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Evokation
  
 
Index
  

 

 

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

 

 

ADVENT 752 ADVENT

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

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

 

 

THURSDAY

THE

THIRTEENTH OF SEPTEMBER 2007

 

 

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

 

 

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

 

 

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

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-``
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
17
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
1+7
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
8
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
8
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

BREATHE ON ME BREATH OF GOD

 

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

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

 

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

 

 

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

 

 

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

 

 

-
BLACK HOLE
-
-
-
5
BLACK
29
11
2
4
HOLE
40
22
4
9
BLACK HOLE
69
33
6
-
-`
6+9
3+3
-
9
BLACK HOLE
15
6
6
-
-`
1+5
-
-
9
BLACK HOLE
6
6
6

 

 

-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
8
6
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
-
-
-
-
8
15
-
-
+
=
23
2+3
=
5
=
5
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
2
3
1
3
2
-
-
-
3
5
+
=
19
1+9
=
10
1+0
1
-
-
2
12
1
3
11
-
-
-
12
5
+
=
46
4+6
=
1
=
1
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
2
12
1
3
11
-
8
15
12
5
+
=
69
6+9
=
15
=
9
-
-
2
3
1
3
2
-
8
6
3
5
+
=
33
3+3
=
6
=
6
-
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
3
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
20
9
B
L
A
C
K
-
H
O
L
E
-
-
25
-
-
9
-
33
2+0
-
-
3
-
3
-
-
-
-
3
-
-
-
2+5
-
-
-
-
3+3
2
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6
-
-
2
3
1
3
2
-
8
6
3
5
-
-
-
-
-
--
-
-
2
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6

 

 

9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
6
-
-
+
=
14
1+4
=
5
=
5
-
-
-
-
-
-
-
8
15
-
-
+
=
23
2+3
=
5
=
5
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
2
3
1
3
2
-
-
-
3
5
+
=
19
1+9
=
10
1+0
1
-
2
12
1
3
11
-
-
-
12
5
+
=
46
4+6
=
1
=
1
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
--
-
-
-
2
12
1
3
11
-
8
15
12
5
+
=
69
6+9
=
15
=
9
-
2
3
1
3
2
-
8
6
3
5
+
=
33
3+3
=
6
=
6
9
B
L
A
C
K
-
H
O
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
-
-
3
-
3
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
9
B
L
A
C
K
-
H
O
L
E
-
-
25
-
-
9
-
33
-
-
3
-
3
-
-
-
-
3
-
-
-
2+5
-
-
-
-
3+3
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6
-
2
3
1
3
2
-
8
6
3
5
-
-
-
-
-
--
-
-
9
B
L
A
C
K
-
H
O
L
E
-
-
7
-
-
9
-
6

 

 

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
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
-
-
-
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
1
Essence of Number
1
1
1

 

 

20
ELECTROMAGNETIC LIGHT
206
98
8
-
-
-
-
-
21
ELECTROMAGNETIC LIGHTS
-
-
-
-
E+L+E+C+T
45
18
9
-
R
18
9
9
-
O+M+A+G
36
18
9
-
N+E+T
39
12
3
-
I
9
9
9
-
C
3
3
3
-
L
12
3
3
-
I
9
9
9
-
G+H+T+S
54
18
9
21
ELECTROMAGNETIC LIGHTS
225
99
63
2+0
-
2+2+5
9+9
6+3
21
ELECTROMAGNETIC LIGHTS
9
18
9
1+0
-
-
1+8
-
21
ELECTROMAGNETIC LIGHTS
9
9
9

 

 

Q
=
8
=
7
QUANTUM
107
26
8
E
=
5
=
7
ELECTRO
78
33
6
G
=
7
=
8
DYNAMICS
88
34
7
-
-
20
-
22
First Total
273
93
21
-
-
2+0
-
2+2
Add to Reduce
2+7+3
9+3
2+1
-
-
2
-
4
Second Total
12
12
3
-
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
2
-
4
Essence of Number
3
3
3

 

 

E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
78
33
6
F
=
6
=
6
FORCES
66
30
3
-
-
15
-
22
First Total
216
93
21
-
-
1+5
-
2+1
Add to Reduce
2+1+6
9+3
2+1
-
-
6
-
3
Second Total
9
12
9
-
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
6
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
18
-
3
-
27
18
18
-
-
-
-
-
-
-
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
27
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 4 = 40

