
4
-
5
THE SOLAR SYSTEM
1
1
1

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
20
-
3
-
26
29
20
-
-
-
-
-
-
-
-
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
Y
=
6
10
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
20
-
4
-
101
38
20
-
4
4
3
4
10
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+0
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
4
4
3
4
1
6
7
8
9
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
1+4
1
9+1
7+3
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM-
10
10
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM
1
1
1
-
4
4
3
4
1
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
9
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
Y
=
6
10
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
4
3
4
10
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+0
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
4
4
3
4
1
6
7
8
9
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
1+4
1
9+1
7+3
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM-
10
10
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM
1
1
1
-
4
4
3
4
1
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
4
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
9
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
12
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
6
10
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
4
4
3
4
10
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+0
-
-
-
-
S
=
1
-
5
SOLAR
65
20
2
-
4
4
3
4
1
6
7
8
9
S
=
1
-
6
SYSTEM
101
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
THE SOLAR SYSTEM
199
73
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
1+4
1
9+1
7+3
1+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM-
10
10
10
-
4
4
3
4
1
6
7
8
9
-
-
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
THE SOLAR SYSTEM
1
1
1
-
4
4
3
4
1
6
7
8
9

 

 

B
=
2
-
4
BLUE
40
13
4
P
=
7
-
6
PLANET
68
23
5
-
-
9
4
10
Add to Reduce
108
36
18
-
-
-
-
1+0
Reduce to Deduce
1+0+8
3+6
1+8
-
-
9
-
1
Essence of Number
9
9
9

 

 

EARTH 7 EARTH

EARTH 25 EARTH

EARTH 52 EARTH

PLANET EARTH PLANT E PLANT EARTH PLANET

EARTH 52 EARTH

EARTH 25 EARTH

EARTH 7 EARTH

 

 

SEVEN EVENS SEVEN

EVENS SEVEN EVENS

SEVEN EVENS SEVEN

 

HEAVEN HA EVEN HA HEAVEN

 

https://en.wikipedia.org/wiki/Sirius
Sirius (/'s?ri?s/, a romanization of Greek Se, Seirios, lit . "glowing" or "scorching") is a star system and the brightest star in the Earth's night sky. With a visual apparent magnitude of -1.46, it is almost twice as bright as Canopus, the next brightest star.

 

https://en.wiktionary.org/wiki/Sirius
Proper noun. Sirius. (astronomy) A binary star system in the constellation Canis Major long understood as a single extremely luminous white star, associated in ancient Egypt with the Nile flood and in Greek and Roman culture with the "dog days" of summer.

 

https://www.behindthename.com/bb/fact/23715
5 Feb 2003 - Indees, Sirius is the Latin form of the Greek Seirios meaning "scorcher". "Seirios kyon" is indeed the Dog Star. Seirios is used as an adjective for ...

 

SEIRIOS E OSIRIS E SEIRIOS

SIRIUS = 95 = SIRIUS

SO

THIS

SOTHIS

IS

 

-
-
-
-
-
SEIRIOS
--
-
-
-
-
-
-
1
S
19
10
1
-
-
-
-
1
E
5
5
5
-
-
-
-
1
I
9
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
1
I
9
9
9
-
-
-
-
1
O
15
6
6
-
-
-
-
1
S
19
10
1
E
=
5
-
7
SEIRIOS
94
58
40
-
-
-
-
-
-
9+4
5+8
4+0
E
=
5
-
7
SEIRIOS
13
13
4
6
-
-
-
-
-
1+3
1+3
-
E
=
5
-
7
SEIRIOS
4
4
4

 

 

SIRIUS R U SERIOUS SERIOUS U R SIRIUS

 

 

-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
9
-
-
-
19
-
+
=
42
4+2
=
6
=
6
=
6
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
21
-
-
22
5
18
-
5
+
=
71
7+1
=
8
=
8
=
8
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
5
+
=
113
1+1+3
=
5
=
5
=
5
-
-
3
5
9
4
5
9
1
5
+
=
41
4+1
=
5
=
5
=
5
-
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
8
U
N
I
V
E
R
S
E
-
-
22
-
-
9
-
41
-
23
2+3
-
-
-
9
-
-
9
-
-
-
-
2+2
-
-
-
-
4+1
-
2+3
5
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5
-
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
5
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5

 

 

8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
+
=
15
1+5
=
6
=
6
=
6
-
-
14
9
-
-
-
19
-
+
=
42
4+2
=
6
=
6
=
6
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
5
+
=
26
2+6
=
8
=
8
=
8
-
21
-
-
22
5
18
-
5
+
=
71
7+1
=
8
=
8
=
8
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
5
+
=
113
1+1+3
=
5
=
5
=
5
-
3
5
9
4
5
9
1
5
+
=
41
4+1
=
5
=
5
=
5
8
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
U
N
I
V
E
R
S
E
-
-
22
-
-
9
-
41
-
23
-
-
-
9
-
-
9
-
-
-
-
2+2
-
-
-
-
4+1
-
2+3
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
8
U
N
I
V
E
R
S
E
-
-
4
-
-
9
-
5
-
5

 

 

-
-
-
-
-
THE UNIVERSE
-
-
-
T
=
2
-
3
THE
33
15
6
U
=
3
-
8
UNIVERSE
113
41
5
-
-
5
-
11
THE UNIVERSE
146
56
11
-
-
-
-
1+1
-
1+4+6
5+6
1+1
-
-
5
-
2
THE UNIVERSE
11
11
2
-
-
-
-
-
-
1+1
1+0
-
-
-
5
-
2
THE UNIVERSE
2
2
2

 

 

-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
-
20
-
5
-
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
-
2
8
5
-
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
-
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
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
-
-
5
occurs
x
4
=
20
2+0
2
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
13
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+3
1+1
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
4
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
-
2
8
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
4
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

 

11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
20
-
5
-
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
2
8
5
-
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
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
-
-
5
occurs
x
4
=
20
2+0
2
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
T
H
E
-
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+1
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
2
8
5
-
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
2
T
H
E
-
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

 

11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
9
-
-
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
14
9
-
-
-
19
-
+
=
50
5+0
=
5
=
5
=
5
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
-
4
5
9
-
5
+
=
33
3+3
=
6
=
6
=
6
-
20
-
5
21
-
-
22
5
18
-
5
+
=
96
9+6
=
15
1+5
6
=
6
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
21
14
9
22
5
18
19
5
+
=
146
1+4+6
=
11
1+1
6
=
5
-
2
8
5
3
5
9
4
5
9
1
5
+
=
56
5+6
=
11
=
5
=
5
11
T
H
E
U
N
I
V
E
R
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
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
-
-
5
occurs
x
4
=
20
2+0
2
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
T
H
E
U
N
I
V
E
R
S
E
-
-
32
-
-
11
-
41
-
23
1+1
-
-
-
-
-
9
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+1
-
2+3
2
T
H
E
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5
-
2
8
5
3
5
9
4
5
9
1
5
-
-
-
-
-
-
-
-
-
-
2
T
H
E
U
N
I
V
E
R
S
E
-
-
5
-
-
2
-
5
-
5

