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Evokation
  
 
Index
  

 

 

 

NUCLEAR FAMILY 19769

 

 

 

 

 

 

 

THE

MAGICALALPHABET

 

..................

 

 

-
-
-
-
-
THE RAINBOW LIGHT
-
-
-
T
=
2
-
3
THE
33
15
6
R
=
9
-
7
RAINBOW
82
37
1
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
THE RAINBOW LIGHT
171
81
9
-
-
1+4
-
1+5
-
1+7+1
8+1
-
Q
-
5
-
6
THE RAINBOW LIGHT
9
9
9

 

 

 

 

 

 

 

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 DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Midway this way of life we're bound upon

I woke to find myself in a dark wood,

Where the right road was wholly lost and gone."

 

 

M
=
4
-
6
MIDWAY
75
30
3
T
=
2
-
4
THIS
56
20
2
W
=
5
-
3
WAY
49
13
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
4
LIFE
32
23
5
W
=
5
-
4
WE'RE
51
24
6
B
=
2
-
5
BOUND
56
20
2
U
=
3
-
4
UPON
66
21
3
-
-
30
-
32
-
406
163
28
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
W
=
5
-
4
WOKE
54
18
9
T
=
2
-
2
TO
35
8
8
F
=
6
-
4
FIND
33
24
6
M
=
4
-
6
MYSELF
80
26
8
I
=
9
-
2
IN
23
14
5
A
=
1
-
1
A
1
1
1
D
=
4
-
4
DARK
34
16
7
W
=
5
-
4
WOOD
57
21
3
-
-
45
-
28
-
326
137
56
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WHERE
59
32
5
T
=
2
-
3
THE
33
15
6
R
=
9
-
5
RIGHT
62
35
8
R
=
9
-
4
ROAD
38
20
2
W
=
5
-
3
WAS
43
7
7
W
=
5
-
6
WHOLLY
95
32
5
L
=
3
-
4
LOST
66
12
3
A
=
1
-
3
AND
19
10
1
G
=
7
-
4
GONE
41
23
5
-
-
46
-
37
-
456
186
42
-
-
-
-
-
-
-
-
-
-
-
121
-
97
First Total
1188
486
126
-
-
1+2+1
-
9+7
Add to Reduce
1+1+8+8
4+8+6
1+2+6
Q
-
4
-
16
Second Total
18
18
9
-
-
-
-
1+6
Reduce to Deduce
1+8
1+8
-
-
-
4
-
7
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Power failed high fantasy here; yet, swift to move

Even as a wheel moves equal, free from jars,

Already my heart and will were wheeled by love,

The Love that moves the sun and other stars."

 

P
=
7
-
5
POWER
77
32
5
F
=
6
-
6
FAILED
37
28
1
H
=
8
-
4
HIGH
32
32
5
F
=
6
-
7
FANTASY
86
23
5
H
=
8
-
4
HERE
36
27
9
Y
=
7
-
3
YET
50
14
5
S
=
1
-
5
SWIFT
77
23
5
T
=
2
-
2
TO
35
8
8
M
=
4
-
4
MOVE
55
19
1
-
-
49
-
40
First Total
485
206
44
-
-
4+9
-
4+0
Add to Reduce
4+8+5
2+0+6
4+4
Q
-
13
-
4
Second Total
17
8
8
-
-
1+3
-
-
Reduce to Deduce
1+7
-
-
-
-
4
-
4
Essence of Number
8
8
8

 

 

E
=
5
-
4
EVEN
46
19
1
A
=
1
-
2
AS
20
2
2
A
=
1
-
1
A
1
1
1
W
=
5
-
5
WHEEL
53
26
8
M
=
4
-
5
MOVES
74
20
2
E
=
5
-
5
EQUAL
56
20
2
F
=
6
-
4
FREE
34
25
7
F
=
6
-
4
FROM
52
25
7
J
=
1
-
4
JARS
48
12
3
-
-
34
-
34
First Total
384
150
33
-
-
3+4
-
3+4
Add to Reduce
3+8+4
1+5+0
3+3
Q
-
7
-
7
Second Total
15
6
6
-
-
-
-
-
Reduce to Deduce
1+5
-
-
-
-
7
-
7
Essence of Number
6
6
6

 

 

A
=
1
-
7
ALREADY
66
30
3
M
=
4
-
2
MY
38
11
2
H
=
8
-
5
HEART
52
25
7
A
=
1
-
3
AND
19
10
1
W
=
5
-
4
WILL
56
20
2
W
=
5
-
4
WERE
51
24
7
W
=
5
-
7
WHEELED
62
35
8
B
=
2
-
2
BY
27
9
9
L
=
3
-
4
LOVE
54
18
9
-
-
34
-
38
First Total
425
182
47
-
-
3+4
-
3+8
Add to Reduce
4+2+5
1+8+2
4+7
Q
-
7
-
11
Second Total
11
11
11
-
-
-
-
1+1
Reduce to Deduce
1+1
1+1
1+1
-
-
7
-
2
Essence of Number
2
2
2

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LOVE
54
18
9
T
=
2
-
4
THAT
49
13
4
M
=
4
-
5
MOVES
74
20
2
T
=
2
-
3
THE
33
15
6
S
=
1
-
3
SUN
54
9
9
A
=
1
-
3
AND
19
10
1
O
=
6
-
5
OTHER
66
30
3
S
=
1
-
5
STARS
77
14
5
-
-
22
-
35
First Total
459
144
45
-
-
2+2
-
3+5
Add to Reduce
4+5+9
1+4+4
4+5
Q
-
4
-
8
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
HOLY
60
24
6
7
MESSAGE
-
-
-
2
M+E
18
9
9
1
S
19
10
1
3
S+A+G
27
18
9
1
E
5
5
5
7
MESSAGE
69
42
24
14
Add
162
81
36
1+4
Reduce
1+6+2
8+1
3+6
5
Deduce
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 NUMBER WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLIED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
14
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

ADVENT 2213 ADVENT

 

-
-
-
-
15
THE SWORD OF WORDS
-
-
-
T
=
2
-
3
THE
33
15
6
S
=
1
-
5
SWORD
79
25
7
O
=
6
-
2
OF
21
12
3
W
=
5
-
5
WORDS
79
25
7
-
-
14
-
15
THE SWORD OF WORDS
212
77
23
-
-
1+4
-
1+5
-
2+1+2
7+7
2+3
-
-
5
-
6
THE SWORD OF WORDS
5
14
5
-
-
-
-
-
-
-
1+4
-
-
-
5
-
6
THE SWORD OF WORDS
5
5
5

 

 

ADVENT 2213 ADVENT

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
2
7
MESSAGE
69
24
6
-
-
-
-
-
-
6
-
-
-
O
=
6
3
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
C
=
3
4
8
CREATION
85
40
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
C
=
3
6
5
CLEAR
39
21
3
-
-
-
3
-
-
-
-
-
-
E
=
5
7
4
EACH
17
17
8
-
-
-
-
-
-
-
-
8
-
L
=
3
8
6
LETTER
80
26
8
-
-
-
-
-
-
-
-
8
-
O
=
6
9
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
T
=
2
10
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
A
=
1
11
8
ALPHABET
65
29
2
-
-
2
-
-
-
-
-
-
-
I
=
9
12
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
G
=
7
13
5
GIVEN
57
30
3
-
-
-
3
-
-
-
-
-
-
A
=
1
14
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
15
9
NUMERICAL
96
42
6
-
-
-
-
-
-
6
-
-
-
V
=
4
16
5
VALUE
62
17
8
-
-
-
-
-
-
-
-
8
-
B
=
2
17
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
18
9
COMBINING
86
50
5
-
-
-
-
-
5
-
-
-
-
T
=
2
19
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
L
=
3
20
7
LETTERS
99
27
9
-
-
-
-
-
-
-
-
-
9
W
=
5
21
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
T
=
2
22
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
S
=
1
23
6
SACRED
50
23
5
-
-
-
-
-
5
-
-
-
-
N
=
5
24
7
NUMBERS
92
29
2
-
-
2
-
-
-
-
-
-
-
-
-
93
-
230
-
1215
513
117
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
3
25
11
REARRANGING
112
67
4
-
-
-
-
4
-
-
-
-
-
T
=
2
26
4
THEM
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
27
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
E
=
5
28
7
ENDLESS
78
24
6
-
-
-
-
-
-
6
-
-
-
C
=
3
29
14
CONFIGURATIONS
171
72
9
-
-
-
-
-
-
-
-
-
9
T
=
2
30
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
31
6
MYSTIC
89
26
8
-
-
-
-
-
-
-
-
8
-
W
=
5
32
6
WEANED
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
33
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
34
4
MIND
40
22
4
-
-
-
-
4
-
-
-
-
-
A
=
2
35
4
AWAY
50
14
5
-
-
-
-
-
5
-
-
-
-
F
=
6
36
4
FROM
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
37
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
N
=
5
38
6
NORMAL
73
28
1
-
1
-
-
-
-
-
-
-
-
C
=
3
39
12
CONNOTATIONS
159
51
6
-
-
-
-
-
-
6
-
-
-
O
=
6
40
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
W
=
5
41
5
WORDS
79
25
7
-
-
-
-
-
-
-
7
-
-
-
-
75
-
96
-
1144
469
91
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
89
-
102
First Total
2359
982
208
-
5
4
15
12
20
72
21
32
27
-
-
8+9
-
1+0+2
Add to Reduce
2+3+5+9
9+8+2
2+0+8
-
-
-
1+5
1+2
2+0
7+2
2+1
3+2
2+7
-
-
17
-
3
Second Total
19
19
10
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+9
1+9
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Third Total
10
10
1
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
1
1
1
-
5
4
6
3
2
9
3
5
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
5
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
12
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
14
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
26
4
THEM
46
19
1
-
1
-
-
-
-
-
-
-
-
N
=
5
38
6
NORMAL
73
28
1
-
1
-
-
-
-
-
-
-
-
A
=
1
11
8
ALPHABET
65
29
2
-
-
2
-
-
-
-
-
-
-
N
=
5
24
7
NUMBERS
92
29
2
-
-
2
-
-
-
-
-
-
-
O
=
6
3
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
C
=
3
6
5
CLEAR
39
21
3
-
-
-
3
-
-
-
-
-
-
O
=
6
9
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
G
=
7
13
5
GIVEN
57
30
3
-
-
-
3
-
-
-
-
-
-
O
=
6
40
2
OF
21
12
3
-
-
-
3
-
-
-
-
-
-
C
=
3
4
8
CREATION
85
40
4
-
-
-
-
4
-
-
-
-
-
R
=
3
25
11
REARRANGING
112
67
4
-
-
-
-
4
-
-
-
-
-
M
=
4
34
4
MIND
40
22
4
-
-
-
-
4
-
-
-
-
-
C
=
3
18
9
COMBINING
86
50
5
-
-
-
-
-
5
-
-
-
-
S
=
1
23
6
SACRED
50
23
5
-
-
-
-
-
5
-
-
-
-
I
=
9
27
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
2
35
4
AWAY
50
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
1
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
M
=
4
2
7
MESSAGE
69
24
6
-
-
-
-
-
-
6
-
-
-
T
=
2
10
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
N
=
5
15
9
NUMERICAL
96
42
6
-
-
-
-
-
-
6
-
-
-
T
=
2
19
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
W
=
5
21
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
T
=
2
22
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
E
=
5
28
7
ENDLESS
78
24
6
-
-
-
-
-
-
6
-
-
-
T
=
2
30
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
T
=
2
33
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
T
=
2
37
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
C
=
3
39
12
CONNOTATIONS
159
51
6
-
-
-
-
-
-
6
-
-
-
W
=
5
32
6
WEANED
52
25
7
-
-
-
-
-
-
-
7
-
-
F
=
6
36
4
FROM
52
25
7
-
-
-
-
-
-
-
7
-
-
W
=
5
41
5
WORDS
79
25
7
-
-
-
-
-
-
-
7
-
-
E
=
5
7
4
EACH
17
17
8
-
-
-
-
-
-
-
-
8
-
L
=
3
8
6
LETTER
80
26
8
-
-
-
-
-
-
-
-
8
-
V
=
4
16
5
VALUE
62
17
8
-
-
-
-
-
-
-
-
8
-
M
=
4
31
6
MYSTIC
89
26
8
-
-
-
-
-
-
-
-
8
-
B
=
2
17
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
L
=
3
20
7
LETTERS
99
27
9
-
-
-
-
-
-
-
-
-
9
C
=
3
29
14
CONFIGURATIONS
171
72
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
89
-
102
First Total
2359
982
208
-
5
4
15
12
20
72
21
32
27
-
-
8+9
-
1+0+2
Add to Reduce
2+3+5+9
9+8+2
2+0+8
-
-
-
1+5
1+2
2+0
7+2
2+1
3+2
2+7
-
-
17
-
3
Second Total
19
19
10
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+9
1+9
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Third Total
10
10
1
-
5
4
6
3
2
9
3
5
9
-
-
1+7
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
1
1
1
-
5
4
6
3
2
9
3
5
9

