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Evokation
  
 
Index
  

 

 

 

 

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

 

 

-
MINDMATTER
-
-
-
4
MIND
40
22
4
6
MATTER
77
23
5
10
MINDMATTER
117
45
9

 

 

-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+1+7
=
9
=
9
=
9
-
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-`
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
--
--
--
--
--
--
--
--
--
--
--
--
6
SIX
6
-
-
-
-
-
7
-
-
--
--
--
--
--
--
--
--
--
--
--
--
7
SEVEN
7
-
-
-
-
-
8
-
-
--
--
--
--
--
--
--
--
--
--
--
--
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
24
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
2+4
1+0
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
6
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
-
--
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
--
-
-
-
-
6
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+1+7
=
9
=
9
=
9
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
4+5
=
9
=
9
=
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
-`
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
1+0
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
--
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
--
-
-
-
-
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
9
5
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
-
9
-
-
-
9
14
-
-
9
-
-
+
=
41
4+1
=
5
=
5
=
5
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
4
1
7
-
-
1
2
-
4
5
+
=
24
2+4
=
6
=
6
=
6
-
-
-
13
1
7
-
-
1
20
-
22
5
+
=
69
6+9
=
15
1+5
6
=
6
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
9
13
1
7
9
14
1
20
9
22
5
+
=
110
1+1+0
=
2
=
2
=
2
-
-
9
4
1
7
9
5
1
2
9
4
5
+
=
56
5+6
=
11
1+1
2
=
2
-
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
-
=
=
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
--
--
--
--
--
--
--
--
--
--
--
--
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
11
I
M
A
G
I
N
A
T
I
V
E
-
-
28
-
-
11
-
56
-
29
1+7
1+1
9
-
-
-
9
-
-
-
9
-
-
-
-
2+8
-
-
1+1
-
5+6
-
2+9
8
2
I
M
A
G
I
N
A
T
I
V
E
-
-
10
-
-
2
-
11
-
11
-
9
4
1
7
9
5
1
2
9
4
5
-
-
1+0
-
-
-
-
1+1
-
1+1
8
11
I
M
A
G
I
N
A
T
I
V
E
-
-
1
-
-
2
-
2
-
2

 

 

11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
-
9
5
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
9
-
-
-
9
14
-
-
9
-
-
+
=
41
4+1
=
5
=
5
=
5
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
4
1
7
-
-
1
2
-
4
5
+
=
24
2+4
=
6
=
6
=
6
-
-
13
1
7
-
-
1
20
-
22
5
+
=
69
6+9
=
15
1+5
6
=
6
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
--
-
-
-
-
-
9
13
1
7
9
14
1
20
9
22
5
+
=
110
1+1+0
=
2
=
2
=
2
-
9
4
1
7
9
5
1
2
9
4
5
+
=
56
5+6
=
11
1+1
2
=
2
11
I
M
A
G
I
N
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
=
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
9
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
I
M
A
G
I
N
A
T
I
V
E
-
-
28
-
-
11
-
56
-
29
1+1
9
-
-
-
9
-
-
-
9
-
-
-
-
2+8
-
-
1+1
-
5+6
-
2+9
2
I
M
A
G
I
N
A
T
I
V
E
-
-
10
-
-
2
-
11
-
11
-
9
4
1
7
9
5
1
2
9
4
5
-
-
1+0
-
-
-
-
1+1
-
1+1
11
I
M
A
G
I
N
A
T
I
V
E
-
-
1
-
-
2
-
2
-
2

 

 

-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

S
=
1
-
9
SPLITTING
126
45
9
T
=
2
-
3
THE
33
15
6
A
=
1
-
4
ATOM
49
13
4
B
-
4
4
16
First Total
208
73
19
-
-
-
-
1+6
Add to Reduce
2+0+8
7+3
1+9
-
-
7
-
7
Second Total
10
10
10
8
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
7
-
7
Essence of Number
1
1
1

 

 

-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
-
8
-
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
-
8
-
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
-
2
-
5
-
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
-
20
-
5
-
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
-
20
8
5
-
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

NUCLEAR UNCLEAR NUCLEAR

 

 

-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
8
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
8
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
2
-
5
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
20
-
5
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
20
8
5
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
-
1
20
-
13
+
=
34
3+4
=
7
=
7
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
-
1
2
6
4
+
=
13
1+3
=
4
=
4
-
4
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
A
T
O
M
-
-
13
-
-
4
-
13
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
4
A
T
O
M
-
-
4
-
-
4
-
4
-
-
1
2
6
4
-
-
-
-
-
-
-
-
5
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
15
-
+
=
15
1+5
=
6
=
6
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
1
20
-
13
+
=
34
3+4
=
7
=
7
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
1
2
6
4
+
=
13
1+3
=
4
=
4
4
A
T
O
M
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
6
occurs
x
1
=
6
4
A
T
O
M
-
-
13
-
-
4
-
13
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
4
A
T
O
M
-
-
4
-
-
4
-
4
-
1
2
6
4
-
-
-
-
-
-
-
-
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
-
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
5
A
T
O
M
S
-
-
13
-
-
5
-
14
3+2
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
5
A
T
O
M
S
-
-
13
-
-
5
-
14
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 

-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
--
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
19
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
1+9
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
10
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
1+0
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
1
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
A
T
O
M
-
-
8
-
-
4
-
1

 

 

3
THE
33
15
6
6
ATOMIC
61
25
7
5
MINDS
59
23
5
1
I
9
9
9
15
Add to Reduce
162
72
27
1+5
Reduce to Deduce
1+6+2
7+2
2+7
8
Essence of Number
9
9
9

 

 

-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
-
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
-
9
-
-
9
5
-
1
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
15
-
9
-
-
9
14
-
19
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
2
-
5
1
2
-
4
-
3
4
-
-
4
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
1
20
-
13
-
3
13
-
-
4
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
20
8
5
1
20
15
13
9
3
13
9
14
4
19
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
1
2
6
4
9
3
4
9
5
4
1
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
4
-
-
4
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
1
2
6
3
9
3
3
9
5
4
1
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
2
-
-
6
-
9
-
9

 

 

A
=
1
-
4
ATOM
49
13
4
C
=
3
-
4
CELL
32
14
5
S
-
4
4
8
Add to Reduce
81
27
9
-
-
-
-
-
Reduce to Deduce
8+1
2+7
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
--
--
--
--
-
-
-
--
--
7
SEVEN
7
-
-
-
-
-
8
-
--
--
--
--
--
--
-
-
-
--
--
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
--
--
9
NINE
9
-
-
-
-
-
24
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
2+4
-
-
-
-
-
-
3
-
3
3
-
-
2+1
-
-
-
-
2+7
-
2+7
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
--
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
-
-
-
-
2+7
-
2+7
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

-
4
C
E
L
L
-
-
-
-
-
-
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
-
-
-
-
-
-
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
T
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-2-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
37
4
C
E
L
L
-
-
8
-
-
4
-
14
3+7
-
3
-
3
3
-
-
-
-
-
-
-
1+4
10
4
C
E
L
L
-
-
8
-
-
4
-
5
1+0
-
3
5
3
3
-
-
-
-
-
-
-
-
1
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

4
C
E
L
L
-
-
-
-
-
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
-
-
-
-
-
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
T
-
-
-
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
5
occurs
x
1
=
5
4
C
E
L
L
-
-
8
-
-
4
-
14
-
3
-
3
3
-
-
-
-
-
-
-
1+4
4
C
E
L
L
-
-
8
-
-
4
-
5
-
3
5
3
3
-
-
-
-
-
-
-
-
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

-
5
C
E
L
L
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
-
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
-
5
C
E
L
L
S
-
-
-
-
-
-
-
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
-
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
-
5
C
E
L
L
S
-
-
-
-
-
-
-
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
-
5
C
E
L
L
S
T
-
-
-
-
-
-
-
--
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-2-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
36
5
C
E
L
L
S
-
-
9
-
-
5
-
15
3+6
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
-
3
5
3
3
1
-
-
-
-
-
-
-
-
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

5
C
E
L
L
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
5
C
E
L
L
S
-
-
-
-
-
-
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
5
C
E
L
L
S
-
-
-
-
-
-
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
5
C
E
L
L
S
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
5
C
E
L
L
S
-
-
9
-
-
5
-
15
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
3
5
3
3
1
-
-
-
-
-
-
-
-
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

-
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
-
-
-
-
15
-
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
-
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
4
1
7
-
5
2
-
3
+
=
49
4+9
=
13
1+3
4
=
4
-
-
5
12
5
3
20
18
-
13
1
7
-
5
20
-
3
+
=
112
1+1+2
=
4
=
4
=
4
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
15
13
1
7
14
5
20
9
3
+
=
150
1+5+0
=
6
=
6
=
6
-
-
5
3
5
3
2
9
6
4
1
7
5
5
2
9
3
+
=
69
6+9
=
15
1+5
6
=
6
-
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
-
-
-
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
8
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
37
-
-
15
-
69
-
42
-
-
--
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
3+7
-
-
1+5
-
6+9
-
4+2
8
15
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
10
-
-
6
-
15
-
6
-
1+5
5
3
5
3
2
9
6
4
1
7
5
5
2
9
3
-
-
1+0
-
-
-
-
1+5
-
-
8
6
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
-
1
-
-
6
-
6
-
6

 

 

15
ELECTROMAGNETIC
150
69
6
5
LIGHT
56
29
2
20
First Total
206
98
8
2+0
Add to Reduce
2+0+6
9+8
-
2
Second Total
8
17
8
-
Reduce to Deduce
-
1+7
-
2
Essence of Number
8
8
8

 

 

15
ELECTROMAGNETIC
150
69
6
6
LIGHTS
75
30
3
21
First Total
225
99
9
2+1
Add to Reduce
2+2+5
9+9
-
3
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
3
Essence of Number
9
9
9

 

 

15
ELECTROMAGNETIC
150
69
6
7
GRAVITY
102
39
3
22
Add to Reduce
252
108
9
2+2
Reduce to Deduce
2+5+2
1+0+8
-
4
Essence of Number
9
9
9

 

 

-
23
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
37
-
-
8
-
-
-
-
-
-
-
-
6
-
-
-
-
5
-
-
9
-
-
-
9
-
-
-
+
=
37
3+7
=
10
1+0
1
=
1
55
-
-
8
-
-
-
-
-
-
-
-
15
-
-
-
-
14
-
-
9
-
-
-
9
-
-
-
+
=
55
5+5
=
10
1+0
1
=
1
-
23
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
74
-
2
-
5
-
5
3
5
3
2
9
-
-
4
1
7
-
5
2
-
3
-
6
-
5
3
4
+
=
74
7+4
=
11
1+1
2
=
2
164
-
20
-
5
-
5
12
5
3
20
18
-
-
13
1
7
-
5
20
-
3
-
6
-
5
12
4
+
=
164
1+6+4
=
11
1+1
2
=
2
-
23
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
219
-
20
8
5
-
5
12
5
3
20
18
15
-
13
1
7
14
5
20
9
3
-
6
9
5
12
4
+
=
219
2+1+9
=
12
1+2
3
=
3
111
-
2
8
5
-
5
3
5
3
2
9
6
-
4
1
7
5
5
2
9
3
-
6
9
5
3
4
+
=
111
1+1+1
=
3
=
3
=
3
-
23
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
5
-
5
-
5
-
-
-
-
-
-
-
-
5
5
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
--
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
45
23
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
45
-
-
23
-
111
-
48
4+5
2+3
-
-
-
-
--
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
--
-
-
-
-
4+5
-
-
2+3
-
1+1+1
-
4+8
9
5
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
9
-
-
5
-
3
-
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+2
9
5
T
H
E
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
9
-
-
5
-
3
-
3

 

 

8
MAGNETIC
72
36
9
4
POLE
48
21
3

 

 

5
NORTH
75
30
3
5
SOUTH
83
20
2

 

 

8
MAGNETIC
72
36
9
5
POLES
67
22
4

 

 

7
CRYSTAL
98
26
8
8
CRYSTALS
117
27
9

 

 

6
SPHERE
71
35
8
5
ROUND
72
27
9

 

 

5
ROUND
72
27
9
7
SPHERES
90
36
9

 

 

-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
1
9
-
9
-
-
-
5
-
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
15
19
9
-
9
-
-
-
14
-
-
-
-
9
-
-
+
=
75
7+5
=
12
1+2
3
=
3
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
2
-
4
5
-
-
5
7
1
2
-
4
5
+
=
42
4+2
=
6
=
6
=
6
-
-
16
-
-
-
20
-
22
5
-
-
5
7
1
20
-
22
5
+
=
123
1+2+3
=
6
=
6
=
6
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
16
15
19
9
20
9
22
5
-
14
5
7
1
20
9
22
5
+
=
198
1+9+8
=
18
1+8
9
=
9
-
-
7
6
1
9
2
9
4
5
-
5
5
7
1
2
9
4
5
+
=
81
8+1
=
9
=
9
=
9
-
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
34
-
-
16
-
81
-
36
1+1
1+6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
3+4
-
-
1+6
-
8+1
-
3+6
2
7
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9
-
-
7
6
1
9
2
9
4
5
-
5
5
7
1
2
9
4
5
-
-
-
-
-
-
-
-
-
-
2
7
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9