 

 

-
INTERSTELLAR
-
-
-
5
INTER
66
30
3
7
STELLAR
87
24
6
12
INTERSTELLAR
153
54
9
1+2
-
1+5+3
5+4
-
3
INTERSTELLAR
9
9
9

 

 

3
THE
33
15
6
5
MILKY
70
25
7
5
WASTE
49
13
4
15
Add to Reduce
153
54
18
1+5
Reduce to Deduce
1+5+3
5+4
1+8
6
Essence of Number
9
9
9

 

 

-
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
-
-
1
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
8
-
-
-
9
-
-
-
-
-
-
19
-
-
+
=
36
3+6
=
9
=
9
=
9
-
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
4
-
3
2
7
-
5
1
-
2
5
+
=
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
13
-
12
11
25
-
23
1
-
20
5
+
=
135
1+3+5
=
9
=
9
=
9
-
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
13
9
12
11
25
-
23
1
19
20
5
+
=
153
1+5+3
=
9
=
9
=
9
-
-
2
8
5
-
4
9
3
2
7
-
5
1
1
2
5
+
=
54
5+4
=
9
=
9
=
9
-
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
39
-
-
13
-
54
-
45
-
1+3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+3
-
5+4
-
4+5
6
4
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
12
-
-
4
-
9
-
9
-
-
2
8
5
-
4
9
3
2
7
-
5
1
1
2
5
-
-
1+2
1
-
-
-
-
-
-
6
4
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
3
-
-
4
-
9
-
9

 

 

13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
-
-
1
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
8
-
-
-
9
-
-
-
-
-
-
19
-
-
+
=
36
3+6
=
9
=
9
=
9
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
4
-
3
2
7
-
5
1
-
2
5
+
=
36
3+6
=
9
=
9
=
9
-
20
-
5
-
13
-
12
11
25
-
23
1
-
20
5
+
=
135
1+3+5
=
9
=
9
=
9
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
13
9
12
11
25
-
23
1
19
20
5
+
=
153
1+5+3
=
9
=
9
=
9
-
2
8
5
-
4
9
3
2
7
-
5
1
1
2
5
+
=
54
5+4
=
9
=
9
=
9
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
39
-
-
13
-
54
-
45
1+3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+3
-
5+4
-
4+5
4
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
12
-
-
4
-
9
-
9
-
2
8
5
-
4
9
3
2
7
-
5
1
1
2
5
-
-
1+2
1
-
-
-
-
-
-
4
T
H
E
-
M
I
L
K
Y
-
W
A
S
T
E
-
-
3
-
-
4
-
9
-
9

 

 

13
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
1
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
8
-
-
9
-
-
-
-
-
19
-
-
+
=
36
3+6
=
9
=
9
=
9
13
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
4
-
3
2
7
5
1
-
2
5
+
=
36
3+6
=
9
=
9
=
9
-
20
-
5
13
-
12
11
25
23
1
-
20
5
+
=
135
1+3+5
=
9
=
9
=
9
13
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
13
9
12
11
25
23
1
19
20
5
+
=
153
1+5+3
=
9
=
9
=
9
-
2
8
5
4
9
3
2
7
5
1
1
2
5
+
=
54
5+4
=
9
=
9
=
9
13
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
-
2
-
-
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
39
-
-
13
-
54
-
45
1+3
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+3
-
5+4
-
4+5
4
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
12
-
-
4
-
9
-
9
-
2
8
5
4
9
3
2
7
5
1
1
2
5
-
-
1+2
1
-
-
-
-
-
-
4
T
H
E
M
I
L
K
Y
W
A
S
T
E
-
-
3
-
-
4
-
9
-
9

 

 

13
THE MILKY WASTE
153
54
9
11
THE MILKY WAY
152
53
8

 

 

3
THE
33
15
6
5
MILKY
70
25
7
3
WAY
49
13
4
11
Add to Reduce
152
53
17
1+1
Reduce to Deduce
1+5+2
5+3
1+7
2
Essence of Number
8
8
8

 

 

-
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
8
-
-
-
9
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
4
-
3
2
7
-
5
1
7
+
=
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
13
-
12
11
25
-
23
1
25
+
=
135
1+3+5
=
9
=
9
=
9
-
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
13
9
12
11
25
-
23
1
25
+
=
152
1+5+2
=
8
=
8
=
8
-
-
2
8
5
-
4
9
3
2
7
-
5
1
7
+
=
53
5+3
=
8
=
8
=
8
-
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
39
-
-
11
-
53
-
35
-
1+1
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+9
-
-
1+1
-
5+3
-
3+5
6
2
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
12
-
-
2
-
8
-
8
-
-
2
8
5
-
4
9
3
2
7
-
5
1
7
-
-
1+2
1
-
-
-
-
-
-
6
2
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
3
-
-
2
-
8
-
8

 

 

11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
8
-
-
-
9
-
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
4
-
3
2
7
-
5
1
7
+
=
36
3+6
=
9
=
9
=
9
-
20
-
5
-
13
-
12
11
25
-
23
1
25
+
=
135
1+3+5
=
9
=
9
=
9
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
13
9
12
11
25
-
23
1
25
+
=
152
1+5+2
=
8
=
8
=
8
-
2
8
5
-
4
9
3
2
7
-
5
1
7
+
=
53
5+3
=
8
=
8
=
8
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
39
-
-
11
-
53
-
35
1+1
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+9
-
-
1+1
-
5+3
-
3+5
2
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
12
-
-
2
-
8
-
8
-
2
8
5
-
4
9
3
2
7
-
5
1
7
-
-
1+2
1
-
-
-
-
-
-
2
T
H
E
-
M
I
L
K
Y
-
W
A
Y
-
-
3
-
-
2
-
8
-
8

 

 