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 4 = 20

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
72
36
9
E
=
5
=
6
ENERGY
74
38
2
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
33
-
7
-
78
33
33
-
-
-
-
-
-
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
10
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
20
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
38
-
6
-
74
38
38
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
G
=
7
10
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
G
=
7
20
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 7 = 35

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 7 = 35

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

ELECTRO MAGNETIC ENERGY

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
72
36
9
E
=
5
=
6
ENERGY
74
38
2
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
-
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
4
2
C+T
23
3
3
-
-
-
-
-
5
-
-
-
-
-
-
-
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
27
18
18
-
-
-
-
-
-
-
-
-
-
-
-
-
8
2
M+A
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
10
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
13
3
T+I+C
32
14
5
-
-
-
-
-
5
-
-
-
-
-
-
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
20
1
G+Y
32
14
5
-
-
-
-
-
5
-
-
-
-
-
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
5
1
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
2
1
L
12
3
3
-
1
2
3
-
-
-
-
8
-
-
-
5
3
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
4
1
C+T
23
3
3
-
1
2
-
-
5
-
-
8
-
-
-
-
6
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
7
1
O
15
6
6
-
1
2
-
-
-
6
-
8
-
-
-
-
8
1
M+A
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
10
1
G
7
7
7
-
1
2
-
-
-
-
7
8
-
-
-
-
11
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
12
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
13
1
T+I+C
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
16
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
17
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
18
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
19
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
20
1
G+Y
32
14
5
-
1
2
-
-
5
-
-
8
-
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
3
2
1
L
12
3
3
-
1
2
3
-
-
-
-
8
-
-
-
5
1
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
5
3
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
4
1
C+T
23
3
3
-
1
2
-
-
5
-
-
8
-
-
-
-
8
1
M+A
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
11
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
12
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
13
1
T+I+C
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
16
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
17
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
18
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
20
1
G+Y
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
7
1
O
15
6
6
-
1
2
-
-
-
6
-
8
-
-
-
-
10
1
G
7
7
7
-
1
2
-
-
-
-
7
8
-
-
-
-
19
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
6
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
3
5
6
7
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
6
7
9
-
-
3
2
1
L
12
3
3
-
3
-
-
-
-
-
-
5
1
1
E
5
5
5
-
-
5
-
-
-
-
-
5
3
1
E
5
5
5
-
-
5
-
-
-
-
-
3
4
1
C+T
23
3
3
-
-
5
-
-
-
-
-
-
8
1
M+A
14
5
5
-
-
5
-
-
-
-
-
-
11
1
N
14
5
5
-
-
5
-
-
-
-
-
-
12
1
E
5
5
5
-
-
5
-
-
-
-
-
-
13
1
T+I+C
32
14
5
-
-
5
-
-
-
-
-
-
16
1
E
5
5
5
-
-
5
-
-
-
-
-
-
17
1
N
14
5
5
-
-
5
-
-
-
-
-
-
18
1
E
5
5
5
-
-
5
-
-
-
-
-
-
20
1
G+Y
32
14
5
-
-
5
-
-
-
-
-
-
7
1
O
15
6
6
-
-
-
6
-
-
-
-
-
10
1
G
7
7
7
-
-
-
-
7
-
-
-
-
19
1
R
18
9
9
-
-
-
-
-
9
-
-
-
6
1
R
18
9
9
-
-
-
-
-
9
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
3
55
6
7
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
5+5
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
3
10
6
7
9
E
=
5
=
6
ENERGY
74
38
2
-
-
1+0
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
3
1
6
7
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
9
1
6
7
9

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

6
SHEMSU
85
22
4
3
HOR
41
23
5
9
Add to Reduce
126
45
9
-
Reduce to Deduce
1+5+9
6+0
-
9
Essence of Number
15
6
9

 

library.thinkquest.org/27356/d_coherentlight.htm

Coherent light

Coherent light are light waves that are "in phase" with one another.

For example, two waves are coherent if the crests of one wave are aligned with the crests of the other and the troughs of one wave are aligned with the troughs of the other. Otherwise, these lightwaves are considered incoherent.