 

 

16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
1
9
-
9
-
-
-
5
-
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
15
19
9
-
9
-
-
-
14
-
-
-
-
9
-
-
+
=
75
7+5
=
12
1+2
3
=
3
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
2
-
4
5
-
-
5
7
1
2
-
4
5
+
=
42
4+2
=
6
=
6
=
6
-
16
-
-
-
20
-
22
5
-
-
5
7
1
20
-
22
5
+
=
123
1+2+3
=
6
=
6
=
6
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
16
15
19
9
20
9
22
5
-
14
5
7
1
20
9
22
5
+
=
198
1+9+8
=
18
1+8
9
=
9
-
7
6
1
9
2
9
4
5
-
5
5
7
1
2
9
4
5
+
=
81
8+1
=
9
=
9
=
9
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
-
5
5
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
34
-
-
16
-
81
-
36
1+6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
3+4
-
-
1+6
-
8+1
-
3+6
7
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9
-
7
6
1
9
2
9
4
5
-
5
5
7
1
2
9
4
5
-
-
-
-
-
-
-
-
-
-
7
P
O
S
I
T
I
V
E
-
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9

 

 

16
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
1
9
-
9
-
-
5
-
-
-
-
9
-
-
+
=
39
3+9
=
12
1+2
3
=
3
-
-
15
19
9
-
9
-
-
14
-
-
-
-
9
-
-
+
=
75
7+5
=
12
1+2
3
=
3
16
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
2
-
4
5
-
5
7
1
2
-
4
5
+
=
42
4+2
=
6
=
6
=
6
-
16
-
-
-
20
-
22
5
-
5
7
1
20
-
22
5
+
=
123
1+2+3
=
6
=
6
=
6
16
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
16
15
19
9
20
9
22
5
14
5
7
1
20
9
22
5
+
=
198
1+9+8
=
18
1+8
9
=
9
-
7
6
1
9
2
9
4
5
5
5
7
1
2
9
4
5
+
=
81
8+1
=
9
=
9
=
9
16
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
9
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
34
-
-
16
-
81
-
36
1+6
-
-
9
-
9
-
-
-
-
-
-
-
9
-
-
-
-
3+4
-
-
1+6
-
8+1
-
3+6
7
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9
-
7
6
1
9
2
9
4
5
5
5
7
1
2
9
4
5
-
-
-
-
-
-
-
-
-
-
7
P
O
S
I
T
I
V
E
N
E
G
A
T
I
V
E
-
-
7
-
-
7
-
9
-
9

 

 

9 LIGHTDARKKRADTHGIL 9

 

-
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
6
-
-
-
-
6
-
-
6
1
9
-
-
1
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
9
-
-
15
-
-
-
-
15
-
-
15
19
9
-
-
19
+
=
92
9+2
=
11
1+1
2
=
2
-
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
-
-
-
-
-
-
-
-
-
-
4
-
9
9
-
9
5
4
-
-
7
7
-
-
-
2
5
-
+
=
61
6+1
=
7
=
7
=
7
-
-
13
-
18
18
-
18
5
4
-
-
16
16
-
-
-
20
5
-
+
=
133
1+3+3
=
7
=
7
=
7
-
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
-
-
-
-
-
-
-
-
-
-
13
9
18
18
15
18
5
4
-
15
16
16
15
19
9
20
5
19
+
=
234
2+3+4
=
9
=
9
=
9
-
-
4
9
9
9
6
9
5
4
-
6
7
7
6
1
9
2
5
1
+
=
99
9+9
=
18
1+8
9
=
9
-
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
-
6
-
-
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
-
-
-
-
-
7
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
5
=
45
4+5
9
11
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
34
-
-
17
-
99
-
36
1+1
-
-
9
9
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+7
-
9+9
-
3+6
2
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
7
-
-
8
-
18
-
9
-
-
4
9
9
9
6
9
5
4
-
6
7
7
6
1
9
2
5
1
-
-
-
-
-
-
-
1+8
-
-
2
17
M
I
R
R
O
R
E
D
-
O
P
P
O
S
I
T
E
S
-
-
7
-
-
8
-
9
-
9

 

 

4
MAAT
35
8
8
2
IS
28
19
1
6
KARMAS
63
18
9
3
LAW
36
9
9
4
REAL
36
18
9
7
REALITY
90
36
9
26
First Total
288
108
45
2+6
Add to Reduce
2+8+8
1+0+8
4+5
8
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
8
Essence of Number
9
9
9

 

 

M
=
4
-
6
MUTUAL
88
16
7
A
=
1
-
7
ASSURED
87
24
6
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
9
Q
23
First Total
323
89
17
-
-
-
-
2+3
Add to Reduce
3+2+3
8+9
1+7
-
-
9
-
5
Second Total
8
17
8
-
-
-
-
-
Reduce to Deduce
-
1+7
-
-
-
9
-
5
Essence of Number
8
8
8

 

MAD 9 MAD

 

M
=
4
-
8
MUTUALLY
125
26
8
A
=
1
-
7
ASSURED
87
24
6
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
9
Q
25
First Total
360
99
18
-
-
-
-
2+5
Add to Reduce
3+6+0
9+9
1+8
-
-
9
-
7
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
9
-
7
Essence of Number
9
9
9

 

 

R
=
9
-
3
RAW
42
15
6
W
=
5
-
3
WAR
42
15
6
S
-
14
4
6
Add
30
30
12
-
-
1+4
-
-
Reduce
3+0
3+0
1+2
S
-
5
4
6
Essence
3
3
3

 

 

-
6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
-
6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
-
6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
-
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
6
R
A
W
-
W
A
R
T
-
-
-
-
-
-
-
-
-
--
-
-
1
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
30
6
R
A
W
-
W
A
R
-
-
15
-
-
6
-
30
-
12
3+0
-
9
-
-
-
-
-
9
-
-
1+5
-
-
-
-
3+0
-
1+2
3
6
R
A
W
-
W
A
R
-
-
6
-
-
6
-
30
-
3
-
-
9
1
5
-
5
1
9
-
-
-
-
-
-
-
-
-
-
3
6
R
A
W
-
W
A
R
-
-
6
-
-
6
-
0
-
3

 

 

6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
6
R
A
W
-
W
A
R
-
-
-
-
-
--
-
-
-
-
-
18
1
23
-
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
-
9
1
5
-
5
1
9
+
=
30
3+0
=
3
=
3
=
3
6
R
A
W
-
W
A
R
T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
5
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
9
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
6
R
A
W
-
W
A
R
-
-
15
-
-
6
-
30
-
12
-
9
-
-
-
-
-
9
-
-
1+5
-
-
-
-
3+0
-
1+2
6
R
A
W
-
W
A
R
-
-
6
-
-
6
-
30
-
3
-
9
1
5
-
5
1
9
-
-
-
-
-
-
-
-
-
-
6
R
A
W
-
W
A
R
-
-
6
-
-
6
-
0
-
3

 

 

6
R
A
W
W
A
R
-
-
-
-
-
--
-
-
-
-
-
9
1
5
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
18
1
23
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
6
R
A
W
W
A
R
-
-
-
-
-
--
-
-
-
-
-
9
1
5
5
1
9
+
=
30
3+0
=
3
=
3
=
3
-
18
1
23
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
6
R
A
W
W
A
R
-
-
-
-
-
--
-
-
-
-
-
18
1
23
23
1
18
+
=
84
8+4
=
12
1+2
3
=
3
-
9
1
5
5
1
9
+
=
30
3+0
=
3
=
3
=
3
6
R
A
W
W
A
R
T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
5
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
9
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
6
R
A
W
W
A
R
-
-
15
-
-
6
-
30
-
12
-
9
-
-
-
-
9
-
-
1+5
-
-
-
-
3+0
-
1+2
6
R
A
W
W
A
R
-
-
6
-
-
6
-
30
-
3
-
9
1
5
5
1
9
-
-
-
-
-
-
-
-
-
-
6
R
A
W
W
A
R
-
-
6
-
-
6
-
0
-
3

 

 

S
=
1
-
5
SHOCK
56
20
2
A
=
1
-
3
AND
19
10
1
A
=
1
-
3
AWE
29
11
2
R
=
9
-
3
RAW
42
15
6
W
=
5
-
3
WAR
42
15
6
S
-
17
4
17
First
188
71
17
-
-
1+7
-``
1+7
Add
1+8+8
7+1
1+7
S
-
8
4
8
Reduce
17
8
8
-
-
-
-
-
Deduce
1+7
-
-
S
-
8
4
8
Essence
8
8
8

 

 

S
=
1
-
5
SHOCK
56
20
2
A
=
1
-
3
AND
19
10
1
A
=
1
-
3
AWE
29
11
2
R
=
9
-
3
RAW
42
15
6
I
=
9
-
2
IS
28
10
1
W
=
5
-
3
WAR
42
15
6
-
-
26
-
19
First
216
72
18
-
-
2+6
-
1+9
Add
2+1+6
7+2
1+8
-
-
8
-
10
Reduce
9
9
9
-
-
-
-
1+0
Deduce
-
-
-
-
-
8
-
1
Essence
9
9
9

 

 

 

8
ATOM BOMB
-
-
-
-
A+T
21
3
3
-
O+M
28
10
1
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
ATOM BOMB
81
27
9
-
-
8+1
2+7
-
8
ATOM BOMB
9
9
9

 

 

-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
+
=
12
1+2
=
3
1+1
3
=
3
-
-
-
-
15
-
-
-
15
-
-
+
=
30
3+0
=
3
1+1
3
=
3
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
2
-
4
2
+
=
15
1+5
=
6
=
6
=
6
-
-
1
20
-
13
-
2
-
13
2
+
=
51
5+1
=
6
=
6
=
6
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
-
2
15
13
2
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
2
6
4
2
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
3
-
-
--
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
--
--
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
32
8
A
T
O
M
-
B
O
M
B
-
-
13
-
-
8
-
27
-
18
3+2
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
2+7
-
1+8
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9
--
-
1
2
6
4
-
2
6
4
2
-
-
--
-
-
-
-
-
-
-
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9

 

 

-
9
H
I
R
O
S
H
I
M
A
-
-
-
-
-
--
-
-
-
-
-
-
8
9
-
6
1
8
9
-
-
+
=
41
4+1
=
5
=
5
=
5
-
-
8
9
-
15
19
8
9
-
-
+
=
68
6+8
=
14
1+4
5
=
5
-
9
H
I
R
O
S
H
I
M
A
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
-
-
-
4
1
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
18
-
-
-
-
13
1
+
=
32
3+2
=
5
=
5
=
5
-
9
H
I
R
O
S
H
I
M
A
-
-
-
-
-
--
-
-
-
-
-
-
8
9
18
15
19
8
9
13
1
+
=
100
1+0+0
=
1
=
1
=
1
-
-
8
9
9
6
1
8
9
4
1
+
=
55
5+5
=
10
1+0
1
=
1
-
9
H
I
R
O
S
H
I
M
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
--
--
--
--
--
--
--
--
--
--
--
2
TWO
2
-
-
-
-
-
3
-
--
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
5
-
--
--
--
--
--
--
--
--
--
--
--
5
FIVE
5
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
--
--
--
--
--
--
--
--
--
7
SEVEN
6
-
-
-
-
-
-
-
8
-
-
-
-
8
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
9
H
I
R
O
S
H
I
M
A
-
-
28
-
-
9
-
55
-
28
-
-
-
9
9
-
-
-
9
-
-
-
-
2+8
-
-
-
-
5+5
-
2+8
17
9
H
I
R
O
S
H
I
M
A
-
-
10
-
-
9
-
10
-
10
1+7
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
-
-
-
1+0
-
1+0
8
9
H
I
R
O
S
H
I
M
A
-
-
1
-
-
9
-
1
-
1

 

 

-
8
N
A
G
A
S
A
K
I
-
-
-
-
-
--
-
-
-
-
5
-
-
-
1
-
-
9
+
=
15
1+5
=
6
=
6
-
-
14
-
-
-
19
-
-
9
+
=
42
4+2
=
6
=
6
-
8
N
A
G
A
S
A
K
I
-
-
-
-
-
--
-
-
-
-
-
1
7
1
-
1
2
-
+
=
12
1+2
=
3
=
3
-
-
-
1
7
1
-
1
11
-
+
=
21
2+1
=
3
=
3
-
8
N
A
G
A
S
A
K
I
-
-
-
-
-
--
-
-
-
-
14
1
7
1
19
1
11
9
+
=
63
6+3
=
9
=
9
-
-
5
1
7
1
1
1
2
9
+
=
27
3+6
=
9
=
9
-
8
N
A
G
A
S
A
K
I
-
-
-
-
-
-
-
-
-
-
-
1
-
1
1
1
-
-
-
-
1
occurs
x
4
=
4
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
3
-
--
--
--
--
--
--
--
--
--
--
3
THREE
3
-
-
-
4
-
--
--
--
--
--
--
--
--
--
--
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
--
--
--
--
--
--
--
--
--
--
6
SIX
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
--
--
--
--
--
--
--
--
--
--
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
21
8
N
A
G
A
S
A
K
I
-
-
24
-
-
8
-
27
2+1
-
-
-
-
-
-
-
-
9
-
-
2+4
-
-
-
-
2+7
3
8
N
A
G
A
S
A
K
I
-
-
6
-
-
8
-
9