11
T
H
E
M
I
L
K
Y
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
-
-
8
-
-
9
-
-
-
-
-
-
+
=
17
1+7
=
8
=
8
=
8
11
T
H
E
M
I
L
K
Y
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
2
-
5
4
-
3
2
7
5
1
7
+
=
36
3+6
=
9
=
9
=
9
-
20
-
5
13
-
12
11
25
23
1
25
+
=
135
1+3+5
=
9
=
9
=
9
11
T
H
E
M
I
L
K
Y
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
20
8
5
13
9
12
11
25
23
1
25
+
=
152
1+5+2
=
8
=
8
=
8
-
2
8
5
4
9
3
2
7
5
1
7
+
=
53
5+3
=
8
=
8
=
8
11
T
H
E
M
I
L
K
Y
W
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
``-
2
-
-
-
-
-
2
-
-
-
-
2
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
5
-
-
-
5
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
T
H
E
M
I
L
K
Y
W
A
Y
-
-
39
-
-
11
-
53
-
35
1+1
-
-
-
-
9
-
-
-
-
-
-
-
-
3+9
-
-
1+1
-
5+3
-
3+5
2
T
H
E
M
I
L
K
Y
W
A
Y
-
-
12
-
-
2
-
8
-
8
-
2
8
5
4
9
3
2
7
5
1
7
-
-
1+2
1
-
-
-
-
-
-
2
T
H
E
M
I
L
K
Y
W
A
Y
-
-
3
-
-
2
-
8
-
8

 

 

3
THE
33
15
6
5
MILKY
70
25
7
3
WAY
49
13
4

 

 

G
=
7
6
GALAXY
70
25
7

 

 

M
=
4
5
MILKY
70
25
7
W
=
5
3
WAY
49
13
4
G
=
7
6
GALAXY
70
25
7
-
-
16
14
First Total
189
63
18
-
-
1+6
1+4
Add to Reduce
1+8+9
6+3
1+8
Q
-
7
5
Second Total
18
9
9
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
7
5
Essence of Number
9
9
9

 

 

-
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
6
-
+
=
15
1+5
=
6
=
6
=
6
=
6
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
24
-
+
=
33
3+3
=
6
=
6
=
6
=
6
-
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
2
7
-
5
1
7
-
7
1
3
1
-
7
+
=
48
4+8
=
12
1+2
3
=
3
=
3
-
-
13
-
12
11
25
-
23
1
25
-
7
1
12
1
-
25
+
=
156
1+5+6
=
12
1+2
3
=
3
=
3
-
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
13
9
12
11
25
-
23
1
25
-
7
1
12
1
24
7
+
=
189
1+8+9
=
18
1+8
9
=
9
=
9
-
-
4
9
3
2
7
-
5
1
7
-
7
1
3
1
6
7
+
=
63
6+3
=
9
-
9
=
9
=
9
-
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
1
occurs
x
3
=
3
=
3
=
3
-
``-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
=
2
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
=
6
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
=
6
-
-
-
-
-
-
7
-
-
-
7
-
7
-
-
-
-
7
-
-
7
occurs
x
4
=
28
2+8
10
1+0
1
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
=
9
8
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
37
-
-
14
-
63
-
36
-
36
-
1+4
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+4
-
6+3
-
3+6
-
3+6
8
5
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
10
-
-
5
-
9
-
9
-
9
-
-
4
9
3
2
7
-
5
1
7
-
7
1
3
1
6
7
-
-
1+0
1
-
-
-
-
-
-
-
-
8
5
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
1
-
-
6
-
9
-
9
-
9

 

 

14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
6
-
+
=
15
1+5
=
6
=
6
=
6
=
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
24
-
+
=
33
3+3
=
6
=
6
=
6
=
6
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
2
7
-
5
1
7
-
7
1
3
1
-
7
+
=
48
4+8
=
12
1+2
3
=
3
=
3
-
13
-
12
11
25
-
23
1
25
-
7
1
12
1
-
25
+
=
156
1+5+6
=
12
1+2
3
=
3
=
3
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
13
9
12
11
25
-
23
1
25
-
7
1
12
1
24
7
+
=
189
1+8+9
=
18
1+8
9
=
9
=
9
-
4
9
3
2
7
-
5
1
7
-
7
1
3
1
6
7
+
=
63
6+3
=
9
-
9
=
9
=
9
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
1
occurs
x
3
=
3
=
3
=
3
``-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
=
6
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
=
6
-
-
-
-
-
7
-
-
-
7
-
7
-
-
-
-
7
-
-
7
occurs
x
4
=
28
2+8
10
1+0
1
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
=
9
14
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
37
-
-
14
-
63
-
36
-
36
1+4
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+4
-
6+3
-
3+6
-
3+6
5
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
10
-
-
5
-
9
-
9
-
9
-
4
9
3
2
7
-
5
1
7
-
7
1
3
1
6
7
-
-
1+0
1
-
-
-
-
-
-
-
-
5
M
I
L
K
Y
-
W
A
Y
-
G
A
L
A
X
Y
-
-
1
-
-
6
-
9
-
9
-
9

 

 

14
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
6
-
+
=
15
1+5
=
6
=
6
=
6
=
6
-
-
9
-
-
-
-
-
-
-
-
-
-
24
-
+
=
33
3+3
=
6
=
6
=
6
=
6
14
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
3
2
7
5
1
7
7
1
3
1
-
7
+
=
48
4+8
=
12
1+2
3
=
3
=
3
-
13
-
12
11
25
23
1
25
7
1
12
1
-
25
+
=
156
1+5+6
=
12
1+2
3
=
3
=
3
14
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
13
9
12
11
25
23
1
25
7
1
12
1
24
7
+
=
189
1+8+9
=
18
1+8
9
=
9
=
9
-
4
9
3
2
7
5
1
7
7
1
3
1
6
7
+
=
63
6+3
=
9
-
9
=
9
=
9
14
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
1
-
-
-
-
1
occurs
x
3
=
3
=
3
=
3
``-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
=
6
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
=
6
-
-
-
-
-
7
-
-
7
7
-
-
-
-
7
-
-
7
occurs
x
4
=
28
2+8
10
1+0
1
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
=
9
14
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
37
-
-
14
-
63
-
36
-
36
1+4
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+7
-
-
1+4
-
6+3
-
3+6
-
3+6
5
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
10
-
-
5
-
9
-
9
-
9
-
4
9
3
2
7
5
1
7
7
1
3
1
6
7
-
-
1+0
1
-
-
-
-
-
-
-
-
5
M
I
L
K
Y
W
A
Y
G
A
L
A
X
Y
-
-
1
-
-
6
-
9
-
9
-
9

 

 

-
-
-
-
-
THE CONSTELLATIONS
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
14
CONSTELLATIONS
65
52
7
-
-
5
-
17
THE CONSTELLATIONS
211
67
13
-
-
-
-
1+7
-
2+1+1
6+7
1+3
-
-
5
-
8
THE CONSTELLATIONS
4
13
4
-
-
-
-
-
-
-
1+3
-
-
-
5
-
8
THE CONSTELLATIONS
4
4
4
-
-
-
-
-
-
-
-
-
-
-
5
-
8
THE CONSTELLATIONS
4
4
4

 

 