 

 

TABLE, ATUM RA AR MUTA, AMUN RE ER NUMA
TABLE, ATUM RA
TABLE, MEMPHIS, ME, MPH, I, S
TABLE, PTAH, PT, AH
TABLE, PTAH, PATH
TABLE, THE, PATH, OF, PTAH
TABLE, ON, THE, PATH, OF, RA
TABLE, MIND + MATTER, THE, MELTING, POT, OF, CREATIVE, ENERGY
TABLE, MIND, MATTER, IMAGERS
TABLE, IMAGERS, CREATORS, OF, THE, MIND, MATTER, REALITY
TABLE, THE, HUMAN
TABLE, HUMANKIND, WOMAN, MAN
TABLE, RARE, RA, RE
TABLE, RARE, R, ARE
TABLE, ABA, LOTUS, BUD
TABLE, THE, QUENI
TABLE, CONSCIOUS, AWARENESS
TABLE, MET, ANKH
TABLE, ALIVE, LIVING
TABLE, DEAD, I, DIE
TABLE, RITES, OF, PASSAGE
TABLE, RITES, DE, PASSAGE
TABLE, RITE OF PASSAGE, RIGHT OF PASSAGE
TABLE, RIGHTS OF PASSAGE
TABLE, RIGHTS
TABLE, REPEAT, REPEATS, REPEATING
TABLE, HORIZON, ORISON, HORISIS
TABLE, THE, TWENTY FIRST, CENTURY
TABLE, THE, NUMBER, OF, LETTERS
TABLE, POLARIZED, OPPOSITES
TABLE, POLAR, POLE, POLARIZED, POLARIZATION, OF, OPPOSITES
TABLE, EYE, OF, HERU
TABLE, CICADA, BEETLE
TABLE, BRAHMA, VISHNU, VISHN, U
TABLE, VISHNUNABHI, VISHN, UNA, BH, I
TABLE, KING, OSORKON, THIRTEEN
TABLE, SED FESTIVAL, S, ED, FEST, I, VAL
TABLE, ELEUSIS, EL, EUS, I, S
TABLE, WORLD, UNDERWORLD, UPPERWORLD
TABLE, SPIRA, SPIRIT, SPIRITUS
TABLE, UNCERTAIN, UNCERTAINTY, PRINCIPLE
TABLE, OUJIA, BOARD
TABLE, NETJER
TABLE, OSIRIS, MANY EYED
TABLE, SAMHAIN, HALLOWEEN
TABLE, AUM MANI PADME HUM

 

 

I
9
9
9
ME
18
9
9
ME - EM
36
18
9
ENERGY- MASS
126
45
9
DIVINE - PUREST - LOVE
216
81
9
THOUGHT
99
36
9
REALITY
90
36
9
THE - HUMAN - RACE  
117
54
9
DOUBLE - HELIX
117
54
9
EGO
27
18
9
CONSCIENCE
90
45
9
SOTHIS
90
27
9
OSIRIS - RA
108
45
9
SOKAR - OSIRIS
153
54
9
EDFU
36
18
9
VENUS
81
18
9
HORUS
81
27
9
PHARAOH - PYRAMID

153
81
9
EHYEH - ASHER - EHYEH

153
90
9
KEBRA - NAGAST
99
36
9
ZARATHUSTRA
153
45
9
QUETZALCOATL
153
45
9
IPSISSIMUS
153
45
9
RELIGIONS 
108
54
9
FAITHS
63
27
9
ALBERT - EINSTEIN
153
63
9
PHYSICS
99
36
9
OXYGEN
90
36
9
SUN
54
9
9
SAGITTARIUS
144
45
9
THIRTEEN
99
45
9
CREATORS
99
36
9
GODS
45
18
9
FIFTYFOUR
126

54
9
EIGHTYONE
108

54
9
EIGHTEENTHIRTYSIX

225
99
9
NEUTRINOS

135

45

9
ZERO
64
28
1

 

 

A
T
U
M
-
R
A
-
A
R
-
M
U
T
A
1
20
21
13
-
18
1
-
1
18
-
13
21
20
1
1
2
3
4
-
9
1
-
1
9
-
4
3
2
1
A
T
U
M
-
R
A
-
A
R
-
M
U
T
A
1
-
-
-
-
-
1
-
1
-
-
-
-
-
1
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
A
T
U
M
-
R
A
-
A
R
-
M
U
T
A

 

 

A
M
U
N
-
R
A
-
A
R
-
N
U
M
A
1
13
21
14
-
18
1
-
1
18
-
14
21
13
1
1
4
3
5
-
9
1
-
1
9
-
5
3
4
1
A
M
U
N
-
R
A
-
A
R
-
N
U
M
A
1
-
-
-
-
-
1
-
1
-
-
-
-
-
1
-
-
3
-
-
-
-
-
-
-
-
-
3
2
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
A
T
U
M
-
R
A
-
A
R
-
M
U
T
A

 

 

6
A
T
U
M
-
R
A
-
-
-
-
-
--
-
-
`-
1
20
21
13
-
18
1
+
=
74
7+4
=
11
1+1
2
-
1
2
3
4
-
9
1
+
=
20
2+0
=
2
-
2
6
A
T
U
M
-
R
A
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
6
A
T
U
M
-
R
A
-
-
19
-
-
6
-
20
-
-
-
-
-
-
9
-
-
-
1+9
-
-
-
Q
2+0
6
A
T
U
M
-
R
A
-
-
10
-
-
6
-
2
-
-
-
-
-
-
9
-
-
-
1+0
-
-
-
Q
2+0
6
A
T
U
M
-
R
A
-
-
1
-
-
6
-
2

 

 

7
MEMPHIS
-
-
Q
-
M+E
18
9
9
-
M+P+H
37
19
1
-
I
9
9
9
-
S
19
10
1
7
MEMPHIS
83
47
20
-
-
8+3
4+7
2+0
7
MEMPHIS
11
11
2
-
-
1+1
1+1
-
7
MEMPHIS
2
2
2

 

 

4
PTAH
-
-
Q
-
P+T
36
9
9
-
A+H
9
9
9
4
PTAH
45
18
18
-
-
4+5
1+8
1+8
4
PTAH
9
9
9

 

 

4
PTAH
45
18
9
4
PATH
45
18
9

 

 

3
THE
33
15
6
4
PATH
45
18
9
2
OF
21
12
3
4
PTAH
45
18
9
13
Add to Reduce
144
63
27
1+3
Reduce to Deduce
1+4+4
6+3
2+7
4
Essence of Number
9
9
9

 

 

2
ON
29
11
2
3
THE
33
15
6
4
PATH
45
18
9
2
OF
21
12
3
2
RA
19
10
1
13
-
147
66
21
1+3
-
1+4+7
6+6
2+1
4
-
12
12
3
-
-
1+2
1+2
-
4
-
3
3
3

 

 

10
MIND + MATTER
-
-
-
3
THE
33
15
6
7
MELTING
80
35
8
3
POT
51
15
6
2
OF
21
12
3
8
CREATIVE
83
38
2
6
ENERGY
74
38
2
39
Add to Reduce
342
153
27
3+9
Reduce to Deduce
3+4+2
1+5+3
2+7
12
Essence of Number
9
9
9
1+2
Reduce to Deduce
-
-
-
3
Essence of Number
9
9
9

 

 

4
MIND
40
22
4
6
MATTER
77
23
5
7
IMAGERS
72
36
9
17
First Total
189
81
18
1+7
Add to Reduce
1+8+9
8+1
1+8
8
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
8
Essence of Number
9
9
9

 

 

7
IMAGERS
72
36
9
8
CREATORS
99
36
9
2
OF
21
12
3
3
THE
33
15
6
4
MIND
40
22
4
6
MATTER
77
23
5
7
REALITY
90
36
9
37
Add to Reduce
432
180
45
3+7
Reduce to Deduce
4+3+2
1+8+0
4+5
10
Essence of Number
9
9
9
1+0
Reduce to Deduce
-
-
-
1
Essence of Number
9
9
9

 

 

3
THE
33
15
6
5
HUMAN
57
21
3
8
-
90
36
9
-
-
9+0
3+6
-
8
-
9
9
9

 

 

9
HUMANKIND
95
41
5
5
WOMAN
66
21
3
3
MAN
28
10
1
17
-
189
72
9
1+7
-
1+8+9
7+2
-
8
-
18
9
9
-
-
1+8
-
-
8
-
9
9
9

 