 

 

11
BIKINI ATOLL
-
-
-
-
BIKINI
54
36
9
-
ATOLL
60
15
6
11
BIKINI ATOLL
114
51
15
1+1
-
1+1+4
5+1
1+5
2
BIKINI ATOLL
6
6
6

 

 

5
JAPAN
42
15
6

 

 

3
THE
33
15
6
4
ATOM
49
13
4
4
BOMB
32
14
5
11
Add to Reduce
114
42
15
1+1
Reduce to Deduce
1+1+4
4+2
1+5
2
Essence of Number
6
6
6

 

 

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

 

 

3
THE
33
15
6
8
HYDROGEN
96
51
6
4
BOMB
32
14
5
15
Add to Reduce
161
80
17
1+5
Reduce to Deduce
1+6+1
8+0
1+7
6
Essence of Number
8
8
8

 

 

8
ATOM BOMB
81
27
9
8
NAGASAKI
63
36
9
9
HIROSHIMA
100
55
1

 

 

 

8
ATOM BOMB
-
-
-
-
A+T
21
3
3
-
O+M
28
10
1
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
ATOM BOMB
81
27
9
-
-
8+1
2+7
-
8
ATOM BOMB
9
9
9

 

 

 

-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
8
-
-
-
-
15
-
9
-
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
2
-
4
2
+
=
25
2+5
=
7
=
7
=
7
-
-
20
-
5
-
1
20
-
13
-
3
-
2
-
13
2
+
=
79
7+9
=
16
=
7
=
7
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
2
15
13
2
+
=
126
1+2+6
=
9
=
9
=
9
-
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
+
=
54
5+4
=
9
=
9
=
9
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
38
-
-
13
-
54
-
45
-
1+3
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+8
-
-
1+3
-
5+4
-
4+5
7
4
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
11
-
-
4
-
9
-
9
-
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
-
-
1+1
-
-
--
-
-
-
-
7
4
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
2
-
-
4
-
9
-
9

 

 

13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
8
-
-
-
-
15
-
9
-
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
2
-
4
2
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
-
1
20
-
13
-
3
-
2
-
13
2
+
=
79
7+9
=
16
=
7
=
7
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
2
15
13
2
+
=
126
1+2+6
=
9
=
9
=
9
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
+
=
54
5+4
=
9
=
9
=
9
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
2
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
38
-
-
13
-
54
-
45
1+3
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+8
-
-
1+3
-
5+4
-
4+5
4
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
11
-
-
4
-
9
-
9
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
-
-
1+1
-
-
--
-
-
-
-
4
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
2
-
-
4
-
9
-
9

 

 

13
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
-
9
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
8
-
-
-
15
-
9
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
13
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
2
-
5
1
2
-
4
-
3
2
-
4
2
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
1
20
-
13
-
3
2
-
13
2
+
=
79
7+9
=
16
=
7
=
7
13
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
20
8
5
1
20
15
13
9
3
2
15
13
2
+
=
126
1+2+6
=
9
=
9
=
9
-
2
8
5
1
2
6
4
9
3
2
6
4
2
+
=
54
5+4
=
9
=
9
=
9
13
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
--
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
38
-
-
13
-
54
-
45
1+3
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
3+8
-
-
1+3
-
5+4
-
4+5
4
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
11
-
-
4
-
9
-
9
-
2
8
5
1
2
6
4
9
3
2
6
4
2
-
-
1+1
-
-
--
-
-
-
-
4
T
H
E
A
T
O
M
I
C
B
O
M
B
-
-
2
-
-
4
-
9
-
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

 

 

3
THE
33
15
6
8
HYDROGEN
96
51
6
4
BOMB
32
14
5
15
Add to Reduce
161
80
17
1+5
Reduce to Deduce
1+6+1
8+0
1+7
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

 

 

 

 

 

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

 

 

3
THE
33
15
6
8
HYDROGEN
96
51
6
4
BOMB
32
14
5
15
Add to Reduce
161
80
17
1+5
Reduce to Deduce
1+6+1
8+0
1+7
6
Essence of Number
8
8
8

 

 

8
ATOM BOMB
-
-
-
-
A+T
21
3
3
-
O+M
28
10
1
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
ATOM BOMB
81
27
9
-
-
8+1
2+7
-
8
ATOM BOMB
9
9
9

 

 

-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
+
=
12
1+2
=
3
1+1
3
=
3
-
-
-
-
15
-
-
-
15
-
-
+
=
30
3+0
=
3
1+1
3
=
3
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
2
-
4
2
+
=
15
1+5
=
6
=
6
=
6
-
-
1
20
-
13
-
2
-
13
2
+
=
51
5+1
=
6
=
6
=
6
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
-
2
15
13
2
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
2
6
4
2
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
3
-
-
--
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
--
--
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
32
8
A
T
O
M
-
B
O
M
B
-
-
13
-
-
8
-
27
-
18
3+2
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
2+7
-
1+8
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9
--
-
1
2
6
4
-
2
6
4
2
-
-
--
-
-
-
-
-
-
-
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9

 

 

8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
+
=
12
1+2
=
3
1+1
3
=
3
-
-
-
15
-
-
-
15
-
-
+
=
30
3+0
=
3
1+1
3
=
3
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
2
-
4
2
+
=
15
1+5
=
6
=
6
=
6
-
1
20
-
13
-
2
-
13
2
+
=
51
5+1
=
6
=
6
=
6
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
-
2
15
13
2
+
=
81
8+1
=
9
=
9
=
9
-
1
2
6
4
-
2
6
4
2
+
=
27
2+7
=
9
=
9
=
9
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
4
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
6
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
8
A
T
O
M
-
B
O
M
B
-
-
13
-
-
8
-
27
-
18
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
2+7
-
1+8
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9
-
1
2
6
4
-
2
6
4
2
-
-
--
-
-
-
-
-
-
-
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9

 

 

8
A
T
O
M
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
+
=
12
1+2
=
3
1+1
3
=
3
-
-
-
15
-
-
15
-
-
+
=
30
3+0
=
3
1+1
3
=
3
8
A
T
O
M
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
2
-
4
2
+
=
15
1+5
=
6
=
6
=
6
-
1
20
-
13
2
-
13
2
+
=
51
5+1
=
6
=
6
=
6
8
A
T
O
M
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
2
15
13
2
+
=
81
8+1
=
9
=
9
=
9
-
1
2
6
4
2
6
4
2
+
=
27
2+7
=
9
=
9
=
9
8
A
T
O
M
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
4
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
8
A
T
O
M
B
O
M
B
-
-
13
-
-
8
-
27
-
18
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
2+7
-
1+8
8
A
T
O
M
B
O
M
B
-
-
4
-
-
8
-
9
-
9
-
1
2
6
4
2
6
4
2
-
-
--
-
-
-
-
-
-
-
8
A
T
O
M
B
O
M
B
-
-
4
-
-
8
-
9
-
9

 

 

8
ATOM BOMB
-
-
-
-
A+T
21
3
3
-
O+M
28
10
1
-
-
-
-
-
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
ATOM BOMB
81
27
9
-
-
8+1
2+7
-
8
ATOM BOMB
9
9
9

 

 

-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
+
=
12
1+2
=
3
1+1
3
=
3
-
-
-
-
15
-
-
-
15
-
-
+
=
30
3+0
=
3
1+1
3
=
3
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
2
-
4
2
+
=
15
1+5
=
6
=
6
=
6
-
-
1
20
-
13
-
2
-
13
2
+
=
51
5+1
=
6
=
6
=
6
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
-
2
15
13
2
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
2
6
4
2
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
3
-
-
--
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
--
--
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
32
8
A
T
O
M
-
B
O
M
B
-
-
13
-
-
8
-
27
-
18
3+2
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
2+7
-
1+8
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9
--
-
1
2
6
4
-
2
6
4
2
-
-
--
-
-
-
-
-
-
-
5
8
A
T
O
M
-
B
O
M
B
-
-
4
-
-
8
-
9
-
9

 

 

8
BOMB
-
-
-
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
BOMB
32
14
9
-
-
3+2
1+4
-
8
BOMB
5
5
5

 

 

-
4
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
1+1
6
-
-
-
15
-
-
+
=
15
1+5
=
6
1+1
6
-
4
B
O
M
B
-
-
-
-
-
-
-
-
-
-
2
-
4
2
+
=
8
-
=
8
=
8
-
-
2
-
13
2
+
=
17
1+7
=
8
=
8
-
4
B
O
M
B
-
-
-
-
-
-
-
-
-
-
2
15
13
2
+
=
32
3+2
=
5
=
5
-
-
2
6
4
2
+
=
14
1+4
=
5
=
5
-
4
B
O
M
B
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
--
--
--
--
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
B
O
M
B
-
-
13
-
-
4
-
14
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
4
B
O
M
B
-
-
4
-
-
4
-
5
-
-
2
6
4
2
-
-
-
-
-
-
-
-
5
4
B
O
M
B
-
-
4
-
-
4
-
5

 

 

8
BOMB
-
-
-
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
8
BOMB
32
14
9
-
-
3+2
1+4
-
8
BOMB
5
5
5

 

 

-
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
+
=
6
-
=
6
1+1
6
-
-
-
-
15
-
-
-
+
=
15
1+5
=
6
1+1
6
-
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
-
2
-
-
4
-
2
+
=
8
-
=
8
=
8
-
-
2
-
-
13
-
2
+
=
17
1+7
=
8
=
8
-
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
-
2
-
15
13
-
2
+
=
32
3+2
=
5
=
5
-
-
2
-
6
4
-
2
+
=
14
1+4
=
5
=
5
-
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
7
-
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
B
-
O
M
-
B
-
-
13
-
-
4
-
14
3+2
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
4
B
-
O
M
-
B
-
-
4
-
-
4
-
5
-
-
2
-
6
4
-
2
-
-
-
-
-
-
-
-
5
4
B
-
O
M
-
B
-
-
4
-
-
4
-
5

 

B OM B BE OM BE B OM B

 

4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
+
=
6
-
=
6
1+1
6
-
-
-
15
-
-
-
+
=
15
1+5
=
6
1+1
6
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
2
-
-
4
-
2
+
=
8
-
=
8
=
8
-
2
-
-
13
-
2
+
=
17
1+7
=
8
=
8
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
2
-
15
13
-
2
+
=
32
3+2
=
5
=
5
-
2
-
6
4
-
2
+
=
14
1+4
=
5
=
5
4
B
-
O
M
-
B
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
4
B
-
O
M
-
B
-
-
13
-
-
4
-
14
-
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
4
B
-
O
M
-
B
-
-
4
-
-
4
-
5
-
2
-
6
4
-
2
-
-
-
-
-
-
-
-
4
B
-
O
M
-
B
-
-
4
-
-
4
-
5

 

B OM B BE OM BE B OM B

 

 

 

-
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
5
-
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
-
8
-
-
8
-
-
-
14
-
-
-
-
-
+
=
30
3+0
=
3
=
3
=
3
-
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
3
4
1
-
-
9
1
3
5
+
=
33
3+3
=
6
=
6
=
6
-
-
20
-
5
-
-
21
13
1
-
-
18
1
3
5
+
=
87
8+7
=
15
1+5
6
=
6
-
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
8
21
13
1
14
-
18
1
3
5
+
=
117
1+1+7
=
9
=
9
=
9
-
-
2
8
5
-
8
3
4
1
5
-
9
1
3
5
+
=
54
5+4
=
9
=
9
=
9
-
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
6
SIX
6
-
-
-
-
-
7
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
13
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
32
-
-
12
-
54
-
36
1+3
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+2
-
-
1+2
-
5+4
-
3+6
4
3
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
5
-
-
3
-
9
-
9
-
-
2
8
5
-
8
3
4
1
5
-
9
1
3
5
-
-
-
-
-
-
-
-
-
-
4
3
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
5
-
-
3
-
9
-
9

 

 

12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
-
-
-
5
-
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
8
-
-
8
-
-
-
14
-
-
-
-
-
+
=
30
3+0
=
3
=
3
=
3
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
3
4
1
-
-
9
1
3
5
+
=
33
3+3
=
6
=
6
=
6
-
20
-
5
-
-
21
13
1
-
-
18
1
3
5
+
=
87
8+7
=
15
1+5
6
=
6
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
8
21
13
1
14
-
18
1
3
5
+
=
117
1+1+7
=
9
=
9
=
9
-
2
8
5
-
8
3
4
1
5
-
9
1
3
5
+
=
54
5+4
=
9
=
9
=
9
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
32
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+2
-
-
1+2
-
5+4
-
3+6
3
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
5
-
-
3
-
9
-
9
-
2
8
5
-
8
3
4
1
5
-
9
1
3
5
-
-
-
-
-
-
-
-
-
-
3
T
H
E
-
H
U
M
A
N
-
R
A
C
E
-
-
5
-
-
3
-
9
-
9

 

 