-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
-
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+1
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
2
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
2
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
8
-
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
20
-
5
-
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
17
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
2
8
5
-
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
8
T
H
E
-
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
5
1
-
-
-
-
-
-
9
6
5
1
+
=
41
4+1
=
5
=
5
=
5
-
-
8
-
-
15
14
19
-
-
-
-
-
-
9
15
14
19
+
=
113
1+1+3
=
5
=
5
=
5
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
2
-
5
3
-
-
-
2
5
3
3
1
2
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
20
-
5
3
-
-
-
20
5
12
12
1
20
-
-
-
-
+
=
98
9+8
=
17
1+7
8
=
8
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
20
8
5
3
15
14
19
20
5
12
12
1
20
9
15
14
19
+
=
211
2+1+1
=
4
=
4
=
4
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
1
+
=
67
6+7
=
13
1+3
4
=
4
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
5
-
-
5
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
17
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
34
-
-
17
-
67
-
40
1+7
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
6+7
-
4+0
8
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
13
-
4
-
2
8
5
3
6
5
1
2
5
3
3
1
2
9
6
5
1
-
-
-
-
-
-
-
-
-
-
8
T
H
E
C
O
N
S
T
E
L
L
A
T
I
O
N
S
-
-
7
-
-
8
-
4
-
4

 

 

3
SUN
54
9
9
7
MERCURY
103
40
4
5
VENUS
81
18
9
5
EARTH
52
25
7
4
MOON
57
21
3
4
MARS
51
15
6
7
JUPITER
99
36
9
6
SATURN
93
21
3
6
URANUS
94
22
4
7
NEPTUNE
95
32
5
5
PLUTO
84
21
3
59
First Total
863
260
62
5+9
Add to Reduce
8+6+3
2+6
6+2
14
Second Total
17
8
8
1+4
Reduce to Deduce
1+7
-
-
5
Essence of Number
8
8
8

 

 

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
1
1
1

 

 

-
THE SOLAR SYSTEM
-
-
-
3
THE
33
15
6
5
SOLAR
65
29
2
6
SYSTEM
101
38
2
14
THE SOLAR SYSTEM
199
82
10
1+4
-
1+9+9
8+2
1+0
5
THE SOLAR SYSTEM
19
10
1
-
-
1+9
1+0
-
5
THE SOLAR SYSTEM
10
1
1
-
-
1+0
-
-
5
THE SOLAR SYSTEM
1
1
1

 

 

S
=
1
-
3
SUN
54
9
9
M
=
4
-
7
MERCURY
103
40
4
V
=
4
-
5
VENUS
81
18
9
E
=
5
-
5
EARTH
52
25
7
M
=
4
-
4
MOON
57
21
3
M
=
4
-
4
MARS
51
15
6
J
=
1
-
7
JUPITER
99
36
9
S
=
1
-
6
SATURN
93
21
3
U
=
3
-
6
URANUS
94
22
4
N
=
5
-
7
NEPTUNE
95
32
5
P
=
7
-
5
PLUTO
84
21
3
-
-
39
-
59
First Total
863
260
62
-
-
3+9
-
5+9
Add to Reduce
8+6+3
2+6+0
6+2
-
-
12
-
14
Second Total
17
8
8
-
-
1+2
-
1+4
Reduce to Deduce
1+7
-
-
-
-
3
-
5
Essence of Number
8
8
8

 

 

1
-
S
=
1
-
3
SUN
54
9
9
2
-
M
=
4
-
7
MERCURY
103
40
4
3
-
V
=
4
-
5
VENUS
81
18
9
4
-
E
=
5
-
5
EARTH
52
25
7
5
-
M
=
4
-
4
MOON
57
21
3
6
-
M
=
4
-
4
MARS
51
15
6
7
-
J
=
1
-
7
JUPITER
99
36
9
8
-
S
=
1
-
6
SATURN
93
21
3
9
-
U
=
3
-
6
URANUS
94
22
4
10
-
N
=
5
-
7
NEPTUNE
95
32
5
11
-
P
=
7
-
5
PLUTO
84
21
3
66
-
-
-
39
-
59
First Total
863
260
62
6+6
-
-
-
3+9
-
5+9
Add to Reduce
8+6+3
2+6+0
6+2
12
-
-
-
12
-
14
Second Total
17
8
8
1+2
-
-
-
1+2
-
1+4
Reduce to Deduce
1+7
-
-
3
-
-
-
3
-
5
Essence of Number
8
8
8

 

 

S
=
1
-
3
SUN
54
9
9
M
=
4
-
7
MERCURY
103
40
4
V
=
4
-
5
VENUS
81
18
9
E
=
5
-
5
EARTH
52
25
7
M
=
4
-
4
MOON
57
21
3
M
=
4
-
4
MARS
51
15
6
J
=
1
-
7
JUPITER
99
36
9
S
=
1
-
6
SATURN
93
21
3
U
=
3
-
6
URANUS
94
22
4
N
=
5
-
7
NEPTUNE
95
32
5
P
=
7
-
5
PLUTO
84
21
3
N
=
5
-
6
NIBIRU
73
37
1
-
-
44
-
65
First Total
936
297
63
-
-
4+4
-
6+5
Add to Reduce
9+3+6
2+9+7
6+3
-
-
8
-
11
Second Total
18
18
9
-
-
-
-
1+1
Reduce to Deduce
1+8
1+8
-
-
-
8
-
2
Essence of Number
9
9
9

 

 

1
-
S
=
1
-
3
SUN
54
9
9
2
-
M
=
4
-
7
MERCURY
103
40
4
3
-
V
=
4
-
5
VENUS
81
18
9
4
-
E
=
5
-
5
EARTH
52
25
7
5
-
M
=
4
-
4
MOON
57
21
3
6
-
M
=
4
-
4
MARS
51
15
6
7
-
J
=
1
-
7
JUPITER
99
36
9
8
-
S
=
1
-
6
SATURN
93
21
3
9
-
U
=
3
-
6
URANUS
94
22
4
10
-
N
=
5
-
7
NEPTUNE
95
32
5
11
-
P
=
7
-
5
PLUTO
84
21
3
12
-
N
=
5
-
6
NIBIRU
73
37
1
78
-
-
-
44
-
65
First Total
936
297
63
7+8
-
-
-
4+4
-
6+5
Add to Reduce
9+3+6
2+9+7
6+3
15
-
-
-
8
-
11
Second Total
18
18
9
1+5
-
-
-
-
-
1+1
Reduce to Deduce
1+8
1+8
-
6
-
-
-
8
-
2
Essence of Number
9
9
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
1
1
1

 

 

-
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
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
1+2
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
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+8
-
-
1+2
-
5+5
-
3+7
7
12
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
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
2
-
-
3
-
1
-
1

 

 

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
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
38
-
-
12
-
55
-
37
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
3+8
-
-
1+2
-
5+5
-
3+7
12
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
12
S
U
N
-
E
A
R
T
H
-
M
O
O
N
-
-
2
-
-
3
-
1
-
1