(Illustration omitted)
[ Two coherent waves ]

Light produced by lasers are coherent light. Light from light bulbs or the sun, however, are incoherent light

 

8
COHERENT
88
43
7
5
LIGHT
56
29
2
13
Add to Reduce
144
72
9
1+3
Reduce to Deduce
1+4+4
7+2
-
4
Essence of Number
9
9
9

 

 

-T
13
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
-
-
-
--
-T
-
-
-
-T
`-
-
6
8
-
-
-
5
-
-
-
9
-
8
-
+
=
36
3+6
=
9
-
9
-
9
-
`-
-
15
8
-
-
-
14
-
-
-
9
-
8
-
+
=
54
5+4
=
9
-
9
-
9
-
13
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
3
-
-
5
9
5
-
2
-
3
-
7
-
2
+
=
36
3+6
=
9
-
9
-
9
-
`-
3
-
-
5
18
5
-
20
-
12
-
7
-
20
+
=
90
9+0
=
9
-
9
-
9
-
13
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
3
15
8
5
18
5
14
20
-
12
9
7
8
20
+
=
144
1+4+4
=
9
-
9
-
9
-
-
3
6
8
5
9
5
5
2
-T
3
9
7
8
2
+
=
72
7+2
=
9
-
9
-
9
-
13
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-T
-T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
8
occurs
x
2
=
16
 1+6
7
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
=
9
5
13
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
40
-
1
13
-
72
-
45
-
 1+3
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
4+0
-
-
1+3
-
7+2
-
4+5
5
4
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
5
-
1
4
-
9
-
9
-
-
3
6
8
5
9
5
5
2
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
5
4
C
O
H
E
R
E
N
T
-
L
I
G
H
T
-
-
5
-
-
4
-
9
-
9

 

 

3
GAS
27
18
9
6
LIQUID
72
36
9
5
SOLID
59
14
5
14
First Total
158
68
23
1+4
Add to Reduce
1+5+8
6+8
2+3
5
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
5
Essence of Number
5
5
5

 

 

3
THE
33
15
6
7
SIXTEEN
96
33
6
5
STATE
65
11
2
15
First Total
194
59
14
1+5
Add to Reduce
1+9+4
5+9
1+4
6
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
6
Essence of Number
5
5
5

 

 

3
THE
33
15
6
9
SIXTEENTH
124
25
7
5
STATE
65
11
2
17
Add to Reduce
222
51
15
1+7
Reduce to Deduce
2+2+2
5+1
1+5
8
Essence of Number
6
6
6

 

 

B
=
2
4
BOSE
41
14
5
E
=
5
8
EINSTEIN
95
41
5
C
=
3
10
CONDENSATE
100
37
1
-
-
10
24
First Total
236
92
11
-
-
 1+0 2+4
Add to Reduce
2+3+6
9+2
1+1
Q
-
1
6
Second Total
11
11
2
-
-
-
=
Reduce to Deduce
1+1
1+1
-
-
-
1
6
Essence of Number
2
2
2

 

 

B
=
2
6
BOSONS
84
21
3
P
=
7
7
PHOTONS
107
35
8
-
-
9
13
First Total
191
56
11
-
-
-
1+3
Add to Reduce
1+9+1
5+6
1+1
Q
-
9
4
Second Total
11
11
2
-
-
-
=
Reduce to Deduce
1+1
1+1
-
-
-
9
4
Essence of Number
2
2
2

 

 

Q
=
8
7
QUANTUM
107
26
8
S
=
1
5
STATE
65
11
2
-
-
9
12
First Total
172
37
10
-
-
-
1+2
Add to Reduce
1+7+2
3+7
1+0
Q
-
9
3
Second Total
10
10
1
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
9
3
Essence of Number
1
1
1

 

 

P
=
7
7
PERFECT
73
37
1
C
=
3
8
COHERENT
88
43
7
L
=
3
5
LIGHT
56
29
2
-
-
13
20
First Total
217
109
10
-
-
1+3
2+0
Add to Reduce
2+1+7
1+0+9
1+0
Q
-
4
2
Second Total
10
10
1
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
4
2
Essence of Number
1
1
1

 

 

9
PERFECTLY
110
47
2
8
COHERENT
88
43
7
5
LIGHT
56
29
2

 

 

5
WHITE
65
29
2
5
LIGHT
56
29
2

 

 