5
SPLIT
76
22
4
3
THE
33
15
6
4
ATOM
49
13
4
2
OF
21
12
3
3
THE
33
15
6
4
MIND
40
22
4
21
First Total
252
99
27
2+1
Add to Reduce
2+5+2
9+9
2+7
3
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
3
Essence of Number
9
9
9

 

 

S
=
1
9
SPLITTING
126
45
9
T
=
2
3
THE
33
15
6
A
=
1
4
ATOM
49
13
4
-
-
4
16
First Total
208
73
19
-
-
-
1+6
Add to Reduce
2+0+8
7+3
1+9
Q
-
4
7
Second Total
10
10
10
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
4
7
Essence of Number
1
1
1

 

 

3
THE
33
15
6
6
ATOMIC
61
25
7
4
MIND
40
22
4
13
Add to Reduce
134
62
17
1+3
Reduce to Deduce
1+3+4
6+2
1+7
4
Essence of Number
8
8
8

 

 

-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
9
-
-
9
5
-
-
-
8
-
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
-
-
19
-
-
9
-
-
9
14
-
-
-
8
-
-
-
-
15
-
+
=
74
7+4
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
7
3
-
2
2
-
-
7
-
2
-
5
-
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
-
-
-
16
12
-
20
20
-
-
7
-
20
-
5
-
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
19
16
12
9
20
20
9
14
7
-
20
8
5
-
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
9
-
-
9
-
-
--
-
-
-
--
-
-
-``
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
-
1+0
9
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
9
-
-
7
-
1
-
1

 

 

9
SPLITTING
126
45
9
5
ATOMS
68
14
5
14
First Total
194
59
14
1+4
Add to Reduce
1+9+4
5+9
1+4
5
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
5
Essence of Number
5
5
5

 

 

NUCLEAR UNCLEAR

C REAL SUN REAL C

SEE REAL SUN REAL SEE

 

 

-
13
N
U
C
L
E
A
R
--
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
--
-
-
1
9
6
5
+
=
26
2+6
=
8
=
8
=
8
-
-
14
-
-
-
-
-
-
-
-
-
19
9
15
14
+
=
71
7+1
=
8
=
8
=
8
-
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
3
5
1
9
-
6
3
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
21
3
12
5
1
18
-
6
21
-
-
-
-
+
=
87
8+7
=
15
1+5
6
=
6
=
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
14
21
3
12
5
1
18
-
6
21
19
9
15
14
+
=
158
1+5+8
=
14
1+4
5
=
5
-
-
5
3
3
3
5
1
9
-
6
3
1
9
6
5
+
=
59
5+9
=
14
1+4
5
=
5
-
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
`-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
21
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
24
-
-
13
-
59
-
23
2+1
1+3
-
3
3
3
-
-
-
-
-
3
-
-
-
-
-
-
2+4
-
-
1+3
-
5+9
-
2+3
3
4
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
6
-
-
4
-
14
-
5
-
-
5
3
3
3
5
1
9
-
6
3
1
9
6
5
-
-
-
-
-
-
-
1+4
-
-
3
4
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
6
-
-
4
-
5
-
5

 

 

3
N
U
C
L
E
A
R
--
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
--
-
-
1
9
6
5
+
=
26
2+6
=
8
=
8
=
8
-
14
-
-
-
-
-
-
-
-
-
19
9
15
14
+
=
71
7+1
=
8
=
8
=
8
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
3
3
3
5
1
9
-
6
3
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
21
3
12
5
1
18
-
6
21
-
-
-
-
+
=
87
8+7
=
15
1+5
6
=
6
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
14
21
3
12
5
1
18
-
6
21
19
9
15
14
+
=
158
1+5+8
=
14
1+4
5
=
5
-
5
3
3
3
5
1
9
-
6
3
1
9
6
5
+
=
59
5+9
=
14
1+4
5
=
5
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
3
3
3
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
24
-
-
13
-
59
-
23
1+3
-
3
3
3
-
-
-
-
-
3
-
-
-
-
-
-
2+4
-
-
1+3
-
5+9
-
2+3
4
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
6
-
-
4
-
14
-
5
-
5
3
3
3
5
1
9
-
6
3
1
9
6
5
-
-
-
-
-
-
-
1+4
-
-
4
N
U
C
L
E
A
R
-
F
U
S
I
O
N
-
-
6
-
-
4
-
5
-
5

 

 

3
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
9
6
5
+
=
26
2+6
=
8
=
8
=
8
-
14
-
-
-
-
-
-
-
-
19
9
15
14
+
=
71
7+1
=
8
=
8
=
8
13
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
3
3
3
5
1
9
6
3
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
21
3
12
5
1
18
6
21
-
-
-
-
+
=
87
8+7
=
15
1+5
6
=
6
13
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
14
21
3
12
5
1
18
6
21
19
9
15
14
+
=
158
1+5+8
=
14
1+4
5
=
5
-
5
3
3
3
5
1
9
6
3
1
9
6
5
+
=
59
5+9
=
14
1+4
5
=
5
13
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
3
3
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
24
-
-
13
-
59
-
23
1+3
-
3
3
3
-
-
-
-
3
-
-
-
-
-
-
2+4
-
-
1+3
-
5+9
-
2+3
4
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
6
-
-
4
-
14
-
5
-
5
3
3
3
5
1
9
6
3
1
9
6
5
-
-
-
-
-
-
-
1+4
-
-
4
N
U
C
L
E
A
R
F
U
S
I
O
N
-
-
6
-
-
4
-
5
-
5

 

 

-
NUCLEAR
-
--
-
1
N
14
5
5
1
U
21
3
3
1
C
3
3
3
1
L
12
3
3
3
EAR
24
15
6
7
NUCLEAR
74
29
20
-
--
7+4
2+9
2+0
7
NUCLEAR
11
11
2
-
--
1+1
1+1
-
7
NUCLEAR
2
2
2

 

 

-
NUCLEAR
-
--
-
2
UN
35
8
8
5
CLEAR
39
21
3
7
NUCLEAR
74
29
11
-
--
7+4
1+0+1
1+1
7
NUCLEAR
11
2
2
-
--
1+1
1+0+1
-
7
NUCLEAR
2
2
2

 

 

-
NUCLEAR
-
--
-
2
UN
35
8
8
4
REAL
36
18
9
1
C
3
3
3
7
NUCLEAR
74
29
20
-
--
7+4
2+9
2+0
7
NUCLEAR
11
11
2
-
--
1+1
1+1
-
7
NUCLEAR
2
2
2

 

 

9
SUFFERING
105
51
6
5
DEATH
38
20
2
11
DESTRUCTION
148
49
4
11
DESTRUCTIVE
146
47
2
5
POWER
77
32
5

 

 

BE OM BE

 

T
=
2
-
3
THE
33
15
6
A
=
1
-
6
ATOMIC
61
25
7
B
=
2
-
4
BOMB
32
14
5
-
-
12
-
13
Add to Reduce
126
54
18
-
-
1+2
-
1+3
Reduce to Deduce
1+2+6
5+4
1+8
-
-
3
-
4
Essence of Number
9
9
9

 

 

-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
8
-
-
-
-
15
-
9
-
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
2
-
4
2
+
=
25
2+5
=
7
=
7
=
7
-
-
20
-
5
-
1
20
-
13
-
3
-
2
-
13
2
+
=
79
7+9
=
16
1+6
7
=
7
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
--
1
20
15
13
9
3
--
2
15
13
2
+
=
126
1+2+6
=
9
=
9
=
9
-
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
+
=
54
5+4
=
9
=
9
=
9
-
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
7
SEVEN
7
-
-
-
-
-
-
-
-
8
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
38
-
-
13
-
54
-
45
-
-
2
-
-
-
-
2
-
-
-
-
-
2
-
-
2
-
-
3+8
-
-
1+3
-
5+4
-
4+5
7
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
11
-
-
4
-
9
-
9
-
-
2
8
5
-
1
2
6
4
9
3
-
2
6
4
2
-
-
1+1
-
-
--
-
-
-
-
7
13
T
H
E
-
A
T
O
M
I
C
-
B
O
M
B
-
-
2
-
-
4
-
9
-
9

 

 

A
=
1
-
6
ATOMIC
61
25
7
N
=
5
-
7
NUMBERS
92
29
2
-
-
6
-
13
Add to Reduce
441
135
27
-
-
3+2
-
1+3
Reduce to Deduce
4+4+1
1+3+5
2+7
-
-
6
-
4
Essence of Number
9
9
9

 

 

92 ELEMENTS 92

 

-
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
-
-
5
-
-
-
-
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
-
-
15
-
9
-
-
14
-
-
-
-
-
19
+
=
57
5+7
=
12
1+2
3
=
3
-
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
3
-
-
3
4
2
5
9
-
+
=
33
3+3
=
6
=
6
=
6
-
-
1
20
-
13
-
3
-
-
21
13
2
5
18
-
+
=
96
9+6
=
15
1+5
6
=
6
-
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
9
3
--
14
21
13
2
5
18
19
+
=
153
1+5+3
=
9
=
9
=
9
-
-
1
2
6
4
9
3
-
5
3
4
2
5
9
1
+
=
54
5+4
=
9
=
9
=
9
-
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
-
-
-
3
-
-
3
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
4
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
--
--
--
--
--
-
-
-
-
-
-
-
--
--
7
SEVEN
7
-
-
-
-
-
8
-
--
--
--
--
--
--
--
-
-
-
-
-
-
-
--
--
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
--
--
9
occurs
x
1
=
18
1+8
9
15
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
38
-
-
13
-
54
-
36
1+5
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+3
-
5+4
-
3+6
6
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
11
-
-
4
-
9
-
9
--
-
1
2
6
4
9
3
-
5
3
4
2
5
9
1
-
-
1+1
-
-
--
-
-
-
-
6
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
2
-
-
4
-
9
-
9

 

 

13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
-
-
5
-
-
-
-
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
-
15
-
9
-
-
14
-
-
-
-
-
19
+
=
57
5+7
=
12
1+2
3
=
3
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
3
-
-
3
4
2
5
9
-
+
=
33
3+3
=
6
=
6
=
6
-
1
20
-
13
-
3
-
-
21
13
2
5
18
-
+
=
96
9+6
=
15
1+5
6
=
6
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
9
3
--
14
21
13
2
5
18
19
+
=
153
1+5+3
=
9
=
9
=
9
-
1
2
6
4
9
3
-
5
3
4
2
5
9
1
+
=
54
5+4
=
9
=
9
=
9
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
-
-
-
3
-
-
3
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
4
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
--
--
9
occurs
x
1
=
18
1+8
9
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
38
-
-
13
-
54
-
36
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+3
-
5+4
-
3+6
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
11
-
-
4
-
9
-
9
-
1
2
6
4
9
3
-
5
3
4
2
5
9
1
-
-
1+1
-
-
--
-
-
-
-
13
A
T
O
M
I
C
-
N
U
M
B
E
R
S
-
-
2
-
-
4
-
9
-
9

 

 

13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
-
5
-
-
-
-
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
-
15
-
9
-
14
-
-
-
-
-
19
+
=
57
5+7
=
12
1+2
3
=
3
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
2
-
4
-
3
-
3
4
2
5
9
-
+
=
33
3+3
=
6
=
6
=
6
-
1
20
-
13
-
3
-
21
13
2
5
18
-
+
=
96
9+6
=
15
1+5
6
=
6
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
20
15
13
9
3
14
21
13
2
5
18
19
+
=
153
1+5+3
=
9
=
9
=
9
-
1
2
6
4
9
3
5
3
4
2
5
9
1
+
=
54
5+4
=
9
=
9
=
9
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
-
-
-
3
-
3
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
9
-
-
-
-
-
-
9
-
--
--
9
occurs
x
2
=
18
1+8
9
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
38
-
-
13
-
54
-
36
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+3
-
5+4
-
3+6
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
11
-
-
4
-
9
-
9
-
1
2
6
4
9
3
5
3
4
2
5
9
1
-
-
1+1
-
-
--
-
-
-
-
13
A
T
O
M
I
C
N
U
M
B
E
R
S
-
-
2
-
-
4
-
9
-
9

 

 

-
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
1
+
=
6
-
=
6
=
6
=
6
-
-
14
-
-
-
-
-
19
+
=
33
3+3
=
6
=
6
=
6
-
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
3
4
2
5
9
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
21
13
2
5
18
-
+
=
59
5+9
=
14
1+4
5
=
5
-
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
14
21
13
2
5
18
19
+
=
92
9+2
=
11
1+1
2
=
2
-
-
5
3
4
2
5
9
1
+
=
29
2+9
=
11
1+1
2
=
2
-
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
-
9
21
7
N
U
M
B
E
R
S
-
-
24
-
-
7
-
29
-
20
2+1
-
-
-
-
-
-
9
-
-
-
2+4
-
-
-
-
2+9
-
2+0
3
7
N
U
M
B
E
R
S
-
-
6
-
-
7
-
11
-
2
-
-
5
3
4
2
5
9
1
-
-
-
-
-
-
-
1+1
-
1+0
3
7
N
U
M
B
E
R
S
-
-
6
-
-
7
-
2
-
2

 

 