 

3
MAN
28
10
1
5
WOMAN
66
21
3
9
HUMANKIND
95
41
5

 

 

3
MAN
28
10
1
9
HUMANKIND
95
41
5
5
WOMAN
66
21
3

 

 

4
RARE
-
-
-
-
R+A
19
10
1
-
R+E
23
14
5
4
RARE
-
-
-

 

 

4
RARE
-
-
-
-
R
18
9
9
-
A+R+E
24
15
6
4
RARE
-
-
-

 

 

3
ABA
4
4
4
5
LOTUS
87
15
6
3
BUD
27
9
9

 

 

3
THE
33
15
6
5
QUENI
66
30
3
8
-
99
45
9
-
-
9+9
4+5
-
8
-
18
9
9
-
-
1+8
-
-
8
-
9
9
9

 

 

9
CONSCIOUS
118
37
1
9
AWARENESS
105
33
6

 

 

3
MET
38
11
2
4
ANKH
34
16
7
7
-
72
27
9
-
-
7+2
2+7
-
7
-
9
9
9

 

 

5
ALIVE
49
22
4
6
LIVING
73
37
1

 

 

4
DEAD
-
-
-
-
I
9
9
9
-
DIE
18
9
9

 

 

5
RITES
71
26
8
2
OF
21
12
3
7
PASSAGE
68
23
5
14
Add to Reduce
160
61
16
1+4
Reduce to Deduce
1+6+0
6+1
1+6
5
Essence of Number
7
7
7

 

 

5
RITES
71
26
8
2
DE
9
9
9
7
PASSAGE
68
23
5
14
First Total
148
58
22
1+4
Add to Reduce
1+4+8
5+8
2+2
5
Second Total
13
13
4
-
Reduce to Deduce
1+3
1+3
-
5
Essence of Number
4
4
4

 

 

13
RITE OF PASSAGE
141
60
6
14
RIGHT OF PASSAGE
151
70
7

 

 

15
RIGHTS OF PASSAGE
170
71
8

 

 

6
RIGHTS
81
36
9

 

 

6
REPEAT
65
29
2
7
REPEATS
84
30
3
9
REPEATING
95
50
5

 

 

7
HORIZON
105
51
6
6
ORISON
90
36
9
7
HORISIS
97
43
7

 

 

3
THE
33
15
6
11
TWENTY FIRST
179
44
8
7
CENTURY
106
34
7
21
First Total
318
93
21
2+1
Add to Reduce
3+1+8
9+3
2+1
3
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
3
Essence of Number
3
3
3

 

 

3
THE
33
15
6
6
NUMBER
73
28
1
2
OF
21
12
3
7
LETTERS
99
27
9
18
-
226
82
19
1+8
-
2+2+6
8+2
1+9
9
-
10
10
10
-
-
1+0
1+0
1+0
9
-
1
1
1

 

 

9
POLARIZED
106
52
7
9
OPPOSITES
134
44
8

 

 

5
POLAR
62
26
8
4
POLE
48
21
3
9
POLARIZED
106
52
7
-
-
-
-
-
-
-
-
-
-
12
POLARIZATION
156
66
3
2
OF
21
12
3
9
OPPOSITES
134
44
8
23
Add to Reduce
311
122
14
2+3
Reduce to Deduce
3+1+1
1+2+2
1+4
5
Essence of Number
5
5
5

 

 

-
EYE OF HERU
-
-
-
3
EYE
35
17
8
2
OF
21
12
3
4
HERU
52
25
7
9
EYE OF HERU
108
54
18
-
-
1+0+8
5+4
1+8
9
EYE OF HERU
9
9
9

 

 

6
CICADA
21
12
3
6
BEETLE
49
22
4
12
-
70
43
7
1+2
-
7+0
4+3
-
3
-
7
7
7

 

 

6
BRAHMA
43
25
7
6
VISHNU
-
-
-
-
V+I+S+H+N
72
27
9
-
U
21
3
3
6
VISHNU
93
30
12
-
-
9+3
3+0
1+2
6
VISHNU
12
3
3
-
-
1+2
-
-
6
VISHNU
3
3
3

 

 

11
VISHNUNABHI
-
-
-
-
V+I+S+H+N
72
27
9
-
U+N+A
36
9
9
-
B+H
10
10
1
-
I
9
9
9
11
VISHNUNABHI
127
55
28
1+1
`-
1+2+7
5+5
2+8
2
VISHNUNABHI
10
10
10
-
-
1+0
1+0
1+0
2
VISHNUNABHI
1
1
1

 

 

4
KING
41
23
5
7
OSORKON
107
35
8
11
-
148
58
13
1+1
-
1+4+8
5+8
1+3
2
-
13
13
4
8
THIRTEEN
99
45
9

 

 

11
SED FESTIVAL
-
-
-
-
S
19
10
1
-
E+D
9
9
9
-
F+E+S+T
50
14
5
-
I
9
9
9
-
V+A+L
35
8
8
11
SED FESTIVAL
122
50
32
1+1
`-
1+2+2
5+0
3+2
2
SED FESTIVAL
5
5
5

 

 

7
ELEUSIS
-
-
-
-
E+L
17
8
8
-
E+U+S
45
18
9
-
I
9
9
9
-
S
19
10
1
7
ELEUSIS
90
45
36
-
`-
9+0
4+5
3+6
7
ELEUSIS
9
9
9

 

 

5
WORLD
72
27
9
10
UNDERWORLD
134
53
8
10
UPPERWORLD
148
58
4

 

 

5
SPIRA
63
36
9
6
SPIRIT
91
46
1
8
SPIRITUS
131
50
5

 

 

9
UNCERTAIN
105
42
6
-
-
-
-
-
-
-
-
-
-
11
UNCERTAINTY
150
51
6
9
PRINCIPLE
102
57
3
20
-
252
108
9
2+0
-
2+5+2
1+0+8
-
2
-
9
9
9

 

 

-
OUIJA BOARD
-
-
-
5
OUIJA
56
20
2
5
BOARD
40
22
4
10
OUIJA BOARD
96
42
6
1+0
-
9+6
4+2
-
1
OUIJA BOARD
15
6
6
-
-
1+5
-
-
1
OUIJA BOARD
6
6
6

 

 

6
NETJER
72
27
9

 

 

6
OSIRIS
89
35
8
8
MANY EYED
92
38
2
14
First Total
181
73
10
1+4
Add to Reduce
1+8+1
7+3
1+0
5
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
5
Essence of Number
1
1
1

 

 

7
SAMHAIN
65
29
2
9
HALLOWEEN
95
41
5
16
-
160
70
7
1+6
-
1+6+0
7+0
-
7
-
7
7
7

 

 

3
AUM
35
8
8
4
MANI
37
19
1
5
PADME
39
21
3
3
HUM
42
15
6
15
-
153
63
18
1+5
-
1+5+3
6+3
1+8
6
-
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
112
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
256
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
113
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
266
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
522
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
225
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
5
-
-
-
6
-
6
-
-
-
-
--
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
45
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
5
-
-
-
-
5
4+5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

Letter frequency -

"The most common letter in the English alphabet is E."

5 x 14 = 70 = 14 x 5

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ZERO
-
-
-
-
-
-
-
-
-
-
-
-
-
Z
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
28
-
4
ZERO
64
28
28
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ONE
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
16
-
3
ONE
34
16
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
TWO
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
13
-
3
TWO
58
13
13
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THREE
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
29
-
5
THREE
56
29
29
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FOUR
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
24
-
4
FOUR
60
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FIVE
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
FIVE
42
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SIX
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
-
-
16
-
3
SIX
52
25
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SEVEN
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
20
-
5
SEVEN
65
29
20
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
31
-
5
EIGHT
49
31
31
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NINE
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
NINE
42
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

Letter frequency -

"The most common letter in the English alphabet is E."

5 x 14 = 70 = 14 x 5

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
0
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
1
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
2
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
3
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
4
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
5
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
6
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
7
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
8
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
9
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
0
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
3
-
T
=
2
3
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
7
-
S
=
1
7
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
2
-
T
=
2
2
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
8
-
E
=
5
8
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
4
-
F
=
6
4
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
5
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
9
-
N
=
5
9
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
1
-
O
=
6
1
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
6
-
S
=
1
6
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
0
4
ZERO
64
28
1
-
1
-
3
-
5
-
-
8
9
3
-
T
=
2
3
5
THREE
56
29
2
-
-
2
3
-
5
-
-
8
9
7
-
S
=
1
7
5
SEVEN
65
20
2
-
-
2
3
-
5
-
-
8
9
2
-
T
=
2
2
3
TWO
58
13
4
-
-
-
3
4
5
-
-
8
9
8
-
E
=
5
8
5
EIGHT
49
31
4
-
-
-
3
4
5
-
-
8
9
4
-
F
=
6
4
4
FOUR
60
24
6
-
-
-
3
-
5
6
-
8
9
5
-
F
=
6
5
4
FIVE
42
24
6
-
-
-
3
-
5
6
-
8
9
9
-
N
=
5
9
4
NINE
42
24
6
-
-
-
3
-
5
6
-
8
9
1
-
O
=
6
1
3
ONE
34
16
7
-
-
-
3
-
5
-
7
8
9
6
-
S
=
1
6
3
SIX
52
16
7
-
-
-
3
-
5
-
7
8
9
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
4
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
0
4
ZERO
64
28
1
-
1
-
-
-
-
3
-
T
=
2
3
5
THREE
56
29
2
-
-
2
-
-
-
7
-
S
=
1
7
5
SEVEN
65
20
2
-
-
2
-
-
-
2
-
T
=
2
2
3
TWO
58
13
4
-
-
-
4
-
-
8
-
E
=
5
8
5
EIGHT
49
31
4
-
-
-
4
-
-
4
-
F
=
6
4
4
FOUR
60
24
6
-
-
-
-
6
-
5
-
F
=
6
5
4
FIVE
42
24
6
-
-
-
-
6
-
9
-
N
=
5
9
4
NINE
42
24
6
-
-
-
-
6
-
1
-
O
=
6
1
3
ONE
34
16
7
-
-
-
-
-
7
6
-
S
=
1
6
3
SIX
52
16
7
-
-
-
-
-
7
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
8
18
14
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
1+8
1+4
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
8
9
5

 

 

I = 9 9 = I
ME = 9 9 = ME
BRAIN + BODY = 9 9 = BODY + BRAIN
LIGHT + DARK = 9 9 = DARK + LIGHT
ENERGY + MASS = 9 9 = MASS +ENERGY
MIND + MATTER = 9 9 = MATTER + MIND
MAGNETIC + FIELD = 9 9 = FIELD + MAGNETIC
POSITIVE + NEGATIVE = 9 9 = NEGATIVE + POSITIVE
973 OM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZAOM 973