-
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
8
9
-
-
-
-
9
-
8
-
+
=
42
4+2
=
6
-
6
-
6
-13
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
5
-
-
2
5
-
3
-
7
-
2
+
=
31
3+1
=
4
-
4
-
4
-
-
20
-
5
-
23
-
-
20
5
-
12
-
7
-
20
+
=
112
1+1+2
=
4
-
4
-
4
-
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
23
8
9
20
5
-
12
9
7
8
20
+
=
154
1+5+4
=
10
1+0
1
-
1
-
-
2
8
5
-
5
8
9
2
5
-
3
9
7
8
2
+
=
73
7+3
=
10
1+0
1
-
1
-
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
8
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
34
-
-
13
-
73
-
37
1+1
1+3
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+3
-
7+3
-
3+7
2
4
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
7
-
-
4
-
10
-
10
-
-
2
8
5
-
5
8
9
2
5
-
3
9
7
8
2
-
-
-
-
-
-
-
1+0
-
1+0
2
4
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
7
-
-
4
-
1
-
1

 

 

13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
8
9
-
-
-
-
9
-
8
-
+
=
42
4+2
=
6
-
6
-
6
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
5
-
-
2
5
-
3
-
7
-
2
+
=
31
3+1
=
4
-
4
-
4
-
20
-
5
-
23
-
-
20
5
-
12
-
7
-
20
+
=
112
1+1+2
=
4
-
4
-
4
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
23
8
9
20
5
-
12
9
7
8
20
+
=
154
1+5+4
=
10
1+0
1
-
1
-
2
8
5
-
5
8
9
2
5
-
3
9
7
8
2
+
=
73
7+3
=
10
1+0
1
-
1
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
5
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
8
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
34
-
-
13
-
73
-
37
1+3
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
3+4
-
-
1+3
-
7+3
-
3+7
4
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
7
-
-
4
-
10
-
10
-
2
8
5
-
5
8
9
2
5
-
3
9
7
8
2
-
-
-
-
-
-
-
1+0
-
1+0
4
T
H
E
-
W
H
I
T
E
-
L
I
G
H
T
-
-
7
-
-
4
-
1
-
1

 

 

-
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
-
-
9
-
-
9
-
-
1
6
-
9
-
+
=
35
3+5
=
8
-
8
-
8
-
-
-
-
19
-
-
9
-
-
9
-
-
19
15
-
9
-
+
=
80
8+0
=
8
-
8
-
8
-
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
-
-
-
-
-
-
-
7
1
-
-
3
-
8
3
-
4
-
-
-
3
-
4
+
=
33
3+3
=
6
=
6
-
6
-
-
7
1
-
-
12
-
17
21
-
4
-
-
-
12
-
4
+
=
78
7+8
=
15
1+5
6
-
6
-
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
7
1
19
-
12
9
17
21
9
4
-
19
15
12
9
4
+
=
158
1+5+8
=
14
1+4
5
-
5
-
-
7
1
1
-
3
9
8
3
9
4
-
1
6
3
9
4
+
=
68
6+8
=
14
1+4
5
-
5
-
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
2
``-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
3
-
-
-
-
3
occurs
x
3
=
9
-
9
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
-
8
5
``-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
38
-
-
14
-
68
-
50
-
1+4
-
-
-
-
-
9
-
-
9
-
-
-
-``
-
9
-
-
-
3+8
-
-
1+4
-
6+8
-
5+0
7
5
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
11
-
-
5
-
14
-
5
-
-
7
1
1
-
3
9
8
3
9
4
-
1
6
3
9
4
-
-
1+1
-
-
-
-
1+4
-
-
7
5
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
2
-
-
5
-
5
-
5

 

 

14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
9
-
-
9
-
-
1
6
-
9
-
+
=
35
3+5
=
8
-
8
-
8
-
-
-
19
-
-
9
-
-
9
-
-
19
15
-
9
-
+
=
80
8+0
=
8
-
8
-
8
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
-
-
-
-
-
-
7
1
-
-
3
-
8
3
-
4
-
-
-
3
-
4
+
=
33
3+3
=
6
=
6
-
6
-
7
1
-
-
12
-
17
21
-
4
-
-
-
12
-
4
+
=
78
7+8
=
15
1+5
6
-
6
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
--
-
-
-
-
-
7
1
19
-
12
9
17
21
9
4
-
19
15
12
9
4
+
=
158
1+5+8
=
14
1+4
5
-
5
-
7
1
1
-
3
9
8
3
9
4
-
1
6
3
9
4
+
=
68
6+8
=
14
1+4
5
-
5
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
3
-
-
3
-
-
-
-
-
3
-
-
-
-
3
occurs
x
3
=
9
-
9
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
14
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
38
-
-
14
-
68
-
50
1+4
-
-
-
-
-
9
-
-
9
-
-
-
-``
-
9
-
-
-
3+8
-
-
1+4
-
6+8
-
5+0
5
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
11
-
-
5
-
14
-
5
-
7
1
1
-
3
9
8
3
9
4
-
1
6
3
9
4
-
-
1+1
-
-
-
-
1+4
-
-
5
G
A
S
-
L
I
Q
U
I
D
-
S
O
L
I
D
-
-
2
-
-
5
-
5
-
5