 

 

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
1+5
6
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
S
U
N
E
A
R
T
H
M
O
O
N
-
-
38
-
-
12
-
55
-
37
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+8
-
-
1+2
-
5+5
-
3+7
12
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
12
S
U
N
E
A
R
T
H
M
O
O
N
-
-
2
-
-
3
-
1
-
1

 

 

SUNMOONEARTH

 

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

 

SUNMOONEARTH

 

 

 

 

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

 

 

3
SUN
54
18
9
5
EARTH
52
25
7
4
MOON
57
21
3
12
First Total
163
64
19
1+2
Add to Reduce
1+6+3
6+4
1+9
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

-
-
-
-
-
SUN EARTH MOON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
3
SUN
54
9
9
-
1
2
-
-
-
-
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
1
2
-
-
-
-
-
-
-
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
55
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
18
-
3
-
54
18
9
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
-
-
25
-
5
-
52
25
25
-
-
-
-
-
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
21
-
4
-
57
21
21
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUN EARTH MOON
-
-
-
-
2
2
3
4
15
12
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
1+5
1+2
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
2
2
3
4
6
3
7
8
9
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
64
19
-
2
2
3
4
6
3
7
8
9
-
-
1+0
-
1+2
-
1+6+3
6+4
1+9
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
10
10
10
-
2
2
3
4
6
3
7
8
9
-
-
-
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
1
1
1
-
2
2
3
4
6
3
7
8
9

 

 

-
-
-
-
-
SUN EARTH MOON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
3
SUN
54
9
9
-
1
2
-
-
-
-
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
1
2
-
-
-
-
-
-
-
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
55
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUN EARTH MOON
-
-
-
-
2
2
3
4
15
12
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
1+5
1+2
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
2
2
3
4
6
3
7
8
9
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
64
19
-
2
2
3
4
6
3
7
8
9
-
-
1+0
-
1+2
-
1+6+3
6+4
1+9
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
10
10
10
-
2
2
3
4
6
3
7
8
9
-
-
-
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
1
1
1
-
2
2
3
4
6
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
SUN EARTH MOON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
3
SUN
54
9
9
-
1
2
-
-
-
-
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
1
2
-
-
-
-
-
-
-
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
55
19
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUN EARTH MOON
-
-
-
-
2
2
3
4
15
12
7
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
1+5
1+2
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
2
2
3
4
6
3
7
8
9
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
64
19
-
2
2
3
4
6
3
7
8
9
-
-
1+0
-
1+2
-
1+6+3
6+4
1+9
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
10
10
10
-
2
2
3
4
6
3
7
8
9
-
-
-
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
1
1
1
-
2
2
3
4
6
3
7
8
9

 

THE SO EVEN SEVEN

THE MISSING NUMBER

 

-
-
-
-
-
SUN EARTH MOON
-
-
-
-
1
2
3
4
5
6
8
9
S
=
1
-
3
SUN
54
9
9
-
1
2
-
-
-
-
-
-
E
=
5
-
5
EARTH
52
25
7
-
1
2
-
-
-
-
-
-
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
55
19
-
1
2
3
4
5
6
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SUN EARTH MOON
-
-
-
-
2
2
3
4
15
12
8
9
S
=
1
-
3
SUN
54
18
9
-
-
-
-
-
1+5
1+2
-
-
E
=
5
-
5
EARTH
52
25
7
-
2
2
3
4
6
3
8
9
M
=
4
-
4
MOON
57
21
3
-
-
-
-
-
-
-
-
-
-
-
10
-
12
SUN EARTH MOON
163
64
19
-
2
2
3
4
6
3
8
9
-
-
1+0
-
1+2
-
1+6+3
6+4
1+9
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
10
10
10
-
2
2
3
4
6
3
8
9
-
-
-
-
-
-
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
1
-
3
SUN EARTH MOON
1
1
1
-
2
2
3
4
6
3
8
9

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
3
GOD
26
17
8
M
=
4
-
4
MIND
40
22
4
-
-
13
-
10
First Total
99
54
18
-
-
1+3
-
1+0
Add to Reduce
9+9
5+4
1+8
-
-
4
-
1
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
-
1
Essence of Number
9
9
9

 

 

3
SUN
54
9
9
5
EARTH
52
25
7
4
MOON
57
21
3

 

 

-
--
-
--
-
SUN
-
--
-
S
=
1
-
1
S
19
10
1
U
=
3
-
1
U
21
3
3
N
=
5
-
1
N
14
5
5
-
-
9
-
3
SUN
54
18
9
-
-
-
-
-
-
5+4
1+8
-
-
-
9
-
3
SUN
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
-
-
-
-
-
-
-
-
-
-
-
-
9
3
S
U
N
-
-
9
-
-
3
-
9
-
-
1
3
5
-
-
-
-
-
-
-
-
9
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
-
-
-
-
-
-
-
-
-
-
-
-
3
S
U
N
-
-
9
-
-
3
-
9
-
1
3
5
-
-
-
-
-
-
-
-
3
S
U
N
-
-
9
-
-
3
-
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

 

 

-
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

 

How Many Tectonic Plates are There?

www.wisegeek.com/how-many-tectonic-plates-are-there.htm - CachedSimilar
11 May 2011 – The Earth has 14 major tectonic plates and 38 minor tectonic plates, 52 plates in total. The major tectonic plates are found...

 

 

-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
-
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
-
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
-
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
17
7
M
E
R
C
U
R
Y
-
-
28
-
-
7
-
40
-
31
1+7
-
-
-
9
-
-
9
-
-
-
2+8
-
-
-
-
4+0
-
3+1
8
7
M
E
R
C
U
R
Y
-
-
10
-
-
7
-
4
-
4
-
-
4
5
9
3
3
9
7
-
-
1+0
-
-
-
-
-
-
-
8
7
M
E
R
C
U
R
Y
-
-
1
-
-
7
-
4
-
4

 

 

7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
13
5
18
3
21
18
25
+
=
103
1+0+3
=
4
=
4
=
4
-
4
5
9
3
3
9
7
+
=
40
4+0
=
4
=
4
=
4
7
M
E
R
C
U
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
7
M
E
R
C
U
R
Y
-
-
28
-
-
7
-
40
-
31
-
-
-
9
-
-
9
-
-
-
2+8
-
-
-
-
4+0
-
3+1
7
M
E
R
C
U
R
Y
-
-
10
-
-
7
-
4
-
4
-
4
5
9
3
3
9
7
-
-
1+0
-
-
-
-
-
-
-
7
M
E
R
C
U
R
Y
-
-
1
-
-
7
-
4
-
4

 

 