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
THIRTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
45
-
8
THIRTEEN
99
45
45
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FOURTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
11
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
41
-
8
FOURTEEN
104
41
41
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FIFTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
18
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
F
=
6
19
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
21
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
23
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
38
-
7
FIFTEEN
65
38
38
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SIXTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
24
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
25
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
26
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
27
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
28
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
30
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
33
-
7
SIXTEEN
96
42
33
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SEVENTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
32
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
33
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
34
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
35
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
36
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
37
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
38
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
39
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
37
-
9
SEVENTEEN
109
46
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EIGHTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
40
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
41
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
42
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
43
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
44
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
45
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
46
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
46
-
8
EIGHTEEN
73
46
46
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NINETEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
48
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
49
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
50
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
51
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
52
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
53
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
54
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
55
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
41
-
8
NINETEEN
86
41
41
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
281
-
55
First Total
632
299
281
-
2
16
3
4
140
30
7
16
63
-
-
2+8+1
-
5+5
Add to Reduce
6+3+2
2+9+9
2+8+1
-
-
1+6
-
-
1+4+0
3+0
-
1+6
1+2
-
-
11
-
10
Second Total
11
11
11
-
2
7
3
4
5
3
7
7
9
-
-
1+1
-
1+0
Reduce to Deduce
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
1
Essence of Number
2
2
2
-
2
7
3
4
5
3
7
7
9

 

THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN NINETEEN

 

-
-
-
-
-
-
-
-
-
-
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
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
11
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
18
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
F
=
6
19
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
21
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
23
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
24
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
25
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
26
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
27
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
28
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
30
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
32
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
33
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
34
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
35
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
36
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
37
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
38
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
39
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
40
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
41
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
42
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
43
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
44
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
45
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
46
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
48
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
49
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
50
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
51
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
52
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
53
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
54
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
55
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
281
-
55
First Total
632
299
281
-
2
16
3
4
140
30
7
16
63
-
-
2+8+1
-
5+5
Add to Reduce
6+3+2
2+9+9
2+8+1
-
-
1+6
-
-
1+4+0
3+0
-
1+6
1+2
-
-
11
-
10
Second Total
11
11
11
-
2
7
3
4
5
3
7
7
9
-
-
1+1
-
1+0
Reduce to Deduce
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
1
Essence of Number
2
2
2
-
2
7
3
4
5
3
7
7
9

 

THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN NINETEEN

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
24
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
27
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
36
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
44
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
52
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
11
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
33
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
15
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
21
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
22
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
23
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
28
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
30
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
32
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
34
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
35
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
37
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
38
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
39
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
40
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
45
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
46
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
48
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
50
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
51
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
53
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
54
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
55
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
9
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
17
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
19
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
26
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
42
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
43
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
18
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
25
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
41
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
49
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
281
-
55
First Total
632
299
281
-
2
16
3
4
140
30
7
16
63
-
-
2+8+1
-
5+5
Add to Reduce
6+3+2
2+9+9
2+8+1
-
-
1+6
-
-
1+4+0
3+0
-
1+6
1+2
-
-
11
-
10
Second Total
11
11
11
-
2
7
3
4
5
3
7
7
9
-
-
1+1
-
1+0
Reduce to Deduce
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
1
Essence of Number
2
2
2
-
2
7
3
4
5
3
7
7
9

 

THIRTEEN FOURTEEN FIFTEEN SIXTEEN SEVENTEEN EIGHTEEN NINETEEN

 

 

CIRCLE = 50 5+0 = 5 = 5+0 50 CIRCLE

1234 5 6789

ONE TWO THREE FOUR = 208 = 2+0+8 = 10 1+0 = 1
NINE EIGHT SEVEN SIX = 208 = 2+0+8 = 10 1+0 = 1

FIVE THE FULCRUM OF THE BALANCES

5FIVE5

THE SPIRIT LEVEL OF THE LEVEL SPIRIT

1234 5 6789

 

 

3
ONE
34
16
7
3
AND
19
10
1
4
ZERO
64
28
1
10
Add to Reduce
117
54
9
1+0
Reduce to Deduce
1+1+7
5+4
-
1
Essence of Number
9
9
9

 

 

Z
=
8
-
0
ZERO
-
-
-
-
-
-
2
-
Z+E
31
13
4
-
-
-
1
-
R
18
9
9
-
-
-
1
-
O
15
6
6
Z
=
8
4
4
ZERO
64
28
19
-
-
-
-
-
-
9+1
1+9
1+9
Z
=
8
4
-
ZERO
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
Z
=
8
4
-
ZERO
1
1
1

 

 

O
=
6
-
1
ONE
-
-
-
-
-
-
1
-
O
15
6
6
-
-
-
1
-
N
14
5
5
-
-
-
1
-
E
5
5
5
O
=
6
3
4
ONE
34
16
16
-
-
-
-
-
-
3+4
1+6
1+6
O
=
6
3
4
ONE
7
7
7

 

 

T
=
2
-
2
TWO
-
-
-
-
-
-
1
-
T
20
2
2
-
-
-
1
-
W
23
5
5
-
-
-
1
-
O
15
6
6
T
=
2
3
4
TWO
58
13
13
-
-
-
-
-
-
5+8
1+3
1+3
T
=
2
3
4
TWO
13
4
4
-
-
-
-
-
-
1+3
-
-
T
=
2
3
4
TWO
4
4
4

 

 

T
=
2
-
3
THREE
-
-
-
-
-
-
1
-
T
20
2
2
-
-
-
1
-
H
8
8
8
-
-
-
1
-
R
18
9
9
-
-
-
2
-
E+E
10
10
1
T
=
2
5
4
THREE
56
29
20
-
-
-
-
-
-
5+6
2+9
2+0
T
=
2
5
4
THREE
11
11
2
-
-
-
-
-
-
1+1
1+1
-
T
=
2
5
4
THREE
2
2
2

 

 

F
=
6
-
4
FOUR
-
-
-
-
-
-
1
-
F
6
6
6
-
-
-
2
-
O+U
36
9
9
-
-
-
1
-
R
18
9
9
F
=
6
4
4
FOUR
60
24
24
-
-
-
-
-
-
6+0
2+4
2+4
F
-
6
4
4
FOUR
6
6
6

 

 

-
-
-
-
5
FIVE
-
-
-
-
-
-
1
-
F
6
6
6
-
-
-
1
-
I
9
9
9
-
-
-
2
-
V+E
27
9
9
F
=
6
4
4
FIVE
42
24
24
-
-
-
-
-
-
4+2
2+4
2+4
F
=
6
4
4
FIVE
6
6
6

 

 

S
=
1
-
6
SIX
-
-
-
-
-
-
1
-
S
19
10
1
-
-
-
1
-
I
9
9
9
-
-
-
1
-
X
24
6
6
S
=
1
3
4
SIX
52
25
16
-
-
-
-
-
-
5+2
2+5
1+6
S
=
1
3
4
SIX
7
7
7

 

 

S
=
1
-
7
SEVEN
-
-
-
-
-
-
1
-
S
19
10
1
-
-
-
2
-
E+V
27
9
9
-
-
-
2
-
E+N
19
10
1
S
=
1
5
4
SEVEN
65
29
11
-
-
-
-
-
-
6+5
2+9
1+1
S
=
2
5
4
SEVEN
11
11
2
-
-
-
-
-
-
1+1
1+1
-
S
=
2
5
4
SEVEN
2
2
2

 

 

E
=
5
-
8
EIGHT
-
-
-
-
-
-
1
-
E
5
5
5
-
-
-
1
-
I
9
9
9
-
-
-
3
-
G+H+T
35
17
8
E
=
5
5
4
EIGHT
49
31
4
-
-
-
-
-
-
4+9
3+1
-
E
=
5
5
4
EIGHT
13
4
4
-
-
-
-
-
-
1+3
-
-
E
=
5
5
4
EIGHT
4
4
4

 

 

N
=
5
-
9
NINE
-
-
-
-
-
-
1
-
N
14
5
5
-
-
-
1
-
I
9
9
9
-
-
-
2
-
N+E
19
10
1
N
=
5
4
4
NINE
42
24
15
-
-
-
-
-
-
4+2
2+4
1+5
N
=
5
3
4
NINE
6
6
6

 

 

-
-
-
10
-
TEN
--
-
-
-
-
-
-
1
T
20
2
2
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
T
=
2
10
3
TEN
39
12
12
-
-
-
-
-
-
3+9
1+2
1+2
T
=
2
10
3
TEN
12
3
3
-
-
-
-
-
-
1+2
-
-
T
=
2
10
3
TEN
3
3
3

 

 

-
-
-
11
-
ELEVEN
--
-
-
-
-
-
-
3
E+L+E
22
13
4
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
N
14
5
5
E
=
5
11
6
ELEVEN
63
27
18
-
-
-
-
-
-
6+3
2+7
1+8
E
=
5
11
6
ELEVEN
9
9
9

 

 

-
-
-
12
-
TWELVE
--
-
-
-
-
-
-
4
T+W+E+L
60
15
6
-
-
-
-
2
V+E
27
9
9
T
=
2
12
6
TWELVE
87
24
15
-
-
-
-
-
-
8+7
2+4
1+5
T
=
2
12
6
TWELVE
15
6
6
6
-
-
-
-
-
1+5
-
-
T
=
2
12
6
TWELVE
6
6
6

 

 

-
-
-
13
-
THIRTEEN
--
-
-
-
-
-
-
2
T+H
28
10
1
-
-
-
-
1
I
9
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
4
T+E+E+N
44
17
8
T
=
2
13
8
THIRTEEN
99
45
27
-
-
-
-
-
-
9+9
4+5
2+7
T
=
2
13
8
THIRTEEN
18
9
9
6
-
-
-
-
-
1+8
-
-
T
=
2
13
8
THIRTEEN
9
9
9

 

 

-
-
-
14
-
FOURTEEN
--
-
-
-
-
-
-
1
F
6
6
6
-
-
-
-
2
O+U
36
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
4
T+E+E+N
44
17
8
F
=
6
14
8
FOURTEEN
104
41
32
-
-
-
-
-
-
1+0+4
4+1
3+2
F
=
6
14
8
FOURTEEN
5
5
5

 

 

-
-
-
15
-
FIFTEEN
--
-
-
-
-
-
-
1
F
6
6
6
-
-
-
-
1
I
9
9
9
-
-
-
-
5
F+T+E+E+N
50
23
5
F
=
6
15
7
FIFTEEN
65
38
20
-
-
-
-
-
-
6+5
3+8
2+0
F
=
6
15
7
FIFTEEN
11
11
2
6
-
-
-
-
-
1+1
1+1
-
F
=
6
15
7
FIFTEEN
2
2
2