 

 

DAILY MAIL

Friday,August 31, 2007

Jonathan Cainer

Page 31

"THEY now tell us, with a straight face, that in deep space, experts have discovered a billion miles of nothing. Sorry, I know I have already written about this. But I can't quite manage to stop thinking, about it. Nothing? Nothing we recognise, perhaps. Nothing we can detect. Nothing doing. Nothing happening. Nothing to report. Nothing to write home about. But surely there can't be absolutely Nothing at all. And why 'a billion miles'? This may sound like a lot, but I rather feel it's not big enough to be convincing. Surely, nothing lasts for ever!

 

1
-
7
NOTHING
87
42
6
2
-
7
NOTHING
87
42
6
3
-
7
NOTHING
87
42
6
4
-
7
NOTHING
87
42
6
5
-
7
NOTHING
87
42
6
6
-
7
NOTHING
87
42
6
7
-
7
NOTHING
87
42
6
8
-
7
NOTHING
87
42
6
9
-
7
NOTHING
87
42
6
10
-
7
NOTHING
87
42
6

 

 

DAILY MAIL

Monday, September 3, 2007

Jonathan Cainer

A BILLION miles of 'nothing' in space. I still can't stop thinking about it. I reckon those people who sell the names of stars as novelty gifts should package it up. This would entitle the new 'owners' to sing the Gershwin lyrics from Porgy And Bess: 'I've got plenty of nothing... and nothing's plenty for me.'
Alternatively, those from a different generation could hum the Dire Straits tune Money For Nothing. Then one day, when we crack the conundrum of how to travel faster than light, tourists can go there for excursions - while singing the movie song Busy Doing Nothing.

 

 

-
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
5
6
-
8
9
5
-
5
-
1
1
+
=
40
4+0
=
4
=
4
=
4
-
-``
14
15
-
8
9
14
-
14
-
19
19
+
=
112
1+1+2
=
4
=
4
=
4
-
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
2
-
-
-
7
-
5
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
-
20
-
-
-
7
-
5
-
-
+
=
32
3+2
=
5
=
5
=
5
-
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
14
15
20
8
9
14
7
14
5
19
19
+
=
144
1+4+4
=
9
=
9
=
9
-
-
5
6
2
8
9
5
7
5
5
1
1
+
=
54
5+4
=
9
=
9
=
9
-
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
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
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
11
N
O
T
H
I
N
G
N
E
S
S
-
-
38
-
-
11
-
54
-
36
-
1+1
5
-
-
-
-
5
-
5
5
-
-
-
-
3+8
-
-
1+1
-
5+4
-
3+6
7
2
N
O
T
H
I
N
G
N
E
S
S
-
-
11
-
-
2
-
9
-
9
-
-
5
6
2
8
9
5
7
5
5
1
1
-
-
1+1
-
-
=
-
-
-
-
7
2
N
O
T
H
I
N
G
N
E
S
S
-
-
2
-
-
2
-
9
-
9

 

 

11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
5
6
-
8
9
5
-
5
-
1
1
+
=
40
4+0
=
4
=
4
=
4
-``
14
15
-
8
9
14
-
14
-
19
19
+
=
112
1+1+2
=
4
=
4
=
4
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
-
2
-
-
-
7
-
5
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
20
-
-
-
7
-
5
-
-
+
=
32
3+2
=
5
=
5
=
5
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
14
15
20
8
9
14
7
14
5
19
19
+
=
144
1+4+4
=
9
=
9
=
9
-
5
6
2
8
9
5
7
5
5
1
1
+
=
54
5+4
=
9
=
9
=
9
11
N
O
T
H
I
N
G
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
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
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
11
N
O
T
H
I
N
G
N
E
S
S
-
-
38
-
-
11
-
54
-
36
1+1
5
-
-
-
-
5
-
5
5
-
-
-
-
3+8
-
-
1+1
-
5+4
-
3+6
2
N
O
T
H
I
N
G
N
E
S
S
-
-
11
-
-
2
-
9
-
9
-
5
6
2
8
9
5
7
5
5
1
1
-
-
1+1
-
-
=
-
-
-
-
2
N
O
T
H
I
N
G
N
E
S
S
-
-
2
-
-
2
-
9
-
9