-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
+
=
6
-
=
6
=
6
=
6
-
-
-
-
14
-
19
+
=
33
3+3
=
6
=
6
=
6
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
4
5
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
22
5
-
21
-
+
=
48
4+8
=
12
1+2
3
=
3
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
22
5
14
21
19
+
=
81
8+1
=
9
=
9
=
9
-
-
4
5
5
3
1
+
=
18
1+8
=
9
=
9
=
9
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
5
-
-
-
-
5
occurs
x
3
=
15
=
6
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
32
5
V
E
N
U
S
-
-
18
-
-
5
-
18
-
9
3+2
-
-
-
-
-
-
-
-
1+8
-
-
-
-
1+8
-
-
5
5
V
E
N
U
S
-
-
9
-
-
5
-
9
-
9
-
-
4
5
5
3
1
-
-
-
-
-
-
-
-
-
-
5
5
V
E
N
U
S
-
-
9
-
-
5
-
9
-
9

 

 

-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
+
=
6
-
=
6
-
6
=
6
-
-
-
-
14
-
19
+
=
33
3+3
=
6
=
6
=
6
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
4
5
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
22
5
-
21
-
+
=
48
4+8
=
12
1+2
3
=
3
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
22
5
14
21
19
+
=
81
8+1
=
9
=
9
=
9
-
-
4
5
5
3
1
+
=
18
1+8
=
9
=
9
=
9
-
5
V
E
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
5
-
-
-
-
5
occurs
x
3
=
15
=
6
32
5
V
E
N
U
S
-
-
18
-
-
5
-
18
-
9
3+2
-
-
-
-
-
-
-
-
1+8
-
-
-
-
1+8
-
-
5
5
V
E
N
U
S
-
-
9
-
-
5
-
9
-
9
-
-
4
5
5
3
1
-
-
-
-
-
-
-
-
-
-
5
5
V
E
N
U
S
-
-
9
-
-
5
-
9
-
9

 

 

-
6
S
A
T
U
R
N
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
5
+
=
6
-
=
6
-
6
-
-
19
-
-
-
-
14
+
=
33
3+3
=
6
=
6
-
6
S
A
T
U
R
N
-
-
-
-
-
--
-
-
-
-
-
1
2
3
9
-
+
=
15
1+5
=
6
=
6
-
-
-
1
20
21
18
-
+
=
60
6+0
=
6
=
6
-
6
S
A
T
U
R
N
-
-
-
-
-
--
-
-
-
`-
19
1
20
21
18
14
+
=
93
9+3
=
12
1+2
3
-
-
1
1
2
3
9
5
+
=
21
2+1
=
3
=
3
-
6
S
A
T
U
R
N
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
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
occurs
x
1
=
9
25
6
S
A
T
U
R
N
-
-
20
-
-
6
-
21
2+5
-
-
-
-
-
9
-
-
-
2+0
-
-
-
-
2+1
7
6
S
A
T
U
R
N
-
-
2
-
-
6
-
3
-
-
1
1
2
3
9
5
-
-
-
-
-
-
-
-
7
6
S
A
T
U
R
N
-
-
2
-
-
6
-
3

 

NATURES SATURN SATURN NATURES

 

6
S
A
T
U
R
N
-
-
-
-
-
-
-
-
-
1
-
-
-
-
5
+
=
6
-
=
6
-
6
-
19
-
-
-
-
14
+
=
33
3+3
=
6
=
6
6
S
A
T
U
R
N
-
-
-
-
-
-
-
-
-
-
1
2
3
9
-
+
=
15
1+5
=
6
=
6
-
-
1
20
21
18
-
+
=
60
6+0
=
6
=
6
6
S
A
T
U
R
N
-
-
-
-
-
-
-
-
-
19
1
20
21
18
14
+
=
93
9+3
=
12
1+2
3
-
1
1
2
3
9
5
+
=
21
2+1
=
3
=
3
6
S
A
T
U
R
N
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
6
S
A
T
U
R
N
-
-
20
-
-
6
-
21
-
-
-
-
-
9
-
-
-
2+0
-
-
-
-
2+1
6
S
A
T
U
R
N
-
-
2
-
-
6
-
3
-
1
1
2
3
9
5
-
-
-
-
-
-
-
-
6
S
A
T
U
R
N
-
-
2
-
-
6
-
3

 

 

-
6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
+
=
6
-
=
6
=
6
-
-
-
-
-
14
-
19
+
=
33
3+3
=
6
=
6
-
6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
-
3
9
1
-
3
-
+
=
16
1+6
=
7
=
7
-
-
21
18
1
-
21
-
+
=
61
6+1
=
7
=
7
-
6
U
R
A
N
U
S
-
-
-
-
-
--
-
-
-
`-
21
18
1
14
21
19
+
=
94
9+4
=
13
1+3
4
-
-
3
9
1
5
3
1
+
=
22
2+2
=
4
=
4
-
6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
1
-
-
1
occurs
x
2
=
2
2
-
-
4
-
-
-
4
-
-
2
TWO
2
-
-
-
-
-
3
4
-
-
3
4
-
-
3
occurs
x
2
=
6
4
-
-
4
-
-
-
4
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
6
-
-
4
-
-
-
4
-
-
6
SIX
6
-
-
-
7
-
-
4
-
-
-
4
-
-
7
SEVEN
7
-
-
-
8
-
-
4
-
-
-
4
-
-
8
EIGHT
8
-
-
-
-
-
9
9
-
-
9
-
-
-
9
occurs
x
1
=
9
27
6
U
R
A
N
U
S
-
-
18
-
-
6
-
22
2+7
-
9
9
-
-
9
-
-
-
1+8
-
-
-
-
2+2
9
6
U
R
A
N
U
S
-
-
9
-
-
6
-
4
-
-
3
9
1
5
3
1
+
=
22
2+2
=
4
=
4
9
6
U
R
A
N
U
S
-
-
9
-
-
6
-
4

 

UR A SUN URANUS A SUN RU

 

6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
+
=
6
-
=
6
=
6
-
-
-
-
14
-
19
+
=
33
3+3
=
6
=
6
6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
3
9
1
-
3
-
+
=
16
1+6
=
7
=
7
-
21
18
1
-
21
-
+
=
61
6+1
=
7
=
7
6
U
R
A
N
U
S
-
-
-
-
-
--
-
-
`-
21
18
1
14
21
19
+
=
94
9+4
=
13
1+3
4
-
3
9
1
5
3
1
+
=
22
2+2
=
4
=
4
6
U
R
A
N
U
S
-
-
-
-
-
-
-
-
-
-
1
1
1
-
1
-
-
1
occurs
x
2
=
2
-
3
4
-
-
3
4
-
-
3
occurs
x
2
=
6
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
9
9
-
-
9
-
-
-
9
occurs
x
1
=
9
6
U
R
A
N
U
S
-
-
18
-
-
6
-
22
-
9
9
-
-
9
-
-
-
1+8
-
-
-
-
2+2
6
U
R
A
N
U
S
-
-
9
-
-
6
-
4
-
3
9
1
5
3
1
-
-
-
-
-
-
-
-
6
U
R
A
N
U
S
-
-
9
-
-
6
-
4