 

 

-
-
-
16
7
SIXTEEN
--
-
-
-
-
-
-
1
S
19
10
1
-
-
-
-
1
I
9
9
9
-
-
-
-
4
X+T+E+E
54
18
9
-
-
-
-
1
N
14
5
5
S
=
1
16
7
SIXTEEN
96
42
24
-
-
-
-
-
-
9+6
4+2
2+4
S
=
1
16
7
SIXTEEN
15
6
6
6
-
-
-
-
-
1+5
-
-
S
=
1
16
7
SIXTEEN
6
6
6

 

 

-
-
-
17
-
SEVENTEEN
--
-
-
-
-
-
-
1
S
19
10
1
-
-
-
-
2
E+V
27
9
9
-
-
-
-
6
E+N+T+E+E+N
63
27
9
S
=
1
17
9
SEVENTEEN
109
46
19
-
-
-
-
-
-
1+0+9
4+6
1+9
S
=
1
17
9
SEVENTEEN
10
10
10
6
-
-
-
-
-
1+0
1+0
1+0
S
=
1
17
9
SEVENTEEN
1
1
1

 

 

-
-
-
18
8
EIGHTEEN
--
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
I
9
9
9
-
-
-
-
5
G+H+T+E+E
45
27
9
-
-
-
-
1
N
14
5
5
E
=
5
18
8
EIGHTEEN
73
46
28
-
-
-
-
-
-
7+3
4+6
2+8
E
=
5
18
8
EIGHTEEN
10
10
10
6
-
-
-
-
-
1+0
1+0
1+0
E
=
5
18
8
EIGHTEEN
1
1
1

 

 

-
NINETEEN
171
81
9
-
9
1
N
14
5
5
-
5
1
I
9
9
9
-
9
1
N
14
5
5
-
5
1
E
5
5
5
-
5
1
T
20
2
2
-
9
1
E
5
5
5
-
5
1
E
5
5
5
-
5
1
N
14
5
5
-
5
8
NINETEEN
86
41
41
-
30
-
-
8+6
4+1
4+1
-
3+0
8
NINETEEN
14
5
5
-
3
-
9
1+4
-
-
-
-
8
NINETEEN
5
5
5
-
3

 

 

N
5
-
8
NINETEEN
-
-
-
-
-
-
1
N
14
5
5
-
-
-
1
I
9
9
9
-
-
-
1
N
14
5
5
-
-
-
1
E
5
5
5
-
-
-
1
T
20
2
2
-
-
-
1
E
5
5
5
-
-
-
1
E
5
5
5
-
-
-
1
N
14
5
5
N
5
-
8
NINETEEN
86
41
41
-
-
-
-
-
8+6
4+1
4+1
N
5
-
8
NINETEEN
14
41
41
-
-
-
-
-
1+4
4+1
4+1
N
5
-
8
NINETEEN
5
5
5

 

 

-
TEEN
--
-
-
1
T
20
2
2
3
E+E+N
24
15
6
4
TEEN
44
17
8
-
-
4+4
1+7
-
4
TEEN
8
8
8

 

 

-
-
-
-
TEEN
--
-
-
-
-
-
1
T
20
2
2
-
-
-
1
E
5
5
5
-
-
-
1
E
5
5
5
-
-
-
1
N
14
5
5
T
=
2
4
TEEN
44
17
17
-
-
-
-
-
4+4
1+7
1+7
T
=
2
4
TEEN
8
8
8

 

 

-
-
-
-
-
-
-
ONE TWO SIX
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
6
-
S
=
1
-
3
SIX
52
16
7
9
-
-
-
9
-
9
ONE TWO SIX
144
45
18
-
-
-
-
-
-
-
-
1+4+4
4+5
1+8
9
-
-
-
9
-
9
ONE TWO SIX
9
9
9

 

 

THE INDEPENDENT MAGAZINE

Wednesday 11 September 2013

Mysteries of the snowflake: The curious world of the ice-crystal experts.

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

"The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,"

 

SORT OUT THE WHEAT FROM THE CHAFF

 

Why is the Letter E the Most Common Letter in the English ...
https://englishlanguagethoughts.com › 2018/04/08 › w...

8 Apr 2018 — The letter makes up 12.702% of the letters in an average text, and is the most commonly-used letter in English. The next most frequently-used ...This is a question I’ve been asking myself ruefully these last few days. The E on my keyboard hasn’t been very coöperative, insisting that I bang it at least a few times for it to make the letter E appear on the screen. This has made me really… appreciate, for wont of a better word, just how often we have to use the letter E.

The letter makes up 12.702% of the letters in an average text, and is the most commonly-used letter in English. The next most frequently-used letter is T, at 9.056%. I think the reason for the frequency of E is pretty simple. I mentioned recently that the schwa is the most common vowel sound in the English language, and of the five vowels, the letter E is the most logical candidate to represent that sound. Let’s look at that word I’ve been using all the time, letter, to see this in action.

The first E in letter is the standard strong vowel sound of the letter E, represented by the symbol /e/ in the phonemic alphabet. The second E is the schwa, represented by /???/. Other vowels can be used to represent the schwa, (e.g capital, pencil, memory, supply, beryl), but the sound of /e/ is similar to the sound of the schwa, and so it works pretty well at representing it.

The schwa is so common because it’s such a short, unstressed sound that’s very useful for joining consonants together. In addition to representing this sound and /e/, E is needed for a lot of othr jobs. It can represent other sounds like the long /?:/ of her, or even /?/ like at the start of English. It’s also worth considering here what John Milton once wrote: They also serve who only stand and wait. Try to think of how many words there are with a silent E. Centre, metre (sorry Americans, but the second E is silent), are, determine, etc. And then there are the words where the E isn’t pronounced, but determines the sound of a preceding vowel, like there, where, smile, knife, mate, and so on.

When you really think about how often we use E, it’s no wonder that it’s the most commonly-used letter in English (and in many other languages). It’s also no wonder that if your E gives up the ghost on your keyboard, you’ll be driven close to tears!

 

Letter Frequencies in the English Language
https://www3.nd.edu › handouts › cryptography › letter...

The letter E is over 56 times more common than Q in forming individual English words. The frequency of letters at the beginnings of words is different again. There ...


The frequency of the letters of the alphabet in English
The inventor of Morse code, Samuel Morse (1791-1872), needed to know this so that he could give the simplest codes to the most frequently used letters. He did it simply by counting the number of letters in sets of printers' type. The figures he came up with were:

12,000 E 2,500 F

9,000 T 2,000 W, Y

8,000 A, I, N, O, S 1,700 G, P

6,400 H 1,600 B

6,200 R 1,200 V

4,400 D 800 K

4,000 L 500 Q

3,400 U 400 J, X

3,000 C, M 200 Z

However, this gives the frequency of letters in English text, which is dominated by a relatively small number of common words . For word games, it is often the frequency of letters in English vocabulary, regardless of word frequency, which is of more interest. The following is a result of an analysis of the letters occurring in the words listed in the main entries of the Concise Oxford Dictionary (9th edition, 1995) and came up with the following table:

E 11.1607% 56.88 M 3.0129% 15.36

A 8.4966% 43.31 H 3.0034% 15.31

R 7.5809% 38.64 G 2.4705% 12.59

I 7.5448% 38.45 B 2.0720% 10.56

O 7.1635% 36.51 F 1.8121% 9.24

T 6.9509% 35.43 Y 1.7779% 9.06

N 6.6544% 33.92 W 1.2899% 6.57

S 5.7351% 29.23 K 1.1016% 5.61

L 5.4893% 27.98 V 1.0074% 5.13

C 4.5388% 23.13 X 0.2902% 1.48

U 3.6308% 18.51 Z 0.2722% 1.39

D 3.3844% 17.25 J 0.1965% 1.00

P 3.1671% 16.14 Q 0.1962% (1)

 


Can You Guess The Most Common Letters in English ...
https://www.rd.com › Humor

11 Jun 2018 — E is everywhere. In an analysis of all 240,000 entries in the Concise Oxford English Dictionary, OED editors found that the letter E appears in ...

This paragraph is abnormal. It contains an oddity, a linguistic quirk that you will find in no popular book or journal or script in any library. Want a hint? A crucial bit of vocabulary is missing (saying it all aloud might aid you, but probably not). Can you spot our anomaly? And if you do, can you say what it is without spoiling it?

The answer is as plain as the nose on your face, or the cream in your coffee, or the vowels in your alphabet. The above paragraph is missing the most common letter in the English language: the letter E.

E is everywhere. In an analysis of all 240,000 entries in the Concise Oxford English Dictionary, OED editors found that the letter E appears in approximately 11% of all words in the common English vocabulary, about 6,000 more words than the runner-up letter, A. What’s more: E is the most commonly struck letter on your keyboard, and the second most popular key after the space bar. It’s one third of the single most-used word in English—“the”—and appears in the most common English noun (“time”), the most common verb (“be”), in ubiquitous pronouns like he, she, me, and we, not to mention tens of thousands of words ending in -ed and -es.

There’s a reason, in other words, that scribes see composing prose without the letter E as one of the ultimate challenges in constrained writing. This hasn’t stopped masochistic wordsmiths from trying. Author Ernest Vincent Wright’s 1939 novel Gadsby, for example, contains some 50,000 words—none of them containing an E—while the 1969 French novel La Disparition has been translated into a dozen different languages, each edition omitting the most common letter in that language. The French and English versions successfully last 300 pages without the letter E; in Spanish, the letter A gets omitted, and in Russian, it’s O.

On the whole, most of the 5 full-time vowels (sorry, “sometimes Y”) appear more frequently in English than most consonants, with a few exceptions. Anyone who’s spent the evening watching Wheel of Fortune can tell you the most common consonants—at least, the ones Pat Sajak gives you for free during the final puzzle—are R, S, T L, and N (tellingly, he also throws in the letter E). Oxford’s analysis confirms that Pat is on the money. The top ten most common letters in the Concise Oxford English Dictionary, and the percentage of words they appear in, are:

1. E – 11.1607%

2. A – 8.4966%

3. R – 7.5809%

4. I – 7.5448%

5. O – 7.1635%

6. T – 6.9509%

7. N – 6.6544%

8. S – 5.7351%

9. L – 5.4893%

10. C – 4.5388%

You can spell a lot of words with those ten letters, including the most complicated word in the English language (hint: it only has three letters). But no letter is an island, and it takes the communal effort of our whole alphabet to make English as wonderful and weird as it is. Case in point: Hubert Wolfe, the man with 26 first names (one for every letter of the alphabet).