7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
1
+
=
6
-
=
6
=
6
=
6
-
14
-
-
-
-
-
19
+
=
33
3+3
=
6
=
6
=
6
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
3
4
2
5
9
-
+
=
23
2+3
=
5
=
5
=
5
-
-
21
13
2
5
18
-
+
=
59
5+9
=
14
1+4
5
=
5
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
14
21
13
2
5
18
19
+
=
92
9+2
=
11
1+1
2
=
2
-
5
3
4
2
5
9
1
+
=
29
2+9
=
11
1+1
2
=
2
7
N
U
M
B
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
-
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
-
9
7
N
U
M
B
E
R
S
-
-
24
-
-
7
-
29
-
20
-
-
-
-
-
-
9
-
-
-
2+4
-
-
-
-
2+9
-
2+0
7
N
U
M
B
E
R
S
-
-
6
-
-
7
-
11
-
2
-
5
3
4
2
5
9
1
-
-
-
-
-
-
-
1+1
-
1+0
7
N
U
M
B
E
R
S
-
-
6
-
-
7
-
2
-
2

 

 

7
SURVIVE
116
35
8
8
SURVIVES
135
36
9
8
SURVIVAL
124
34
7
8
SURVIVED
120
39
3
8
SURVIVING
141
51
6

 

 

7
EXTINCT
95
32
5
10
EXTINGUISH
136
55
1
12
EXTINGUISHED
145
64
1
12
EXTINGUISHES
160
61
7
10
EXTINCTION
133
52
7

 

 

10
OBLITERATE
107
44
8
11
OBLITERATES
126
45
9
11
OBLITERATED
116
53
8

 

 

MUTUALLY ASSURED DESTRUCTION

 

M
=
4
8
MUTUALLY
125
26
8
A
=
1
7
ASSURED
87
24
6
D
=
4
11
DESTRUCTION
148
49
4
-
-
9
26
First Total
360
99
18
-
-
-
2+6
Add to Reduce
3+6+0
9+9
1+8
Q
-
9
8
Second Total
9
18
9
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
9
8
Essence of Number
9
9
9

 

 

-
26
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
1
-
-
-
-
-
9
6
5
+
=
23
2+3
=
9
=
9
=
5
-
-
-
-
-
-
-
-
-
-
-
-
19
19
-
-
-
-
-
-
-
19
-
-
-
-
-
9
15
14
+
=
95
9+5
=
14
1+4
5
=
5
-
26
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
4
3
2
3
1
3
3
7
-
1
-
-
3
9
5
4
-
4
5
-
2
9
3
3
2
-
-
-
+
=
76
7+6
=
13
1+3
4
=
4
-
-
13
21
20
21
1
12
12
25
-
1
-
-
21
18
5
4
-
4
5
-
20
18
21
3
20
-
-
-
+
=
265
2+6+5
=
13
1+3
4
=
4
-
26
M
U
T
U
A
L
L
Y
--
A
S
S
U
R
E
D
--
D
E
S
T
R
U
C
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
13
21
20
21
1
12
12
25
-
1
19
19
21
18
5
4
-
4
5
19
20
18
21
3
20
9
15
14
+
=
360
3+6+0
=
9
=
9
=
9
-
-
4
3
2
3
1
3
3
7
-
1
1
1
3
9
5
4
-
4
5
1
2
9
3
3
2
9
6
5
+
=
99
9+9
=
18
1+8
9
=
9
-
26
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
1
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
5
=
5
=
5
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
3
-
3
3
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
occurs
x
7
=
21
=
3
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-`
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
--
-
--
-
-
-
-
--
--
--
-
--
--
-
-
-
-
--
--
--
-
-
--
-
6
-
--
--
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
EIGHT
8
--
--
--
--
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
8
26
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
39
-
-
26
-
99
-
45
-
2+6
-
3
-
3
-
3
3
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3+9
-
-
2+6
-
9+9
-
4+5
8
8
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
12
-
-
8
-
18
-
9
-
-
4
3
2
3
1
3
3
7
-
1
1
1
3
9
5
4
-
4
5
1
2
9
3
3
2
9
6
5
-
-
1+2
-
-
-
-
1+8
-
-
8
8
M
U
T
U
A
L
L
Y
-
A
S
S
U
R
E
D
-
D
E
S
T
R
U
C
T
I
O
N
-
-
3
-
-
8
-
9
-
9

 

 

THOSE WHOM THE GODS WOULD DESTROY THEY FIRST MAKE MAD

 

-
3
M
-
A
-
D
-
-
-
-
-
-
-
-
-
-
4
-
1
-
4
+
=
9
-
=
9
=
9
-
-
13
-
1
-
4
+
=
18
1+8
=
9
=
9
-
3
M
-
A
-
D
-
-
-
-
-
-
-
-
-
-
4
-
1
-
4
+
=
9
-
=
9
=
9
-
-
13
-
1
-
4
+
=
18
1+8
=
9
=
9
-
3
M
--
A
--
D
-
-
-
-
-
-
-
-
-
-
13
-
1
-
4
+
=
9
-
=
9
=
9
-
-
4
-
1
-
4
+
=
18
1+8
=
9
=
9
-
3
M
-
A
-
D
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
2
TWO
2
--
--
--
3
-
-
-
-
-
-
-
-
3
THREE
3
--
--
--
-
-
4
-
-
-
4
-
-`
4
occurs
x
2
=
8
5
-
-
-
-
-
-
-
-
5
FIVE
5
--
--
--
6
-
-
-
--
-
-
--
--
6
SIX
6
--
--
--
7
-
-
-
-
-
-
-
-
7
SEVEN
7
--
--
--
8
-
-
-
-
-
-
-
-
8
EIGHT
8
--
--
--
9
-
-
-
-
-
-
-
-
9
NINE
9
--
--
--
40
3
M
-
A
-
D
-
-
5
-
-
3
-
9
4+0
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MAD

MUTUALLY ASSURED DESTRUCTION

 

Mutual assured destruction - Wikipedia, the free encyclopedia Mutual assured destruction (MAD) is a doctrine of military strategy in which a full-scale use of nuclear weapons by two opposing sides would effectively ...

Theory - History - Official policy - Criticism and challengable ...
en.wikipedia.org/wiki/Mutual_assured_destruction - Cached - Similar

 

Mutual assured destruction
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Mutual assured destruction (MAD) is a doctrine of military strategy in which a full-scale use of nuclear weapons by two opposing sides would effectively result in the destruction of both the attacker and the defender.[1] It is based on the theory of deterrence according to which the deployment of strong weapons is essential to threaten the enemy in order to prevent the use of the very same weapons. The strategy is effectively a form of Nash equilibrium, in which both sides are attempting to avoid their worst possible outcome—nuclear annihilation.

Contents [hide]
1 Theory
2 History
2.1 Pre-1945
2.2 Early Cold War
2.3 Second strike capability
2.4 Late Cold War
2.5 Post Cold War
3 Official policy
4 Criticism and challengable assumptions
5 See also
5.1 Media
6 References
7 External links

[edit] Theory
MAD is a "Poison Pill" strategy. The doctrine assumes that each side has enough nuclear weaponry to destroy the other side and that either side, if attacked for any reason by the other, would retaliate with equal or greater force. The expected result is an immediate escalation resulting in both combatants' total and assured destruction. It is now generally hypothesized that the nuclear fallout or nuclear winter resulting from a large scale nuclear war would bring about worldwide devastation, though this was not a critical assumption to the theory of MAD.

The doctrine further assumes that neither side will dare to launch a first strike because the other side will launch on warning (also called fail-deadly) or with secondary forces (second strike) resulting in the destruction of both parties. The payoff of this doctrine is expected to be a tense but stable peace.

The primary application of this doctrine started during the Cold War (1940s to 1990s) in which MAD was seen as helping to prevent any direct full-scale conflicts between the United States and the Soviet Union while they engaged in smaller proxy wars around the world. It was also responsible for the arms race, as both nations struggled to keep nuclear parity, or at least retain second-strike capability. Although the Cold War ended in the early 1990s, the doctrine of Mutually Assured Destruction certainly continues to be in force.

Proponents of MAD as part of U.S. and USSR strategic doctrine believed that nuclear war could best be prevented if neither side could expect to survive a full scale nuclear exchange as a functioning state. Since the credibility of the threat is critical to such assurance, each side had to invest substantial capital in their nuclear arsenals even if they were not intended for use. In addition, neither side could be expected or allowed to adequately defend itself against the other's nuclear missiles. This led both to the hardening and diversification of nuclear delivery systems (such as nuclear missile silos, ballistic missile submarines and nuclear bombers kept at fail-safe points) and to the Anti-Ballistic Missile Treaty.

This MAD scenario is often referred to as nuclear deterrence. The term deterrence was first used in this context after World War II; prior to that time, its use was limited to legal terminology.

In practice, the theory proved both utterly effective and exceptionally dangerous (e.g., Cuban Missile Crisis) through the end of the Cold War. Today, all lesser nations are believed to be keenly aware that any use of nuclear weapons, in any context, is the recipe for their annihilation. Significant nuclear powers, such as the United States, the Russian Federation, and the People's Republic of China (PRC), operate under the deterrent effect of potential retaliation with respect to "first use" in the conduct of brush fire wars and other lesser conflagrations. The U.S., as possessor of the largest and most deployable stockpile of nuclear weapons,[citation needed] continues to exercise its vast nuclear might as a cornerstone of its foreign policy with regard to rogue states and communist nations that currently or may soon possess nuclear weapons technology. U.S. military forces stand on permanent alert in order to deter potential nuclear adversaries. Likewise, non-democratic nations cannot use nuclear weapons against the U.S., or her critical allies (United Kingdom, Canada, Japan, Germany, Israel, Australia, and South Korea) without threat of (as U.S. President John F. Kennedy said) a "full retaliatory" response by the United States.[2]

[edit] History
[edit] Pre-1945
Perhaps the earliest reference to the concept comes from the English author Wilkie Collins, writing at the time of the Franco-Prussian War in 1870: "I begin to believe in only one civilising influence—the discovery one of these days of a destructive agent so terrible that War shall mean annihilation and men's fears will force them to keep the peace".

Echoes of the doctrine can be found in the first document which outlined how the atomic bomb was a practical proposition. In March 1940, the Frisch-Peierls memorandum anticipated deterrence as the principal means of combating an enemy with nuclear weapons.

In practice during World War II, utter annihilation from the air had already been visited upon the enemies of the Allied forces, both in Europe and Japan, well before use of the Atomic Bomb, and with perhaps even deadlier results. The incendiary attacks on Dresden in Germany, e.g., and Tokyo in efforts to finally force surrender and end both the European and Pacific Wars, set the stage for the concepts of Total War and MAD.

[edit] Early Cold War
In August 1945, the United States accepted the surrender of Japan after the nuclear attacks on Hiroshima and Nagasaki. Four years later, on August 29, 1949, the Soviet Union detonated its own nuclear weapon. At the time, both sides lacked the means to effectively use nuclear devices against each other. However, with the development of aircraft like the Convair B-36, both sides were gaining a greater ability to deliver nuclear weapons into the interior of the opposing country. The official nuclear policy of the United States was one of "massive retaliation", as coined by President Dwight D. Eisenhower's Secretary of State John Foster Dulles, which called for massive attack against the Soviet Union if they were to invade Europe, regardless of whether it was a conventional or a nuclear attack.

During the Cuban Missile Crisis, the Soviet Union truly developed an understanding of the effectiveness of the U.S. ballistic missile submarine forces, and work on Soviet ballistic missile submarines began in earnest. For the remainder of the Cold War, although official positions on MAD changed in the United States, the consequences of the second strike from ballistic missile submarines was never in doubt.

The multiple independently targetable re-entry vehicle (MIRV) was another weapons system designed specifically to aid with the MAD nuclear deterrence doctrine. With a MIRV payload, one ICBM could hold many separate warheads. MIRVs were first created by the United States in order to counterbalance Soviet anti-ballistic missile systems around Moscow. Since each defensive missile could only be counted on to destroy one offensive missile, making each offensive missile have, for example, three warheads (as with early MIRV systems) meant that three times as many defensive missiles were needed for each offensive missile. This made defending against missile attacks more costly and difficult. One of the largest U.S. MIRVed missiles, the LGM-118A Peacekeeper, could hold up to 10 warheads, each with a yield of around 300 kilotons—all together, an explosive payload equivalent to 230 Hiroshima-type bombs. The multiple warheads made defense untenable with the technology available, leaving only the threat of retaliatory attack as a viable defensive option. MIRVed land-based ICBMs are considered destabilizing because they tend to put a premium on striking first. It is because of this that this type of weapon was banned under the START II agreement.

In the event of a Soviet conventional attack on Western Europe, NATO planned to use tactical nuclear weapons. The Soviet Union countered this threat by issuing a statement that any use of nuclear weapons against Soviet forces, tactical or otherwise, was grounds for a full-scale Soviet retaliatory strike. As such, it was generally assumed that any combat in Europe would end with apocalyptic conclusions. The quote "I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones" is generally attributed to Albert Einstein.[1]

[edit] Second strike capability
It was only with the advent of ballistic missile submarines, starting with the George Washington class in 1959, that a survivable nuclear force became possible and second strike capability credible. This was not fully understood until the 1960s when the strategy of mutually assured destruction was first fully described, largely by United States Secretary of Defense Robert McNamara.