 

 

-
4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
-
4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
4
1
9
-
+
=
14
1+4
=
5
=
5
-
-
13
1
18
-
+
=
32
3+2
=
5
=
5
-
4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
13
1
18
19
+
=
51
5+1
=
6
=
6
-
-
4
1
9
1
+
=
15
1+5
=
6
=
6
-
4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
31
4
M
A
R
S
-
-
14
-
-
4
-
15
3+1
-
-
-
9
-
-
-
1+4
-
-
-
-
1+5
4
4
M
A
R
S
-
-
5
-
-
4
-
6
-
-
4
1
9
1
-
-
-
-
-
-
-
-
4
4
M
A
R
S
-
-
5
-
-
4
-
6

 

 

4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
4
M
A
R
S
-
-
-
-
-
-
-
-
-
4
1
9
-
+
=
14
1+4
=
5
=
5
-
13
1
18
-
+
=
32
3+2
=
5
=
5
4
M
A
R
S
-
-
-
-
-
-
-
-
-
13
1
18
19
+
=
51
5+1
=
6
=
6
-
4
1
9
1
+
=
15
1+5
=
6
=
6
4
M
A
R
S
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
occurs
x
2
=
2
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
9
-
-
-
9
occurs
x
1
=
9
4
M
A
R
S
-
-
14
-
-
4
-
15
-
-
-
9
-
-
-
1+4
-
-
-
-
1+5
4
M
A
R
S
-
-
5
-
-
4
-
6
-
4
1
9
1
-
-
-
-
-
-
-
-
4
M
A
R
S
-
-
5
-
-
4
-
6

 

 

-
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
7
3
3
2
-
+
=
15
1+5
=
6
=
6
-
-
16
12
21
20
-
+
=
69
6+9
=
15
1+5
6
-
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
16
12
21
20
15
+
=
84
8+4
=
12
1+2
3
-
-
7
3
3
2
6
+
=
21
2+1
=
3
=
3
-
5
P
L
U
T
O
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
-
3
3
-
-
-
-
3
occurs
x
2
=
9
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
27
5
P
L
U
T
O
-
-
18
-
-
5
-
21
2+7
-
-
-
-
-
-
-
-
2+1
-
-
-
-
2+1
9
5
P
L
U
T
O
-
-
3
-
-
5
-
3
-
-
7
3
3
2
6
-
-
-
-
-
-
-
-
9
5
P
L
U
T
O
-
-
3
-
-
5
-
3

 

 

5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
7
3
3
2
-
+
=
15
1+5
=
6
=
6
-
16
12
21
20
-
+
=
69
6+9
=
15
1+5
6
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
16
12
21
20
15
+
=
84
8+4
=
12
1+2
3
-
7
3
3
2
6
+
=
21
2+1
=
3
=
3
5
P
L
U
T
O
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
3
3
-
-
-
-
3
occurs
x
2
=
9
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
5
P
L
U
T
O
-
-
18
-
-
5
-
21
-
-
-
-
-
-
-
-
2+1
-
-
-
-
2+1
5
P
L
U
T
O
-
-
3
-
-
5
-
3
-
7
3
3
2
6
-
-
-
-
-
-
-
-
5
P
L
U
T
O
-
-
3
-
-
5
-
3

 

 

-
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
+
=
10
1+0
=
1
=
1
=
1
-
-
14
-
-
-
-
14
-
+
=
28
2+8
=
10
1+0
1
=
1
-
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
7
2
3
-
5
+
=
22
2+2
=
4
=
4
=
4
-
-
-
5
16
20
21
-
5
+
=
67
6+7
=
13
1+3
4
=
4
-
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
14
5
16
20
21
14
5
+
=
95
9+5
=
14
1+4
5
1+4
5
-
-
5
5
7
2
3
5
5
+
=
32
3+2
=
5
=
5
=
5
-
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
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
7
N
E
P
T
U
N
E
-
-
17
-
-
7
-
32
-
14
2+8
-
5
5
-
-
-
5
5
-
-
1+7
-
-
-
-
3+2
-
1+4
10
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5
1+0
-
5
5
7
2
3
5
5
-
-
-
-
-
-
-
-
-
-
1
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5

 

 

7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
+
=
10
1+0
=
1
=
1
=
1
-
14
-
-
-
-
14
-
+
=
28
2+8
=
10
1+0
1
=
1
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
7
2
3
-
5
+
=
22
2+2
=
4
=
4
=
4
-
-
5
16
20
21
-
5
+
=
67
6+7
=
13
1+3
4
=
4
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
14
5
16
20
21
14
5
+
=
95
9+5
=
14
1+4
5
1+4
5
-
5
5
7
2
3
5
5
+
=
32
3+2
=
5
=
5
=
5
7
N
E
P
T
U
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
5
5
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
7
N
E
P
T
U
N
E
-
-
17
-
-
7
-
32
-
14
-
5
5
-
-
-
5
5
-
-
1+7
-
-
-
-
3+2
-
1+4
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5
-
5
5
7
2
3
5
5
-
-
-
-
-
-
-
-
-
-
7
N
E
P
T
U
N
E
-
-
8
-
-
7
-
5
-
5

 

 

-
JUPITER RED
-
-
-
7
JUPITER
99
36
9
3
RED
27
18
9
10
RED JUPITER
126
54
18
1+0
-`
1+2+6
5+ 4
1+8
1
JUPITER RED
9
9
9

 

 

-
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
=
9
=
9
=
9
-
-
-
-
-
9
-
-
-
-
-
9
-
=
9
=
9
=
9
-
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
3
7
-
2
5
9
+
=
27
2+7
=
9
=
9
=
9
-
-
10
21
16
-
20
5
18
+
=
90
9+0
=
9
=
9
=
9
-
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
10
21
16
9
20
5
18
+
=
99
9+9
=
18
1+8
9
=
9
-
-
1
3
7
9
2
5
9
+
=
36
3+6
=
9
=
9
=
9
-
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
--
--
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
--
--
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
--
--
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
18
7
J
U
P
I
T
E
R
-
-
27
-
-
7
-
36
-
27
1+8
-
-
-
-
9
-
-
9
-
-
2+7
-
-
-
-
3+6
-
2+7
9
7
J
U
P
I
T
E
R
-
-
9
-
-
7
-
9
-
9
-
-
1
3
7
9
2
5
9
-
-
-
-
-
-
-
-
-
-
9
7
J
U
P
I
T
E
R
-
-
9
-
-
7
-
9
-
9

 