 

English ...https://english.stackexchange

As for the letter 'e', it often represents very easy to pronounce vowels, and orthographically it is also used in English orthography to "silently" affect another vowel (e.g. 'ate' vs. 'at'). Added up, it's a pretty useful little letter!
Why is letter E the most common used letter? -

 

Letter frequency - Wikipedia
https://en.wikipedia.org › wiki › Letter_frequency

Relative frequencies of letters in the English language — The first method, used in the chart ... of the most used English words on the Internet. ... In English, the space is slightly more frequent than the top letter (e) and the ...

 

Letter frequency

From Wikipedia, the free encyclopedia


Letter frequency is simply the number of times letters of the alphabet appear on average in written language. Letter frequency analysis dates back to the Arab mathematician Al-Kindi (c. 801–873 AD), who formally developed the method to break ciphers. Letter frequency analysis gained importance in Europe with the development of movable type in 1450 AD, where one must estimate the amount of type required for each letterform. Linguists use letter frequency analysis as a rudimentary technique for language identification, where it is particularly effective as an indication of whether an unknown writing system is alphabetic, syllabic, or ideographic.

The use of letter frequencies and frequency analysis plays a fundamental role in cryptograms and several word puzzle games, including Hangman, Scrabble and the television game show Wheel of Fortune. One of the earliest descriptions in classical literature of applying the knowledge of English letter frequency to solving a cryptogram is found in Edgar Allan Poe's famous story The Gold-Bug, where the method is successfully applied to decipher a message instructing on the whereabouts of a treasure hidden by Captain Kidd.[1]

Letter frequencies also have a strong effect on the design of some keyboard layouts. The most frequent letters are on the bottom row of the Blickensderfer typewriter, and the home row of the Dvorak keyboard layout.

 

The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Iraqi mathematician Al-Kindi (c. 801–873 AD), who formally developed the method (the ciphers breakable by this technique go back at least to the Caesar cipher invented by Julius Caesar, so this method could have been explored in classical times). Letter frequency analysis gained additional importance in Europe with the development of movable type in 1450 AD, where one must estimate the amount of type required for each letterform, as evidenced by the variations in letter compartment size in typographer's type cases.

No exact letter frequency distribution underlies a given language, since all writers write slightly differently. However, most languages have a characteristic distribution which is strongly apparent in longer texts. Even language changes as extreme as from old English to modern English (regarded as mutually unintelligible) show strong trends in related letter frequencies: over a small sample of Biblical passages, from most frequent to least frequent, enaid sorhm tgþlwu æcfy ðbpxz of old English compares to eotha sinrd luymw fgcbp kvjqxz of modern English, with the most extreme differences concerning letterforms not shared.[2]

Linotype machines for the English language assumed the letter order, from most to least common, to be etaoin shrdlu cmfwyp vbgkjq xz based on the experience and custom of manual compositors. The equivalent for the French language was elaoin sdrétu cmfhyp vbgwqj xz.

Arranging the alphabet in Morse into groups of letters that require equal amounts of time to transmit, and then sorting these groups in increasing order, yields e it san hurdm wgvlfbk opxcz jyq.[a] Letter frequency was used by other telegraph systems, such as the Murray Code.

Similar ideas are used in modern data-compression techniques such as Huffman coding.

Letter frequencies, like word frequencies, tend to vary, both by writer and by subject. One cannot write an essay about x-rays without using frequent Xs, and the essay will have an idiosyncratic letter frequency if the essay is about the use of x-rays to treat zebras in Qatar. Different authors have habits which can be reflected in their use of letters. Hemingway's writing style, for example, is visibly different from Faulkner's. Letter, bigram, trigram, word frequencies, word length, and sentence length can be calculated for specific authors, and used to prove or disprove authorship of texts, even for authors whose styles are not so divergent.

Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text. With the availability of modern computing and collections of large text corpora, such calculations are easily made. Examples can be drawn from a variety of sources (press reporting, religious texts, scientific texts and general fiction) and there are differences especially for general fiction with the position of 'h' and 'i', with 'h' becoming more common.

Herbert S. Zim, in his classic introductory cryptography text "Codes and Secret Writing", gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKJXZQ", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC".[3]

Also, to note that different dialects of a language will also affect a letter's frequency. For example, an author in the United States would produce something in which the letter 'z' is more common than an author in the United Kingdom writing on the same topic: words like "analyze", "apologize", and "recognize" contain the letter in American English, whereas the same words are spelled "analyse", "apologise", and "recognise" in British English. This would highly affect the frequency of the letter 'z' as it is a rarely used letter by British speakers in the English language.[4]

The "top twelve" letters constitute about 80% of the total usage. The "top eight" letters constitute about 65% of the total usage. Letter frequency as a function of rank can be fitted well by several rank functions, with the two-parameter Cocho/Beta rank function being the best.[5] Another rank function with no adjustable free parameter also fits the letter frequency distribution reasonably well[6] (the same function has been used to fit the amino acid frequency in protein sequences.[7]) A spy using the VIC cipher or some other cipher based on a straddling checkerboard typically uses a mnemonic such as "a sin to err" (dropping the second "r")[8][9] or "at one sir"[10] to remember the top eight characters.

Relative frequencies of letters in the English language?[edit]

The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters
There are three ways to count letter frequency that result in very different charts for common letters. The first method, used in the chart below, is to count letter frequency in root words of a dictionary. The second is to include all word variants when counting, such as "abstracts", "abstracted" and "abstracting" and not just the root word of "abstract". This system results in letters like 's' appearing much more frequently, such as when counting letters from lists of the most used English words on the Internet. A final variant is to count letters based on their frequency of use in actual texts, resulting in certain letter combinations like 'th' becoming more common due to the frequent use of common words like "the", "then", "both", etc. Absolute usage frequency measures like this are used when creating keyboard layouts or letter frequencies in old fashioned printing presses.

An analysis of entries in the Concise Oxford dictionary, ignoring frequency of word use, gives an order of "EARIOTNSLCUDPMHGBFYWKVXZJQ".[11]

The letter-frequency table below is taken from Pavel Micka's website, which cites Robert Lewand's Cryptological Mathematics.[12]

According to Lewand, arranged from most to least common in appearance, the letters are: etaoinshrdlcumwfgypbvkjxqz. Lewand's ordering differs slightly from others, such as Cornell University Math Explorer's Project, which produced a table after measuring 40,000 words.[13]

In English, the space is slightly more frequent than the top letter (e)[14] and the non-alphabetic characters (digits, punctuation, etc.) collectively occupy the fourth position (having already included the space) between t and a.[15]


The frequency of the first letters of words or names is helpful in pre-assigning space in physical files and indexes.[16] Given 26 filing cabinet drawers, rather than a 1:1 assignment of one drawer to one letter of the alphabet, it is often useful to use a more equal-frequency-letter code by assigning several low-frequency letters to the same drawer (often one drawer is labeled VWXYZ), and to split up the most-frequent initial letters ('S', 'A', and 'C') into several drawers (often 6 drawers Aa-An, Ao-Az, Ca-Cj, Ck-Cz, Sa-Si, Sj-Sz). The same system is used in some multi-volume works such as some encyclopedias. Cutter numbers, another mapping of names to a more equal-frequency code, are used in some libraries.

Both the overall letter distribution and the word-initial letter distribution approximately match the Zipf distribution and even more closely match the Yule distribution.[17]

Often the frequency distribution of the first digit in each datum is significantly different from the overall frequency of all the digits in a set of numeric data, see Benford's law for details.

An analysis by Peter Norvig on Google Books data determined, among other things, the frequency of first letters of English words.[18]

Relative frequencies of letters in other languages?[edit]

Text document with red question mark.svg

The figure below illustrates the frequency distributions of the 26 most common Latin letters across some languages. All of these languages use a similar 25+ character alphabet.

 

E - Wikipedia
https://en.wikipedia.org › wiki › E

Most common letter — 'E' is the most common (or highest-frequency) letter in the English language alphabet (starting off the typographer's phrase ...

E

E, or e, is the fifth letter and the second vowel letter in the modern English alphabet and the ISO basic Latin alphabet. Its name in English is e (pro
d /'i?/), plural ees.[1] It is the most commonly used letter in many languages, including Czech, Danish, Dutch, English, French, German, Hungarian, Latin, Latvian, Norwegian, Spanish, and Swedish.[2][3][4][5][6]

 

The Latin letter 'E' differs little from its source, the Greek letter epsilon, '?'. This in turn comes from the Semitic letter hê, which has been suggested to have started as a praying or calling human figure (hillul 'jubilation'), and was most likely based on a similar Egyptian hieroglyph that indicated a different pronunciation. In Semitic, the letter represented /h/ (and /e/ in foreign words); in Greek, hê became the letter epsilon, used to represent /e/. The various forms of the Old Italic script and the Latin alphabet followed this usage.

Use in writing systems

Pronunciation of the name of the letter ?e? in European languages
English

Although Middle English spelling used ?e? to represent long and short /e/, the Great Vowel Shift changed long /e?/ (as in 'me' or 'bee') to /i?/ while short /?/ (as in 'met' or 'bed') remained a mid vowel. In other cases, the letter is silent, generally at the end of words.

Other languages

In the orthography of many languages it represents either [e], [e?], [?], or some variation (such as a nasalized version) of these sounds, often with diacritics (as: ?e ê é è ë e e e ? e ? e ??) to indicate contrasts. Less commonly, as in French, German, or Saanich, ?e? represents a mid-central vowel /?/. Digraphs with ?e? are common to indicate either diphthongs or monophthongs, such as ?ea? or ?ee? for /i?/ or /e?/ in English, ?ei? for /a?/ in German, and ?eu? for /ø/ in French or /??/ in German.

Other systems

The International Phonetic Alphabet uses ?e? for the close-mid front unrounded vowel or the mid front unrounded vowel.