In McNamara's formulation, MAD meant that nuclear nations either had first strike or second strike capability. A nation with first strike capability would be able to destroy the entire nuclear arsenal of another nation and thus prevent any nuclear retaliation. Second strike capability indicated that a nation could uphold a promise to respond to a nuclear attack with enough force to make such a first attack highly undesirable. According to McNamara, the arms race was in part an attempt to make sure that no nation gained first strike capability.

An early form of second strike capability had already been provided by the use of continual patrols of nuclear-equipped bombers, with a fixed number of planes always in the air (and therefore untouchable by a first strike) at any given time. The use of this tactic was reduced however, by the high logistic difficulty of keeping enough planes active at all times, and the increasing priority given to ICBMs over bombers (which might be shot down by air defenses before reaching their targets).

Ballistic missile submarines established a second strike capability through their stealth and by the number fielded by each Cold War adversary—it was highly unlikely that all of them could be targeted and preemptively destroyed (in contrast to, for example, a missile bunker with a fixed location that could be targeted during a first strike). Given their long range, high survivability and ability to carry many medium- and long-range nuclear missiles, submarines were credible and effective means for full-scale retaliation even after a massive first strike.

[edit] Late Cold War
The original doctrine of U.S. MAD was modified on July 25, 1980, with U.S. President Jimmy Carter's adoption of countervailing strategy with Presidential Directive 59. According to its architect, Secretary of Defense Harold Brown, "countervailing strategy" stressed that the planned response to a Soviet attack was no longer to bomb Russian population centers and cities primarily, but first to kill the Soviet leadership, then attack military targets, in the hope of a Russian surrender before total destruction of the USSR (and the United States). This modified version of MAD was seen as a winnable nuclear war, while still maintaining the possibility of assured destruction for at least one party. This policy was further developed by the Reagan Administration with the announcement of the Strategic Defense Initiative (nicknamed "Star Wars"), the goal of which was to develop space-based technology to destroy Soviet missiles before they reached the U.S.

SDI was criticized by both the Soviets and many of America's allies (including Prime Minister of the United Kingdom Margaret Thatcher) because, were it ever operational and effective, it would have undermined the "assured destruction" required for MAD. If America had a guarantee against Soviet nuclear attacks, its critics argued, it would have first strike capability which would have been a politically and militarily destabilizing position. Critics further argued that it could trigger a new arms race, this time to develop countermeasures for SDI. Despite its promise of nuclear safety, SDI was described by many of its critics (including Soviet nuclear physicist and later peace activist Andrei Sakharov) as being even more dangerous than MAD because of these political implications. Supporters also argued that SDI could trigger a new arms race, forcing the USSR to spend an increasing proportion of GDP on defense - something which has been claimed to have been an indirect cause of the eventual collapse of the Soviet Union.

Proponents of Ballistic Missile Defense (BMD) argue that MAD is exceptionally dangerous in that it essentially offers a single course of action in the event of nuclear attack: full retaliatory response. The fact that nuclear proliferation has led to an increase in the number of nations in the "nuclear club", including nations of questionable stability (Pakistan, North Korea, Israel[3] and Iran, e.g.), and that a nuclear nation might be hijacked by a despot or other person or persons who might use nuclear weapons without sane regard for the consequences, presents a strong case for proponents of BMD who seek a policy which both protects against attack, but also does not require an escalation into what might become global nuclear war. Russia continues to have a strong public distaste for Western BMD initiatives, presumably because proprietary operative BMD systems could exceed their technical and financial resources, and therefore degrade their larger military standing and sense of security in a post-MAD environment. Russian refusal to accept invitations to participate in NATO BMD may be indicative of the lack of an alternative to MAD in current Russian nuclear-war-fighting strategy and capability.

[edit] Post Cold War
After the fall of the Soviet Union, Russia emerged as a sovereign entity encompassing most of the territory of the former USSR. Relations between the U.S. and this new power have been less tense then they had been with its predecessor. Tensions also decreased between the U.S and China.

The administration of U.S. President George W. Bush withdrew from the Anti-Ballistic Missile Treaty in June 2002, claiming that the limited national missile defense system which they propose to build is designed only to prevent nuclear blackmail by a state with limited nuclear capability and is not planned to alter the nuclear posture between Russia and the United States.

While relations have improved and an intentional nuclear exchange is increasingly unlikely, the decay in Russian nuclear capability in the post Cold War era has had an effect on the continued viability of the MAD doctrine. An article by Keir Lieber and Daryl Press stated that the United States could carry out a nuclear first strike on Russia and would "have a good chance of destroying every Russian bomber base, submarine, and ICBM." This was attributed to reductions in Russian nuclear stockpiles and the increasing inefficiency and age of that which remains. Lieber and Press argued that the MAD era is coming to an end and that U.S. is on the cusp of global nuclear primacy.[4]

However, in a follow up article in the same publication, others criticized the analysis, including Peter Flory, the U.S. Assistant Secretary of Defense for International Security Policy, who began by writing "The essay by Keir Lieber and Daryl Press contains so many errors, on a topic of such gravity, that a Department of Defense response is required to correct the record."[5] Regarding reductions in Russian stockpiles, another response stated that "a similarly one-sided examination of [reductions in] U.S. forces would have painted a similarly dire portrait".

A situation in which the United States might actually be expected to carry out a "successful" attack is perceived as a disadvantage for both countries. The strategic balance between the United States and Russia is becoming less stable, and the objective, technical possibility of a first strike by the United States is increasing. At a time of crisis, this instability could lead to an accidental nuclear war. For example, if Russia feared a U.S. nuclear attack, Moscow might make rash moves (such as putting its forces on alert) that would provoke a U.S. preemptive strike.[5] An outline of current United States nuclear strategy toward both Russia and other nations was published as the document "Essentials of Post-Cold War Deterrence" in 1995.

[edit] Official policy
Whether MAD was the officially accepted doctrine of the United States military during the Cold War is largely a matter of interpretation. The term MAD was not coined by the military but was, however, based on the policy of "Assured Destruction" advocated by U.S. Secretary of Defense Robert McNamara during the 1960s. The United States Air Force, for example, has retrospectively contended that it never advocated MAD as a sole strategy, and that this form of deterrence was seen as one of numerous options in U.S. nuclear policy.[6] Former officers have emphasized that they never felt as limited by the logic of MAD (and were prepared to use nuclear weapons in smaller scale situations than "Assured Destruction" allowed), and did not deliberately target civilian cities (though they acknowledge that the result of a "purely military" attack would certainly devastate the cities as well). MAD was implied in several U.S. policies and used in the political rhetoric of leaders in both the U.S. and the USSR during many periods of the Cold War.

To continue to deter in an era of strategic nuclear equivalence, it is necessary to have nuclear (as well as conventional) forces such that in considering aggression against our interests any adversary would recognize that no plausible outcome would represent a victory or any plausible definition of victory. To this end and so as to preserve the possibility of bargaining effectively to terminate the war on acceptable terms that are as favorable as practical, if deterrence fails initially, we must be capable of fighting successfully so that the adversary would not achieve his war aims and would suffer costs that are unacceptable, or in any event greater than his gains, from having initiated an attack.

– President Jimmy Carter in 1980, Presidential Directive 59, Nuclear Weapons Employment Policy

[edit] Criticism and challengable assumptions
This section does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2008)

Critics of the MAD doctrine note the similarity between the acronym and the common word for mental illness. The doctrine of nuclear deterrence depends on several challengeable assumptions:

Second-strike capability

A first strike must not be capable of preventing a retaliatory second strike or else mutual destruction is not assured. In this case, a state would have nothing to lose with a first strike; or might try to preempt the development of an opponent's second-strike capability with a first strike (i.e., decapitation strike).
Perfect detection

No false positives (errors) in the equipment and/or procedures that must identify a launch by the other side. The implication of this is that an accident could lead to a full nuclear exchange. During the Cold War there were several instances of false positives, as in the case of Stanislav Petrov.
No possibility of camouflaging a launch. The use of stealth technology in aircraft such as the B-2 bomber makes this assumption less likely to be fulfilled.
No means of delivery that does not have the characteristics of a long range missile delivery, i.e. detectable far ahead of detonation. Again this assumption is challengeable with for instance stealth aircraft but also with other means, such as smuggling weapons to the target undetected. A close range missile attack from a submarine would also negate this assumption, as would positioning the weapons close to the intended target (exemplified in the Cuban Missile Crisis).
Perfect attribution. If there is a launch from the Sino-Russian border, it could be difficult to distinguish which nation is responsible and, hence, against which nation retaliation should occur.
Perfect rationality

No "rogue states" will develop nuclear weapons. Or, if they do, they will stop behaving as rogue states and subject themselves to the logic of MAD.
No rogue commanders will have the ability to corrupt the launch decision process.
All leaders with launch capability care about the survival of their subjects.
No leader with launch capability would strike first and gamble that the opponent's response system would fail.
Inability to defend

No shelters sufficient to protect population and/or industry.
No development of anti-missile technology or deployment of remedial protective gear.
[edit] See also
Absolute war
Bulletin of the Atomic Scientists
Balance of terror
Counterforce
Doomsday clock
Force de frappe
Fail-deadly
Game theory
Herman Kahn
John von Neumann
Moral equivalence
Nuclear-free zone
Nuclear disarmament
Nuclear missile defense
Nuclear peace
Nuclear utilization target selection (NUTS)
Nuclear strategy
Peace through strength
RAND Corporation
Suicide weapon
Single Integrated Operational Plan (SIOP)
Weapons of Mass Destruction
Stability-instability paradox
[edit] Media
Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb, a film where a paranoid US general activates first strike bomber planes. One target is attacked despite all efforts at recall, triggerring a recently activated Soviet device that destroys the Earth's surface.
Essence of Decision, a book which disputes the MAD doctrine
Fail-Safe, a second film that takes a more serious view of the MAD situation.
On Thermonuclear War Herman Kahn's book on thermonuclear deterrence.
Red Alert, the Peter George book upon which Dr. Strangelove is based.
WarGames, presented MAD by juxtaposing human fear with computed game theory
Defcon, a video game where the player is on the cusp of MAD and must be careful not to provoke the enemy lest they achieve MAD
Wild Fire Nelson DeMille's fictional book. Plot relates to a Mutually Assured Destruction scenario known in the book as Operation Wild Fire.[7]
The term is mentioned in Megadeth's single Sweating Bullets
Sigue Sigue Sputnik song M.A.D. - from their second album Dress For Excess, it is an anti-war song typical of the 1980s. In true Sputnik fashion, the song includes samples from many mutual-assured-destruction movies such as Dr. Strangelove, WarGames and The Living Daylights.
British Band "Hadouken!" released a song in 2009 known as M.A.D, the term standing for Mutually Assured Destruction.
In the 1960s TV Series Star Trek, we see a device (known as the Planet Killer) that serves as an example of MAD.
In the video game Command & Conquer: Red Alert, there is a Soviet weapon called the MAD Tank.
[edit] References
1.^ Mutual Assured Destruction; Col. Alan J. Parrington, USAF, Mutually Assured Destruction Revisited, Strategic Doctrine in Question, Airpower Journal, Winter 1997.
2.^ JFK Broadcast Address, 10/22/62, "It shall be the policy of this Nation to regard any nuclear missile launched from Cuba against any nation in the Western Hemisphere as an attack by the Soviet Union on the United States, requiring a full retaliatory response upon the Soviet Union."
3.^ "Revealed: Israel plans nuclear strike on Iran"
4.^ Keir A. Lieber and Daryl G. Press "The Rise of U.S. Nuclear Primacy," Foreign Affairs, March/April 2006, pp 42-55.
5.^ a b Peter C. W. Flory Nuclear Exchange: Does Washington Really Have (or Want) Nuclear Primacy? Foreign Affairs, September/October 2006
6.^ [National Archives and Records Administration, RG 200, Defense Programs and Operations, LeMay's Memo to President and JCS Views, Box 83. Secret.]
7.^ http://www.nelsondemille.net/books/wild_fire.asp?id=desc
[edit] External links
"The Rise of U.S. Nuclear Primacy" from Foreign Affairs, March/April 2006
In the Shadow of MAD, an article critical of the idea of MAD as US policy.
Herman Kahn's Doomsday Machine
Excerpts of Gorbachev-Reagan Reykjavik Talks, 1986 (regards SDI as a threat to MAD)
Robert McNamara's "Mutual Deterrence" speech from 1967
Getting MAD: Nuclear Mutual Assured Destruction
Center for Arms Control and Non-Proliferation
Council for a Livable World
Nuclear Files.org Mutual Assured Destruction
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MUTUALLY ASSURED DESTRUCTION

 