 

 

-
8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
-
1
1
+
=
7
-
=
7
=
7
=
7
-
-``
-
-
-
-
14
-
19
19
+
=
52
5+2
=
7
=
7
=
7
-
8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
6
3
3
3
-
5
-
-
+
=
20
2+0
=
2
-
2
=
2
-
-
6
21
12
12
-
5
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
6
21
12
12
14
5
19
19
+
=
108
1+0+8
=
9
=
9
=
9
-
-
6
3
3
3
5
5
1
1
+
=
27
2+7
=
9
=
9
=
9
-
8
F
U
L
L
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
30
8
F
U
L
L
N
E
S
S
-
-
15
-
-
8
-
27
-
18
3+0
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
-
2+7
-
1+8
3
8
F
U
L
L
N
E
S
S
-
-
6
-
-
8
-
9
-
9
-
-
6
2
2
2
5
5
1
1
-
-
-
-
-
=
-
-
-
-
3
8
F
U
L
L
N
E
S
S
-
-
6
-
-
8
-
9
-
9

 

 

8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
1
1
+
=
7
-
=
7
=
7
=
7
-``
-
-
-
-
14
-
19
19
+
=
52
5+2
=
7
=
7
=
7
8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
6
3
3
3
-
5
-
-
+
=
20
2+0
=
2
-
2
=
2
-
6
21
12
12
-
5
-
-
+
=
56
5+6
=
11
1+1
2
=
2
8
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
6
21
12
12
14
5
19
19
+
=
108
1+0+8
=
9
=
9
=
9
-
6
3
3
3
5
5
1
1
+
=
27
2+7
=
9
=
9
=
9
8
F
U
L
L
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
-
-
3
3
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
5
5
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
8
F
U
L
L
N
E
S
S
-
-
15
-
-
8
-
27
-
18
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
-
2+7
-
1+8
8
F
U
L
L
N
E
S
S
-
-
6
-
-
8
-
9
-
9
-
6
2
2
2
5
5
1
1
-
-
-
-
-
=
-
-
-
-
8
F
U
L
L
N
E
S
S
-
-
6
-
-
8
-
9
-
9

 

 

-
19
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
5
6
-
8
9
5
-
5
-
1
1
-
-
-
-
-
5
-
1
1
+
=
47
4+7
=
11
1+1
2
=
2
-
-``
14
15
-
8
9
14
-
14
-
19
19
-
-
-
-
-
14
-
19
19
+
=
164
1+6+4
=
11
1+1
2
=
2
-
19
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
2
-
-
-
7
-
5
-
-
-
6
3
3
3
-
5
-
-
+
=
34
3+4
=
7
-
7
=
7
-
-
-
-
20
-
-
-
7
-
5
-
-
-
6
21
12
12
-
5
-
-
+
=
88
8+8
=
16
1+6
7
=
7
-
19
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
-
-
-
--
-
-
-
-
-
-
14
15
20
8
9
14
7
14
5
19
19
-
6
21
12
12
14
5
19
19
+
=
252
2+5+2
=
9
=
9
=
9
-
-
5
6
2
8
9
5
7
5
5
1
1
-
6
3
3
3
5
5
1
1
+
=
81
8+1
=
9
=
9
=
9
-
19
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
3
3
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
-
-
-
-
-
-
-
5
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
7
=-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
4
19
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
41
-
-
19
-
81
-
45
-
1+9
5
-
-
-
-
5
-
5
5
-
-
-
-
-
-
-
5
5
-
-
-
-
4+1
-
-
1+9
-
8+1
-
4+5
4
10
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
5
-
-
10
-
9
-
9
-
1+0
5
6
2
8
9
5
7
5
5
1
1
-
6
2
2
2
5
5
1
1
-
-
-
-
-
1+0
-
-
-
-
4
1
N
O
T
H
I
N
G
N
E
S
S
-
F
U
L
L
N
E
S
S
-
-
5
-
-
1
-
9
-
9