Most common letter

'E' is the most common (or highest-frequency) letter in the English language alphabet (starting off the typographer's phrase ETAOIN SHRDLU) and several other European languages, which has implications in both cryptography and data compression. In the story "The Gold-Bug" by Edgar Allan Poe, a character figures out a random character code by remembering that the most used letter in English is E. This makes it a hard and popular letter to use when writing lipograms. Ernest Vincent Wright's Gadsby (1939) is considered a "dreadful" novel, and supposedly "at least part of Wright's narrative issues were caused by language limitations imposed by the lack of E."[7] Both Georges Perec's novel A Void (La Disparition) (1969) and its English translation by Gilbert Adair omit 'e' and are considered better works.[8]

Related characters

Descendants and related characters in the Latin alphabet
E with diacritics: E e ? ? ? ? Ê ê ʯ ê¯ Ê? ê? ? ? ? ? ? ? ? ? ? ? ? ? ? ? E e ? ? E e E´ e´ E~ e~ ? ? Ë ë È è È? è? ? ? É é É? E e ? ? ? ? ? ? ? ? E e E´ e´ E~ e~ ? ? E? e? ?[9]
? : E with notch is used in the Swedish Dialect Alphabet[10]
Æ æ : Latin AE ligature
Œ œ : Latin OE ligature
The umlaut diacritic ¨ used above a vowel letter in German and other languages to indicate a fronted or front vowel (this sign originated as a superscript e)
Phonetic alphabet symbols related to E (the International Phonetic Alphabet only uses lowercase, but uppercase forms are used in some other writing systems): ? ? : Latin letter epsilon / open e, which represents an open-mid front unrounded vowel in the IPA
? : Epsilon / open e with retroflex hook[9]
? ? : Latin letter reversed epsilon / open e, which represents an open-mid central unrounded vowel in the IPA
? : Latin small letter reversed epsilon / open e with hook, which represents a rhotacized open-mid central vowel in the IPA
? : Reversed epsilon / open e with retroflex hook[9]
? : Modifier letter small reversed epsilon / open e[9]
? : Latin small letter closed reversed open e, which represents an open-mid central rounded vowel in IPA (shown as ? on the 1993 IPA chart)
? ? : Latin letter schwa, which represents a mid central vowel in the IPA
? ? : Latin letter turned e, which is used in the writing systems of some African languages
? : Latin letter reversed e, which represents a close-mid central unrounded vowel in the IPA

The Uralic Phonetic Alphabet uses various forms of e and epsilon / open e:[11] U+1D07 ? LATIN LETTER SMALL CAPITAL E
U+1D08 ? LATIN SMALL LETTER TURNED OPEN E
U+1D31 ? MODIFIER LETTER CAPITAL E
U+1D32 ? MODIFIER LETTER CAPITAL REVERSED E
U+1D49 ? MODIFIER LETTER SMALL E
U+1D4B ? MODIFIER LETTER SMALL OPEN E
U+1D4C ? MODIFIER LETTER SMALL TURNED OPEN E
U+2C7B ? LATIN LETTER SMALL CAPITAL TURNED E[12]

e : Subscript small e is used in Indo-European studies[13]
Teuthonista phonetic transcription system symbols related to E:[14] U+AB32 ? LATIN SMALL LETTER BLACKLETTER E
U+AB33 ? LATIN SMALL LETTER BARRED E
U+AB34 ? LATIN SMALL LETTER E WITH FLOURISH

Ancestors and siblings in other alphabets
?? : Semitic letter He (letter), from which the following symbols originally derive ? e : Greek letter Epsilon, from which the following symbols originally derive ? ? : Cyrillic letter Ye
? ? : Ukrainian Ye
? ? : Cyrillic letter E
? ? : Coptic letter Ei
?? : Old Italic E, which is the ancestor of modern Latin E ? : Runic letter Ehwaz, which is possibly a descendant of Old Italic E

?? : Gothic letter eyz

Derived signs, symbols and abbreviations
€ : Euro sign.
e : Estimated sign (used on prepackaged goods for sale within the European Union).
e : the symbol for the elementary charge (the electric charge carried by a single proton)
? : existential quantifier in predicate logic.
? : the symbol for set membership in set theory.
?? : the base of the natural logarithm.

 


Most Common Letters in the Alphabet Used in the English ...
https://listafterlist.com › Popular Questions

Most Common Letters in the Alphabet Used in the English Language · E – 57 · A – 43 · R – 39 · I – 38 · O – 37 · T – 35 · N – 34 · S – 29 ...

According to a study done by AskOxford, using thier Concise English Dictionary, these are the most common letters in the English language. The letter “E” is the most common, 57 times more common than the letter “Q.” (rounded percentages)
?E – 57
?A – 43
?R – 39
?I – 38
?O – 37
?T – 35
?N – 34
?S – 29
?L – 28
?C – 23
?U – 19
?D – 17
?P – 16
?M – 15+
?H – 15
?G – 13
?B – 11
?F – 9+
?Y – 9
?W – 7
?K – 6
?V – 5
?X – 1+
?Z – 1+
?J – 1+
?Q – 1

 

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

A B C D 5 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

 

 

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

A B C D 5 F G H I J K L M 5 O P Q R S T U V 5 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

 

 

THE INDEPENDENT MAGAZINE

Wednesday 11 September 2013

Mysteries of the snowflake: The curious world of the ice-crystal experts.

Inevitably, though, the most common question is, how can Libbrecht be so sure no two snowflakes are ever identical? He likes to tell people that physics has a Zen-like answer, “which is that it depends largely on what you mean by the question. The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf, then the number of ways of making a complex snowflake is so staggeringly large that, over the history of our planet, I’m confident no two identical flakes have ever fallen. The long answer is more involved – depending on what you mean by ‘alike’ and ‘snowflake’. There could be some extremely small, simple-shaped crystals that looked so alike under a microscope as to be indistinguishable – and if you sifted through enough Arctic snow, where these simple crystals are common, you could probably find a few twins.”

"The short answer is that if you consider there’s over a trillion ways you could arrange 15 different books on your bookshelf,"

 

-
-
-
-
-
THIRTEEN
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
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20
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-
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2
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H
=
8
2
1
H
8
8
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8
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I
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9
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-
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-
-
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9
R
=
9
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5
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45
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8
THIRTEEN
99
45
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9
-
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FOURTEEN
-
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F
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6
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6
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6
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6
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U
=
3
11
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9
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9
T
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41
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FOURTEEN
104
41
41
5
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FIFTEEN
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FIFTEEN
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=
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33
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SIXTEEN
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-
-
-
-
-
-
SEVENTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
32
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
33
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
34
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
35
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
36
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
37
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
38
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
39
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
37
-
9
SEVENTEEN
109
46
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EIGHTEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
40
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
41
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
42
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
43
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
44
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
45
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
46
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
47
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
46
-
8
EIGHTEEN
73
46
46
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NINETEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
48
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
49
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
50
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
51
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
52
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
53
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
54
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
55
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
41
-
8
NINETEEN
86
41
41
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
281
-
55
First Total
632
299
281
-
2
16
3
4
140
30
7
16
63
-
-
2+8+1
-
5+5
Add to Reduce
6+3+2
2+9+9
2+8+1
-
-
1+6
-
-
1+4+0
3+0
-
1+6
1+2
-
-
11
-
10
Second Total
11
11
11
-
2
7
3
4
5
3
7
7
9
-
-
1+1
-
1+0
Reduce to Deduce
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
1
Essence of Number
2
2
2
-
2
7
3
4
5
3
7
7
9

 

 

CODE BREAKER

 

C
=
3
-
4
CODE
27
18
9
B
=
2
-
7
BREAKER
60
33
6
-
-
5
-
11
First Total
87
51
15
-
-
-
-
1+1
Add to Reduce
8+7
5+1
1+5
Q
-
5
-
2
Second Total
15
6
6
-
-
-
-
1+1
Reduce to Deduce
1+5
-
-
Q
-
5
-
2
Essence of Number
6
9
6

 

 

-
-
-
-
-
CODE BREAKER
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
CODE
-
-
-
-
-
-
-
-
-
-
-
-
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
3
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
18
-
4
CODE
27
18
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
BREAKER
-
-
-
-
-
-
-
-
-
-
-
-
-
B
=
2
5
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
K
=
2
9
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
33
-
7
BREAKER
60
33
33
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
51
-
11
CODE BREAKER
87
51
15
-
1
4
3
4
15
6
7
8
18
-
-
5+1
-
1+1
-
8+7
5+1
1+5
-
-
-
-
-
1+5
-
-
-
1+8
Q
-
6
-
2
CODE BREAKER
15
6
6
-
1
4
3
4
6
6
7
8
9
-
-
-
-
1+1
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
1
CODE BREAKER-
6
6
6
-
1
4
3
4
6
6
7
8
9

 

 

-
-
-
-
-
CODE BREAKER
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
3
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
B
=
2
5
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
K
=
2
9
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
51
-
11
CODE BREAKER
87
51
15
-
1
4
3
4
15
6
7
8
18
-
-
5+1
-
1+1
-
8+7
5+1
1+5
-
-
-
-
-
1+5
-
-
-
1+8
Q
-
6
-
2
CODE BREAKER
15
6
6
-
1
4
3
4
6
6
7
8
9
-
-
-
-
1+1
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
1
CODE BREAKER-
6
6
6
-
1
4
3
4
6
6
7
8
9

 

LETTERS TRANPOSEED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
CODEBREAKER
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
7
8
-
B
=
2
5
1
B
2
2
2
-
-
2
-
-
-
-
7
8
-
K
=
2
9
1
K
11
2
2
-
-
2
-
-
-
-
7
8
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
7
8
-
D
=
4
3
1
D
4
4
4
-
-
-
-
4
-
-
7
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
7
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
7
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
7
8
9
-
-
51
-
11
CODEBREAKER
87
51
15
-
1
4
3
4
15
6
7
8
18
-
-
5+1
-
1+1
-
8+7
5+1
1+5
-
-
-
-
-
1+5
-
-
-
1+8
Q
-
6
-
2
CODEBREAKER
15
6
6
-
1
4
3
4
6
6
7
8
9
-
-
-
-
1+1
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
1
CODEBREAKER-
6
6
6
-
1
4
3
4
6
6
7
8
9

 

 

T
=
2
-
3
THE
33
15
6
A
=
1
-
6
ATOMIC
61
25
7
B
=
2
-
4
BOMB
32
14
5
Q
-
5
-
13
Add to Reduce
126
54
18
-
-
-
-
1+3
Reduce to Deduce
1+2+6
5+4
1+8
-
-
5
-
4
Essence of Number
9
9
9

 

B - OM - B

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
8
HYDROGEN
96
51
6
B
=
2
-
4
BOMB
32
14
5
Q
-
12
-
15
Add to Reduce
161
80
17
-
-
1+2
-
1+5
Reduce to Deduce
1+6+1
8+0
1+7
-
-
3
-
6
Essence of Number
8
8
8

 

 

T
=
2
-
3
THE
33
15
6
A
=
1
-
6
ATOMIC
61
25
7
B
=
2
-
4
BOMB
32
14
5
Q
-
5
-
13
Add to Reduce
126
54
18
-
-
-
-
1+3
Reduce to Deduce
1+2+6
5+4
1+8
-
-
5
-
4
Essence of Number
9
9
9

 

 

-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE
-
-
-
-
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
THE
33
15
15
-
-
-
-
-
-
-
-
-
-
-
-
-
ATOMIC
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
8
1
I
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
25
-
6
ATOMIC
61
25
25
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
13
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
-
14
-
4
BOMB
32
14
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
8
3
8
5
12
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
1+2
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
1
8
3
8
5
3
7
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
8
3
8
5
3
7
8
9
-
-
-
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
9
9
9
-
1
8
3
8
5
3
7
8
9