M
=
4
8
MUTUALLY
125
26
8
A
=
1
7
ASSURED
87
42
6
D
=
4
11
DESTRUCTION
148
58
4
-
-
9
26
First Total
360
126
18
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
1+8
Q
-
9
8
Second Total
9
18
9
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
9
8
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
8
MUTUALLY
125
26
8
-
-
-
-
-
-
-
-
-
-
A
=
1
-
7
ASSURED
87
24
6
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
99
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
U
=
3
4
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
26
-
8
-
125
26
26
-
-
-
-
-
-
-
-
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
D
=
4
15
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
24
-
7
-
87
42
24
-
-
-
-
-
-
-
-
8
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
R
=
9
20
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
22
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
24
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
25
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
26
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
61
-
11
-
148
58
49
-
5
6
21
12
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
1+2
1+5
-
-
-
2+7
M
=
4
-
8
MUTUALLY
125
26
26
-
5
6
3
3
6
6
7
8
9
A
=
1
-
7
ASSURED
87
42
24
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
58
49
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
126
99
-
5
6
3
3
6
6
7
8
9
-
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
9+9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
9
9
18
-
5
6
3
3
6
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
5
6
3
3
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
8
MUTUALLY
125
26
8
-
-
-
-
-
-
-
-
-
-
A
=
1
-
7
ASSURED
87
24
6
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
99
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
U
=
3
4
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
D
=
4
15
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
R
=
9
20
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
22
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
24
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
25
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
26
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
-
-
-
-
-
-
-
-
-
6
21
12
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
1+2
1+5
-
-
-
2+7
M
=
4
-
8
MUTUALLY
125
26
26
-
5
6
3
3
6
6
7
8
9
A
=
1
-
7
ASSURED
87
42
24
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
58
49
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
126
99
-
5
6
3
3
6
6
7
8
9
-
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
9+9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
9
9
18
-
5
6
3
3
6
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
5
6
3
3
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
8
MUTUALLY
125
26
8
-
-
-
-
-
-
-
-
-
-
A
=
1
-
7
ASSURED
87
24
6
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
99
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
U
=
3
4
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
22
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
D
=
4
15
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
26
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
25
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
20
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
24
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
5
6
21
12
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
1+2
1+5
-
-
-
2+7
M
=
4
-
8
MUTUALLY
125
26
26
-
5
6
3
3
6
6
7
8
9
A
=
1
-
7
ASSURED
87
42
24
-
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
58
49
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
126
99
-
5
6
3
3
6
6
7
8
9
-
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
9+9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
9
9
18
-
5
6
3
3
6
6
7
8
9
-
-
-
-
-
Reduce to Deduce
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
5
6
3
3
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
M
=
4
-
8
MUTUALLY
125
26
8
-
-
-
-
-
-
-
-
-
A
=
1
-
7
ASSURED
87
24
6
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
49
4
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
99
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
S
=
1
18
1
S
19
10
1
-
1
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
T
=
2
19
1
T
20
2
2
-
-
2
-
-
-
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
U
=
3
4
1
U
21
3
3
-
-
-
3
-
-
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
-
U
=
3
12
1
U
21
3
3
-
-
-
3
-
-
-
-
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
-
C
=
3
22
1
C
3
3
3
-
-
-
3
-
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
D
=
4
15
1
D
4
4
4
-
-
-
-
4
-
-
-
-
D
=
4
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
N
=
5
26
1
N
14
5
5
-
-
-
-
-
5
-
-
-
O
=
6
25
1
O
15
6
6
-
-
-
-
-
-
6
-
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
R
=
9
13
1
R
18
9
9
-
-
-
-
-
-
-
-
9
R
=
9
20
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
24
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
5
6
21
12
15
6
7
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
1+2
1+5
-
-
2+7
M
=
4
-
8
MUTUALLY
125
26
26
-
5
6
3
3
6
6
7
9
A
=
1
-
7
ASSURED
87
42
24
-
-
-
-
-
-
-
-
-
D
=
4
-
11
DESTRUCTION
148
58
49
-
-
-
-
-
-
-
-
-
-
-
9
-
26
First Total
360
126
99
-
5
6
3
3
6
6
7
9
-
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
9+9
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
9
9
18
-
5
6
3
3
6
6
7
9
-
-
-
-
-
Reduce to Deduce
-
-
1+8
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
5
6
3
3
6
6
7
9

 

 

M
=
4
8
MUTUALLY
125
26
8
A
=
1
7
ASSURED
87
42
6
D
=
4
11
DESTRUCTION
148
58
4
-
-
9
26
First Total
360
126
18
-
-
-
2+6
Add to Reduce
3+6+0
1+2+6
1+8
Q
-
9
8
Second Total
9
18
9
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
9
8
Essence of Number
9
9
9

 

 

 

Macbeth, Act III, Scene 4 :|: Open Source Shakespeare

https://www.opensourceshakespeare.org/views/plays/play_view.php?...Act...

Lady Macbeth. Pronounce it for me, sir, to all our friends; ... But now I am cabin'd, cribb'd, confined, bound in 1300. To saucy .... By the worst means, the worst. For mine own good, All causes shall give way: I am in blood 1440. Stepp'd in so far ...

Macbeth. I hear it by the way; but I will send:
There's not a one of them but in his house
I keep a servant fee'd. I will to-morrow,
And betimes I will, to the weird sisters:
More shall they speak; for now I am bent to know,
By the worst means, the worst. For mine own good,
All causes shall give way: I am in blood
Stepp'd in so far that, should I wade no more,
Returning were as tedious as go o'er:
Strange things I have in head, that will to hand;
Which must be acted ere they may be scann'd.

 

BY THE WORST MEANS THE WORST FOR MINE OWN GOOD

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
B
=
2
1
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
2
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
W
=
5
3
5
WORST
95
32
5
-
-
-
-
-
5
-
-
-
-
M
=
4
4
5
MEANS
52
25
7
-
-
-
-
-
-
-
7
-
-
T
=
2
5
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
W
=
5
6
5
WORST
95
32
5
-
-
-
-
-
5
-
-
-
-
F
=
6
7
3
FOR
39
21
3
-
-
-
3
-
-
-
-
-
-
M
=
4
8
2
MINE
41
23
5
-
-
-
-
-
5
-
-
-
-
O
=
6
9
3
OWN
52
16
7
-
-
-
-
-
-
-
7
-
-
G
=
7
10
4
GOOD
41
23
5
-
-
-
-
-
5
-
-
-
-
-
-
43
-
37
First Total
508
211
58
-
1
2
3
4
20
12
14
8
9
-
-
4+3
-
3+7
Add to Reduce
5+0+8
2+1+1
5+8
-
-
-
-
-
2+0
1+2
1+4
-
-
-
-
7
-
10
Second Total
13
13
13
-
1
2
3
4
2
3
5
8
9
-
-
-
-
1+0
Reduce to Deduce
1+3
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
1
Essence of Number
4
4
4
-
1
2
3
4
2
3
5
8
9

 

ALL CAUSES SHALL GIVE WAY I AM IN BLOOD

STEPP'D IN SO FAR THAT SHOULD I WADE NO MORE

RETURNING WERE AS TEDIOUS AS GO O'ER

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
C
=
3
2
6
CAUSES
68
32
5
-
-
-
-
-
5
-
-
-
-
S
=
1
3
5
SHALL
52
25
7
-
-
-
-
-
-
-
7
-
-
G
=
7
4
4
GIVE
43
25
7
-
-
-
-
-
-
-
7
-
-
W
=
5
5
3
WAY
49
13
4
-
-
-
-
4
-
-
-
-
-
17
-
21
-
237
102
30
-
-
-
-
-
-
-
-
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
7
2
AM
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
8
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
B
=
2
9
5
BLOOD
48
12
3
-
-
-
3
-
-
-
-
-
-
21
-
10
-
94
40
22
-
-
-
-
-
-
-
-
-
-
S
=
1
10
6
STEPP'D
80
35
8
-
-
-
-
-
-
-
-
8
-
I
=
9
11
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
S
=
1
12
2
SO
34
16
7
-
-
-
-
-
-
-
7
-
-
F
=
6
13
3
FAR
25
16
7
-
-
-
-
-
-
-
7
-
-
T
=
2
14
4
THAT
49
13
4
-
-
-
-
4
-
-
-
-
-
S
=
1
15
6
SHOULD
79
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
16
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
W
=
5
17
4
WADE
33
15
6
-
-
-
-
-
-
6
-
-
-
N
=
5
18
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
M
=
4
19
4
MORE
51
24
6
-
-
-
-
-
-
6
-
-
-
43
-
34
-
412
187
61
-
-
-
-
-
-
-
-
-
-
9
=
9
20
9
RETURNING
126
54
9
-
-
-
-
-
-
-
-
-
9
W
=
5
2`
4
WERE
51
24
6
-
-
-
-
-
-
6
-
-
-
A
=
1
22
2
AS
20
11
2
-
-
2
-
-
-
-
-
-
-
T
=
2
23
7
TEDIOUS
93
39
3
-
-
-
3
-
-
-
-
-
-
A
=
1
24
2
AS
20
11
2
-
-
2
-
-
-
-
-
-
-
G
=
7
25
2
GO
22
13
4
-
-
-
-
4
-
-
-
-
-
O
=
6
26
3
O'ER
38
20
2
-
-
2
-
-
-
-
-
-
-
31
-
29
-
370
172
28
-
1
8
6
12
20
18
42
8
36
-
-
-
-
-
-
-
-
-
-
-
-
-
1+2
2+0
1+8
4+2
-
3+6
-
-
112
-
94
First Total
1113
501
141
-
1
8
6
3
2
9
6
8
9
-
-
1+1+2
-
9+4
Add to Reduce
1+1+1+3
5+0+1
1+4+1
-
-
-
-
-
-
-
-
-
-
-
-
4
-
13
Second Total
6
6
6
-
1
8
6
3
2
9
6
8
9
-
-
-
-
1+3
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
6
6
6
-
1
8
6
3
2
9
6
8
9

 

ALL CAUSES SHALL GIVE WAY I AM IN BLOOD

STEPP'D IN SO FAR THAT SHOULD I WADE NO MORE

RETURNING WERE AS TEDIOUS AS GO O'ER

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
3
ALL
25
7
7
-
1
-
-
-
-
-
7
-
-
C
=
3
2
6
CAUSES
68
32
5
-
1
-
-
-
5
-
-
-
-
S
=
1
3
5
SHALL
52
25
7
-
1
-
-
-
-
-
7
-
-
G
=
7
4
4
GIVE
43
25
7
-
1
-
-
-
-
-
7
-
-
W
=
5
5
3
WAY
49
13
4
-
1
-
-
4
-
-
-
-
-
I
=
9
6
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
A
=
1
7
2
AM
14
5
5
-
1
-
-
-
5
-
-
-
-
I
=
9
8
2
IN
23
14
5
-
1
-
-
-
5
-
-
-
-
B
=
2
9
5
BLOOD
48
12
3
-
1
-
3
-
-
-
-
-
-
S
=
1
10
6
STEPP'D
80
35
8
-
1
-
-
-
-
-
-
8
-
I
=
9
11
2
IN
23
14
5
-
1
-
-
-
5
-
-
-
-
S
=
1
12
2
SO
34
16
7
-
1
-
-
-
-
-
7
-
-
F
=
6
13
3
FAR
25
16
7
-
1
-
-
-
-
-
7
-
-
T
=
2
14
4
THAT
49
13
4
-
1
-
-
4
-
-
-
-
-
S
=
1
15
6
SHOULD
79
34
7
-
1
-
-
-
-
-
7
-
-
I
=
9
16
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
W
=
5
17
4
WADE
33
15
6
-
1
-
-
-
-
6
-
-
-
N
=
5
18
2
NO
29
11
2
-
1
2
-
-
-
-
-
-
-
M
=
4
19
4
MORE
51
24
6
-
1
-
-
-
-
6
-
-
-
9
=
9
20
9
RETURNING
126
54
9
-
1
-
-
-
-
-
-
-
9
W
=
5
2`
4
WERE
51
24
6
-
1
-
-
-
-
6
-
-
-
A
=
1
22
2
AS
20
11
2
-
1
2
-
-
-
-
-
-
-
T
=
2
23
7
TEDIOUS
93
39
3
-
1
-
3
-
-
-
-
-
-
A
=
1
24
2
AS
20
11
2
-
1
2
-
-
-
-
-
-
-
G
=
7
25
2
GO
22
13
4
-
1
-
-
4
-
-
-
-
-
O
=
6
26
3
O'ER
38
20
2
-
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
12
20
18
42
8
36
-
-
112
-
94
First Total
1113
501
141
-
-
8
6
1+2
2+0
1+8
4+2
-
3+6
-
-
1+1+2
-
9+4
Add to Reduce
1+1+1+3
5+0+1
1+4+1
-
-
-
-
3
2
9
6
8
9
-
-
4
-
13
Second Total
6
6
6
-
-
8
6
-
-
-
-
-
-
-
-
-
-
1+3
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
6
6
6
-
1
8
6
3
2
9
6
8
9

 