JUPITER WHEN STOOD IN LINE WEIGHS IN AT NINETY NINE

 

7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
=
9
=
9
=
9
-
-
-
-
9
-
-
-
-
-
9
-
=
9
=
9
=
9
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
1
3
7
-
2
5
9
+
=
27
2+7
=
9
=
9
=
9
-
10
21
16
-
20
5
18
+
=
90
9+0
=
9
=
9
=
9
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
10
21
16
9
20
5
18
+
=
99
9+9
=
18
1+8
9
=
9
-
1
3
7
9
2
5
9
+
=
36
3+6
=
9
=
9
=
9
7
J
U
P
I
T
E
R
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
--
--
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
--
--
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
5
-
--
--
5
occurs
x
1
=
5
=
5
-
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
9
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
7
J
U
P
I
T
E
R
-
-
27
-
-
7
-
36
-
27
-
-
-
-
9
-
-
9
-
-
2+7
-
-
-
-
3+6
-
2+7
7
J
U
P
I
T
E
R
-
-
9
-
-
7
-
9
-
9
-
1
3
7
9
2
5
9
-
-
-
-
-
-
-
-
-
-
7
J
U
P
I
T
E
R
-
-
9
-
-
7
-
9
-
9

 

 

WORLD W LORD WORD L WORD LORD W WORLD

WASTE

NOT WANT NOT

 

 

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE CODING
33
15
15
-
-
-
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
34
-
-
THE CODING
52
34
34
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 


The Discovery of the Expanding Universe - SDSS SkyServer

https://skyserver.sdss.org › astro › universe › universe

The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers ...

The Expanding Universe

For thousands of years, astronomers wrestled with basic questions about the size and age of the universe. Does the universe go on forever, or does it have an edge somewhere? Has it always existed, or did it come to being some time in the past? In 1929, Edwin Hubble, an astronomer at Caltech, made a critical discovery that soon led to scientific answers for these questions: he discovered that the universe is expanding.

The ancient Greeks recognized that it was difficult to imagine what an infinite universe might look like. But they also wondered that if the universe were finite, and you stuck out your hand at the edge, where would your hand go? The Greeks' two problems with the universe represented a paradox - the universe had to be either finite or infinite, and both alternatives presented problems.

After the rise of modern astronomy, another paradox began to puzzle astronomers. In the early 1800s, German astronomer Heinrich Olbers argued that the universe must be finite. If the Universe were infinite and contained stars throughout, Olbers said, then if you looked in any particular direction, your line-of-sight would eventually fall on the surface of a star. Although the apparent size of a star in the sky becomes smaller as the distance to the star increases, the brightness of this smaller surface remains a constant. Therefore, if the Universe were infinite, the whole surface of the night sky should be as bright as a star. Obviously, there are dark areas in the sky, so the universe must be finite.

But, when Isaac Newton discovered the law of gravity, he realized that gravity is always attractive. Every object in the universe attracts every other object. If the universe truly were finite, the attractive forces of all the objects in the universe should have caused the entire universe to collapse on itself. This clearly had not happened, and so astronomers were presented with a paradox.

When Einstein developed his theory of gravity in the General Theory of Relativity, he thought he ran into the same problem that Newton did: his equations said that the universe should be either expanding or collapsing, yet he assumed that the universe was static. His original solution contained a constant term, called the cosmological constant, which cancelled the effects of gravity on very large scales, and led to a static universe. After Hubble discovered that the universe was expanding, Einstein called the cosmological constant his "greatest blunder."

At around the same time, larger telescopes were being built that were able to accurately measure the spectra, or the intensity of light as a function of wavelength, of faint objects. Using these new data, astronomers tried to understand the plethora of faint, nebulous objects they were observing. Between 1912 and 1922, astronomer Vesto Slipher at the Lowell Observatory in Arizona discovered that the spectra of light from many of these objects was systematically shifted to longer wavelengths, or redshifted. A short time later, other astronomers showed that these nebulous objects were distant galaxies.

The Discovery of the Expanding Universe

Meanwhile, other physicists and mathematicians working on Einstein's theory of gravity discovered the equations had some solutions that described an expanding universe. In these solutions, the light coming from distant objects would be redshifted as it traveled through the expanding universe. The redshift would increase with increasing distance to the object.

Edwin Hubble

In 1929 Edwin Hubble, working at the Carnegie Observatories in Pasadena, California, measured the redshifts of a number of distant galaxies. He also measured their relative distances by measuring the apparent brightness of a class of variable stars called Cepheids in each galaxy. When he plotted redshift against relative distance, he found that the redshift of distant galaxies increased as a linear function of their distance. The only explanation for this observation is that the universe was expanding.

Once scientists understood that the universe was expanding, they immediately realized that it would have been smaller in the past. At some point in the past, the entire universe would have been a single point. This point, later called the big bang, was the beginning of the universe as we understand it today.

The expanding universe is finite in both time and space. The reason that the universe did not collapse, as Newton's and Einstein's equations said it might, is that it had been expanding from the moment of its creation. The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers from ancient times until the early 20th Century.

The Heavy Elements

Astronomers are not only interested in the fate of the universe; they are also interested in understanding its present physical state. One question they try to answer is why the universe is primarily composed of hydrogen and helium, and what is responsible for the relatively small concentration of the heavier elements.

With the rise of nuclear physics in the 1930s and 40s, scientists started to try to explain the abundances of heavier elements by assuming they were synthesized out of primordial hydrogen in the early universe. In the late 1940s, American physicists George Gamow, Robert Herman, and Ralph Alpher realized that long ago, the universe was much hotter and denser. They made calculations to show whether nuclear reactions that took place at those higher temperatures could have created the heavy elements.

Unfortunately, with the exception of helium, they found that it was impossible to form heavier elements in any appreciable quantity. Today, we understand that heavy elements were synthesized either in the cores of stars or during supernovae, when a large dying star implodes.

Gamow, Herman, and Alpher did realize, though, that if the universe were hotter and denser in the past, radiation should still be left over from the early universe. This radiation would have a well-defined spectrum (called a blackbody spectrum) that depends on its temperature. As the universe expanded, the spectrum of this light would have been redshifted to longer wavelengths, and the temperature associated with the spectrum would have decreased by a factor of over one thousand as the universe cooled.

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
T
=
2
-
3
THE
33
15
6
E
=
5
-
9
EXPANDING
94
49
4
U
=
3
-
8
UNIVERSE
113
41
5
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
-
1+0
-
2+0
-
2+4+0
1+0+5
1+5
-
-
1
-
2
THE EXPANDING UNIVERSE
6
6
6

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE EXPANDING UNIVERSE
33
15
15
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
49
4
-
THE EXPANDING UNIVERSE
94
49
49
-
-
-
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
20
THE EXPANDING UNIVERSE
113
15
15
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

 
 
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