 

 

-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
I
=
9
8
1
I
18
9
9
-
-
-
-
-
-
-
7
-
9
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
B
=
2
13
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
8
3
8
5
12
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
1+2
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
1
8
3
8
5
3
7
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
8
3
8
5
3
7
8
9
-
-
-
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
9
9
9
-
1
8
3
8
5
3
7
8
9

 

LETTERS TRANPOSEED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
B
=
2
10
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
B
=
2
13
1
B
2
2
2
-
-
2
-
-
-
-
7
-
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
M
=
4
12
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
I
=
9
8
1
I
18
9
9
-
-
-
-
-
-
-
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE ATOMIC BOMB
-
-
-
-
1
8
3
8
5
12
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
1+2
-
-
-
A
=
1
-
6
ATOMIC
61
25
7
-
1
8
3
8
5
3
7
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
126
54
18
-
1
8
3
8
5
3
7
8
9
-
-
-
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
5
-
13
THE ATOMIC BOMB
9
9
9
-
1
8
3
8
5
3
7
8
9

 

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
8
HYDROGEN
96
51
6
B
=
2
-
4
BOMB
32
14
5
Q
-
12
-
15
Add to Reduce
161
80
17
-
-
1+2
-
1+5
Reduce to Deduce
1+6+1
8+0
1+7
-
-
3
-
6
Essence of Number
8
8
8

 

 

-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE
-
-
-
-
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
THE
33
15
15
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
D
=
4
6
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
8
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
51
-
6
HYDROGEN
96
51
51
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
15
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
-
14
-
4
BOMB
32
14
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
6
3
8
15
12
14
16
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+5
1+2
1+4
1+6
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
6
3
8
6
3
5
7
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
6
3
8
6
3
5
7
9
-
-
1+2
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
6
THE HYDROGEN BOMB
9
9
9
-
1
6
3
8
6
3
5
7
9

 

 

-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
3
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
H
=
8
4
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
Y
=
7
5
1
Y
25
7
7
-
1
-
3
-
-
-
7
-
-
D
=
4
6
1
D
4
4
4
-
1
-
3
4
-
-
-
-
-
R
=
9
7
1
R
18
9
9
-
1
-
3
-
-
-
-
-
9
O
=
6
8
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
3
-
-
-
7
-
-
E
=
5
10
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
1
-
3
-
5
-
-
-
-
B
=
2
12
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
O
=
6
13
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
M
=
4
14
1
M
13
4
4
-
1
-
3
4
-
-
-
-
-
B
=
2
15
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
6
3
8
15
12
14
16
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+5
1+2
1+4
1+6
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
6
3
8
6
3
5
7
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
6
3
8
6
3
5
7
9
-
-
1+2
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
6
THE HYDROGEN BOMB
9
9
9
-
1
6
3
8
6
3
5
7
9

 

 

-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
3
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
H
=
8
4
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
Y
=
7
5
1
Y
25
7
7
-
1
-
3
-
-
-
7
-
-
D
=
4
6
1
D
4
4
4
-
1
-
3
4
-
-
-
-
-
R
=
9
7
1
R
18
9
9
-
1
-
3
-
-
-
-
-
9
O
=
6
8
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
3
-
-
-
7
-
-
E
=
5
10
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
1
-
3
-
5
-
-
-
-
B
=
2
12
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
O
=
6
13
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
M
=
4
14
1
M
13
4
4
-
1
-
3
4
-
-
-
-
-
B
=
2
15
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
6
3
8
15
12
14
16
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+5
1+2
1+4
1+6
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
6
3
8
6
3
5
7
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
6
3
8
6
3
5
7
9
-
-
1+2
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
6
THE HYDROGEN BOMB
9
9
9
-
1
6
3
8
6
3
5
7
9

 

LETTERS TRANPOSEED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
1
2
3
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
B
=
2
15
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
3
4
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
1
-
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
1
-
3
-
5
-
-
-
-
O
=
6
8
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
Y
=
7
5
1
Y
25
7
7
-
1
-
3
-
-
-
7
-
-
G
=
7
9
1
G
7
7
7
-
1
-
3
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
R
=
9
7
1
R
18
9
9
-
1
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
1
6
3
8
15
12
14
16
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
1+5
1+2
1+4
1+6
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
6
3
8
6
3
5
7
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
1
6
3
8
6
3
5
7
9
-
-
1+2
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
6
THE HYDROGEN BOMB
9
9
9
-
1
6
3
8
6
3
5
7
9

 

 

-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
2
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
2
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
2
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
2
-
-
-
-
-
-
B
=
2
15
1
B
2
2
2
-
2
-
-
-
-
-
-
D
=
4
6
1
D
4
4
4
-
-
4
-
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
5
-
-
-
-
O
=
6
8
1
O
15
6
6
-
-
-
-
6
-
-
-
O
=
6
13
1
O
15
6
6
-
-
-
-
6
-
-
-
Y
=
7
5
1
Y
25
7
7
-
-
-
-
-
7
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THE HYDROGEN BOMB
-
-
-
-
6
8
15
12
14
16
9
T
=
2
-
3
THE
33
15
6
-
-
-
1+5
1+2
1+4
1+6
-
H
=
8
-
8
HYDROGEN
96
51
6
-
6
8
6
3
5
7
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
Q
-
12
-
15
THE HYDROGEN BOMB
161
80
17
-
6
8
6
3
5
7
9
-
-
1+2
-
1+5
-
1+2+6
5+4
-
-
-
-
-
-
-
-
-
Q
-
3
-
6
THE HYDROGEN BOMB
9
9
9
-
6
8
6
3
5
7
9

 

 

HYDROGEN BOMB

 

H
=
8
-
8
HYDROGEN
96
51
6
B
=
2
-
4
BOMB
32
14
5
Q
-
10
-
12
First Total
128
65
11
-
-
1+0
-
1+2
Add to Reduce
1+2+8
6+5
1+1
-
-
1
-
3
Second Total
11
11
2
-
-
-
-
-
Reduce to Deduce
1+1
1+1
-
-
-
1
-
3
Essence of Number
2
2
2

 

 

-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
10
-
12
HYDROGEN BOMB
128
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
1
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
D
=
4
3
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
51
-
6
HYDROGEN
96
51
51
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
-
14
-
4
BOMB
32
14
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
4
3
8
10
12
14
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
1+0
1+2
1+4
-
-
Q
-
12
-
12
HYDROGEN BOMB
128
65
11
-
1
4
3
8
1
3
5
8
9
-
-
1+2
-
1+2
-
1+2+8
6+5
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
11
11
2
-
1
4
3
8
1
3
5
8
9
-
-
1+2
Q
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
2
2
2
-
1
4
3
8
1
3
5
8
9

 

 

-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
10
-
12
HYDROGEN BOMB
128
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
1
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
Y
=
7
2
1
Y
25
7
7
-
1
-
3
-
-
-
7
-
-
D
=
4
3
1
D
4
4
4
-
1
-
3
4
-
-
-
-
-
R
=
9
4
1
R
18
9
9
-
1
-
3
-
-
-
-
-
9
O
=
6
5
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
1
-
3
-
-
-
7
-
-
E
=
5
7
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
1
-
3
-
5
-
-
-
-
B
=
2
9
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
M
=
4
11
1
M
13
4
4
-
1
-
3
4
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
4
3
8
10
12
14
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
1+0
1+2
1+4
-
-
Q
-
12
-
12
HYDROGEN BOMB
128
65
11
-
1
4
3
8
1
3
5
8
9
-
-
1+2
-
1+2
-
1+2+8
6+5
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
11
11
2
-
1
4
3
8
1
3
5
8
9
-
-
1+2
Q
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
2
2
2
-
1
4
3
8
1
3
5
8
9

 

LETTERS TRANPOSEED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
-
-
Q
-
10
-
12
HYDROGEN BOMB
128
65
11
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN
-
-
-
-
1
2
3
4
5
6
7
8
9
B
=
2
9
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
1
2
3
-
-
-
-
-
-
D
=
4
3
1
D
4
4
4
-
1
-
3
4
-
-
-
-
-
M
=
4
11
1
M
13
4
4
-
1
-
3
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
1
-
3
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
1
-
3
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
O
=
6
10
1
O
15
6
6
-
1
-
3
-
-
6
-
-
-
Y
=
7
2
1
Y
25
7
7
-
1
-
3
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
1
-
3
-
-
-
7
-
-
H
=
8
1
1
H
8
8
8
-
1
-
3
-
-
-
-
8
-
R
=
9
4
1
R
18
9
9
-
1
-
3
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
1
4
3
8
10
12
14
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
1+0
1+2
1+4
-
-
Q
-
12
-
12
HYDROGEN BOMB
128
65
11
-
1
4
3
8
1
3
5
8
9
-
-
1+2
-
1+2
-
1+2+8
6+5
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
11
11
2
-
1
4
3
8
1
3
5
8
9
-
-
1+2
Q
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
2
2
2
-
1
4
3
8
1
3
5
8
9

 

 

-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
2
4
5
6
7
8
9
H
=
8
-
8
HYDROGEN
96
51
6
-
-
-
-
-
-
-
-
B
=
2
-
4
BOMB
32
14
5
-
-
-
-
-
-
-
-
Q
-
10
-
12
HYDROGEN BOMB
128
65
11
-
2
4
5
6
7
8
9
-
-
-
-
1+5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN
-
-
-
-
2
4
5
6
7
8
9
B
=
2
9
1
B
2
2
2
-
2
-
-
-
-
-
-
B
=
2
12
1
B
2
2
2
-
2
-
-
-
-
-
-
D
=
4
3
1
D
4
4
4
-
-
4
-
-
-
-
-
M
=
4
11
1
M
13
4
4
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
6
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
7
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
1
1
H
8
8
8
-
-
-
-
-
-
8
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HYDROGEN BOMB
-
-
-
-
-
-
-
-
-
-
-
H
=
8
-
8
HYDROGEN
96
51
6
-
4
8
10
12
14
8
9
B
=
2
-
4
BOMB
32
14
5
-
-
-
1+0
1+2
1+4
-
-
Q
-
12
-
12
HYDROGEN BOMB
128
65
11
-
4
8
1
3
5
8
9
-
-
1+2
-
1+2
-
1+2+8
6+5
1+1
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
11
11
2
-
4
8
1
3
5
8
9
-
-
1+2
Q
-
-
1+1
1+1
-
-
-
-
-
-
-
-
-
Q
-
3
-
3
HYDROGEN BOMB
2
2
2
-
4
8
1
3
5
8
9

 

 

 

 

 
 
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