ALL CAUSES SHALL GIVE WAY I AM IN BLOOD

STEPP'D IN SO FAR THAT SHOULD I WADE NO MORE

RETURNING WERE AS TEDIOUS AS GO O'ER

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
N
=
5
18
2
NO
29
11
2
-
1
2
-
-
-
-
-
-
-
A
=
1
22
2
AS
20
11
2
-
1
2
-
-
-
-
-
-
-
A
=
1
24
2
AS
20
11
2
-
1
2
-
-
-
-
-
-
-
B
=
2
9
5
BLOOD
48
12
3
-
1
-
3
-
-
-
-
-
-
T
=
2
23
7
TEDIOUS
93
39
3
-
1
-
3
-
-
-
-
-
-
W
=
5
5
3
WAY
49
13
4
-
1
-
-
4
-
-
-
-
-
T
=
2
14
4
THAT
49
13
4
-
1
-
-
4
-
-
-
-
-
C
=
3
2
6
CAUSES
68
32
5
-
1
-
-
-
5
-
-
-
-
A
=
1
7
2
AM
14
5
5
-
1
-
-
-
5
-
-
-
-
I
=
9
8
2
IN
23
14
5
-
1
-
-
-
5
-
-
-
-
I
=
9
11
2
IN
23
14
5
-
1
-
-
-
5
-
-
-
-
W
=
5
17
4
WADE
33
15
6
-
1
-
-
-
-
6
-
-
-
M
=
4
19
4
MORE
51
24
6
-
1
-
-
-
-
6
-
-
-
W
=
5
2`
4
WERE
51
24
6
-
1
-
-
-
-
6
-
-
-
A
=
1
1
3
ALL
25
7
7
-
1
-
-
-
-
-
7
-
-
S
=
1
3
5
SHALL
52
25
7
-
1
-
-
-
-
-
7
-
-
G
=
7
4
4
GIVE
43
25
7
-
1
-
-
-
-
-
7
-
-
S
=
1
12
2
SO
34
16
7
-
1
-
-
-
-
-
7
-
-
F
=
6
13
3
FAR
25
16
7
-
1
-
-
-
-
-
7
-
-
S
=
1
15
6
SHOULD
79
34
7
-
1
-
-
-
-
-
7
-
-
S
=
1
10
6
STEPP'D
80
35
8
-
1
-
-
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
I
=
9
16
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
9
=
9
20
9
RETURNING
126
54
9
-
1
-
-
-
-
-
-
-
9
G
=
7
25
2
GO
22
13
4
-
1
-
-
4
-
-
-
-
-
O
=
6
26
3
O'ER
38
20
2
-
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
12
20
18
42
8
36
-
-
112
-
94
First Total
1113
501
141
-
-
8
6
1+2
2+0
1+8
4+2
-
3+6
-
-
1+1+2
-
9+4
Add to Reduce
1+1+1+3
5+0+1
1+4+1
-
-
-
-
3
2
9
6
8
9
-
-
4
-
13
Second Total
6
6
6
-
-
8
6
-
-
-
-
-
-
-
-
-
-
1+3
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
6
6
6
-
1
8
6
3
2
9
6
8
9

 

 

ALL CAUSES SHALL GIVE WAY I AM IN BLOOD

STEPP'D IN SO FAR THAT SHOULD I WADE NO MORE

RETURNING WERE AS TEDIOUS AS GO O'ER

 


 

THE SCULPTURE OF VIBRATIONS 1971

 

 

M
=
4
6
MENTAL
65
20
2
B
=
2
5
BLOCK
43
16
7
-
-
6
11
Add to Reduce
108
36
9
-
-
-
1+1
Reduce to Deduce
1+0+8
3+6
-
Q
-
6
2
Essence of Number
9
9
9

 

 

 

 

Daily Mail Monday, September 14, 2015

ANSWERS TO CORRESPONDENTS

Compiled by Charles Legge

QUESTION If the Japanese had not surrendered, was a third bomb considered after Hiroshima and Nagasaki?
AFTER dropping the second atomic bomb, on Nagasaki on August 9, 1945, President Harry S. Truman hoped the Japanese would surrender unconditionally. He said the thought of wiping out another 100,000 people is too horrible and I don't like the idea of killing all those kids'.
A third bomb was ready, but would not have been available until two weeks later. A list of targets, including Sapporo, Hakodate, Oyabu, Yokosuka, Osaka and Nagoya, had already been drawn up. My father was languishing in a Japanese PoW camp in Thailand when the bombs were dropped and they probably saved his life. Cecil Lowry, author: No Mercy From The Japanese (Pen and Sword Books), Stockport, Cheshire.

 

 

B
=
2
-
3
BAN
17
8
8
T
=
2
-
3
THE
33
15
6
B
=
2
-
4
BOMB
32
14
5
-
-
6
4
10
First Total
82
37
19
-
-
-
-
1+0
Add to Reduce
8+2
3+7
1+9
Q
-
6
-
1
Second Total
10
10
10
-
-
-
4
-
Reduce to Deduce
1+0
1+0
1+0
-
-
6
5
1
Essence of Number
1
1
1

 

 

-
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
8
-
-
-
6
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
14
-
-
8
-
-
-
15
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
2
1
-
-
2
-
5
-
2
-
4
2
+
=
18
1+8
=
9
=
9
=
9
-
-
2
1
-
-
20
-
5
-
2
-
13
2
+
=
45
4+5
=
9
=
9
=
9
-
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
2
1
14
-
20
8
5
-
2
15
13
2
+
=
82
8+2
=
10
1+0
1
=
1
-
-
2
1
5
-
2
8
5
-
2
6
4
2
+
=
37
3+7
=
10
1+0
1
=
1
-
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
-
--
-
--
--
--
--
--
--
--
--
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
19
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
26
-
-
10
-
37
-
28
1+9
1+0
2
-
-
-
2
-
-
-
2
-
-
2
-
-
2+6
-
-
1+0
-
3+7
-
2+8
10
1
B
A
N
-
T
H
E
-
B
O
M
B
-
-
8
-
-
1
-
10
-
10
1+0
--
2
1
5
-
2
8
5
-
2
6
4
2
-
-
-
-
-
--
-
1+0
-
1+0
1
1
B
A
N
-
T
H
E
-
B
O
M
B
-
-
8
-
-
1
-
1
-
1

 

 

10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
8
-
-
-
6
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
14
-
-
8
-
-
-
15
-
-
+
=
37
3+7
=
10
1+0
1
=
1
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
--
-
-
-
-
-
2
1
-
-
2
-
5
-
2
-
4
2
+
=
18
1+8
=
9
=
9
=
9
-
2
1
-
-
20
-
5
-
2
-
13
2
+
=
45
4+5
=
9
=
9
=
9
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
--
-
-
-
-
-
2
1
14
-
20
8
5
-
2
15
13
2
+
=
82
8+2
=
10
1+0
1
=
1
-
2
1
5
-
2
8
5
-
2
6
4
2
+
=
37
3+7
=
10
1+0
1
=
1
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
2
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
6
-
-
--
--
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
10
B
A
N
-
T
H
E
-
B
O
M
B
-
-
26
-
-
10
-
37
-
28
1+0
2
-
-
-
2
-
-
-
2
-
-
2
-
-
2+6
-
-
1+0
-
3+7
-
2+8
1
B
A
N
-
T
H
E
-
B
O
M
B
-
-
8
-
-
1
-
10
-
10
--
2
1
5
-
2
8
5
-
2
6
4
2
-
-
-
-
-
--
-
1+0
-
1+0
1
B
A
N
-
T
H
E
-
B
O
M
B
-
-
8
-
-
1
-
1
-
1

 

 

S
=
1
-
12
SCHRODINGERS
139
67
4
C
=
3
-
3
CAT
24
6
6
D
=
4
-
3
DID
17
17
8
C
=
3
-
10
CURIOUSITY
160
52
7
K
=
2
-
4
KILL
44
17
6
T
=
2
-
3
THE
33
15
6
C
=
3
-
3
CAT
24
6
6
-
-
18
4
38
First Total
441
180
19
-
-
1+8
-
3+8
Add to Reduce
4+4+1
1+8+0
6+2
-
-
9
-
11
Second Total
9
10
10
4
4
-
4
1+1
Reduce to Deduce
-
1+0
1+0
Q
-
9
5
2
Essence of Number
9
7
7

 

 

THOUGHT NEGATIVE BALANCING POSITIVE THOUGHT

THOUGHT POSITIVE BALANCING NEGATIVE THOUGHT

FIRST LAW GODS LAW FIRST

 

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

14
ALBERT EINSTEIN
153
63
9
25
GENERAL THEORY OF RELATIVITY
315
135
9

 

 

3
THE
33
15
6
4
LAWS
55
10
1
2
OF
21
12
3
15
ELECTRODYNAMICS
166
67
4
24
First Total
275
104
14
2+4
Add to Reduce
2+7+5
1+0+4
1+4
6
Second Total
14
5
5
-
Reduce to Deduce
1+4
-
-
6
Essence of Number
5
5
5

 

 

T
=
2
14
THERMODYNAMICS
167
68
5
E
=
5
15
ELECTRODYNAMICS
166
67
4
-
-
7
29
Add to Reduce
333
135
9
-
-
-
11
Reduce to Deduce
3+3+3
1+3+5
-
-
-
7
2
Essence of Number
9
9
9

 

 

6
DYNAMO
72
54
9
7
DYNAMIC
69
33
6
8
DYNAMICS
88
34
7

 

 

-
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
-
-
-
6
-
-
-
9
1
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
14
-
9
-
-
-
15
-
-
-
9
19
-
+
=
66
6+6
=
12
1+2
3
=
3
-
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
-
-
3
3
-
3
2
5
-
-
5
+
=
24
2+4
=
6
=
6
=
6
-
-
1
-
20
-
-
3
12
-
3
11
23
-
-
5
+
=
78
7+8
=
15
1+5
6
=
6
-
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
1
14
20
9
-
3
12
15
3
11
23
9
19
5
+
=
144
1+4+4
=
9
=
9
=
9
-
-
1
5
2
9
-
3
3
6
3
2
5
9
1
5
+
=
54
5+4
=
9
=
9
=
9
-
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
3
-
3
-
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
19
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
26
-
-
13
-
54
-
36
1+9
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
2+6
-
-
1+3
-
5+4
-
3+6
10
13
A
N
T
I
-
C
L
O
C
K
W
I
S
E
-
-
8
-
-
4
-
9
-
9

 

 

13
ANTI CLOCKWISE
-
-
-
-
CLOCKWISE
100
37
1
-
ANTI
44
17
8
13
ANTI CLOCKWISE
144
54
9
1+3
-
1+4+4
5+4
-
4
ANTI CLOCKWISE
9
9
9

 

 

-
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
9
-
-
-
9
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
-
-
14
-
-
9
-
-
-
9
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
-
-
4
1
7
-
5
2
-
3
-
6
-
5
3
4
+
=
40
4+0
=
4
=
4
=
4
-
-
13
1
7
-
5
20
-
3
-
6
-
5
12
4
+
=
76
7+6
=
13
1+3
4
=
4
-
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
-
-
13
1
7
14
5
20
9
3
-
6
9
5
12
4
+
=
108
1+0+8
=
9
=
9
=
9
-
-
4
1
7
5
5
2
9
3
-
6
9
5
3
4
+
=
63
6+3
=
9
=
9
=
9
-
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
6
--
-
-
-
--
--
6
occurs
x
1
=
6
=
6
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
37
-
-
13
-
63
-
45
-
-
-
-
-
-
-
-
9
-
-
-
9
--
-
-
-
-
10
-
-
1+3
-
6+3
-
4+5
8
13
M
A
G
N
E
T
I
C
-
F
I
E
L
D
-
-
1
-
-
4
-
9
-
9

 

 

6
GLOBAL
49
22
4
7
WARNING
86
41
5
13
Add to Reduce
135
63
9
1+3
Reduce to Deduce
1+3+5
6+3
-
4
Essence of Number
9
9
9

 

 

6
GLOBAL
49
22
4
7
WARMING
85
40
4
13
Add to Reduce
134
62
8
1+3
Reduce to Deduce
1+3+4
6+2
-
4
Essence of Number
8
8
8

 

 

6
LIVING
73
37
1
3
THE
33
15
6
4
MYTH
66
21
3
13
First Total
172
73
10
1+3
Add to Reduce
1+7+2
7+3
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

3
THE
33
15
6
5
POINT
74
29
2
2
OF
21
12
3
2
NO
29
11
2
6
RETURN
96
33
6
18
First Total
253
100
19
1+8
Add to Reduce
2+5+3
1+0+0
1+9
9
Second Total
10
1
10
-
Reduce to Deduce
1+0
-
1+0
9
Essence of Number
1
1
1

 

 

T
=
2
-
3
THE
33
15
6
A
=
1
-
6
ATOMIC
61
25
7
B
=
2
-
4
BOMB
32
14
5
-
-
12
-
13
Add to Reduce
126
54
18
-
-
1+2
-
1+3
Reduce to Deduce
1+2+6
5+4
1+8
-
-
3
-
4
Essence of Number
9
9
9

 

 

AT OM I SEE BE OM BE

 

 

10
ATOMIC BOMB
-
-
-
-
A+T
21
3
3
-
O+M
28
10
1
-
I
9
9
9
-
C
3
3
3
-
B
2
2
2
-
O+M
28
10
1
-
B
2
2
2
10
ATOMIC BOMB
93
39
21
1+0
-
9+3
3+9
2+1
1
ATOMIC BOMB
12
12
3
-
-
1+2
1+2
-
1
ATOMIC BOMB
3
3
3

......

 
 
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