 

 

9
SPRINKLED
108
45
9
9
STARLIGHT
114
42
6

 

 

4
STAR
58
13
4
8
STARDUST
122
23
5

 

 

I

ME

ENTANGLEMENTS

 

 

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other ...en.wikipedia.org/wiki/Quantum_entanglement

Quantum entanglement

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. This leads to correlations between observable physical properties of the systems. For example, it is possible to prepare two particles in a single quantum state such that when one is observed to be spin-up, the other one will always be observed to be spin-down and vice versa, this despite the fact that it is impossible to predict, according to quantum mechanics, which set of measurements will be observed. As a result, measurements performed on one system seem to be instantaneously influencing other systems entangled with it. But quantum entanglement does not enable the transmission of classical information faster than the speed of light (see discussion in next section below).

Quantum entanglement applications in the emerging technologies of quantum computing and quantum cryptography, and has been used to realize quantum teleportation experimentally. At the same time, it prompts some of the more philosophically oriented discussions concerning quantum theory. The correlations predicted by quantum mechanics, and observed in experiment, reject the principle of local realism , which is that information about the state of a system should only be mediated by interactions in its immediate surroundings. Different views of what is actually occurring in the process of quantum entanglement can be related to different interpretations of quantum mechanics.

 

 

Quantum entanglement just got a whole lot weirder, says Michael Brooks ... The team believe that quantum entanglement between the atoms is the only ..www.biophysica.com/quantum

Entanglement:  The weirdest link

New Scientist vol 181 issue 2440 - 27 March 2004, page 32

That spooky connection between tiny particles is appearing everywhere, and its consequences are even affecting the world that we experience. It seems to unravel the past, and may be what keeps us alive. Quantum entanglement just got a whole lot weirder, says Michael Brooks

ENTANGLEMENT. Erwin Schrödinger called this phenomenon the defining trait of quantum theory. Einstein famously dubbed it spukhafte Fernwirkungen: "spooky action at a distance". It is not hard to understand why. Set things up correctly, and you can instantaneously affect the physical properties of a particle on the other side of the universe simply by prodding its entangled twin.

This is no longer just a curiosity of the quantum world, visible only in excruciatingly delicate experiments. Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, "macroscopic" world that we inhabit.

It is a discovery that might have far-reaching consequences. Not only will it give us a better grip on technological applications, such as quantum computing and cryptography, and the teleportation of quantum states, it could also open up a whole new realm of reality, enabling us to retain and control quantum weirdness in our everyday world. And it's not just a strange kind of "remote control" over matter that is at stake. Entanglement could even be the key to understanding what gives rise to the phenomenon of life. It's enough to set Einstein spinning in his grave.

Entanglement has been an affront to our sensibilities for several decades now. Schrödinger discovered it through his newly formed quantum theory, when he examined the mathematical descriptions of two quantum particles that bump into one other. After the interaction, it is impossible to tease apart the two particles' characteristics. Once they are entangled, it makes no sense to talk about the properties of just one of them. All the information about the particles, such as their momentum and spin, lies only in their joint properties. So if something affects the quantum state of one particle, it will inevitably affect the quantum state of the other, no matter how far apart they are. It is this that gives entanglement the "spooky" character that Einstein found so distasteful.

Although it seems like something from the realm of fantasy, many physicists now use entanglement as a kind of resource for experiments and applications. Entangled pairs of quantum particles such as photons are routinely created and sent down microscopes or fired across vast distances. Their spooky properties are used to perform such feats as high-resolution imaging, quantum teleportation or quantum cryptography.

But, despite the growing use of entanglement as a technological tool, physicists are beginning to realise we have only just scratched the surface of its potential. "Are there some other forms of entanglement that we haven't yet discovered?" asks Benni Reznik, a theoretical physicist at Tel Aviv University in Israel. "I think there are."

Just how little we know about entanglement was made crystal clear last year by a collaboration led by Sayantani Ghosh at the University of Chicago (Nature, vol 425, p 48). The team analysed experiments done more than a decade ago with a sample of a magnetic salt containing holmium atoms, and compared them with theoretical predictions. What they found is extraordinary.

The holmium atoms within the salt behave like tiny magnets and respond to each others' magnetic fields by adjusting their relative orientation, just as a compass needle orients itself to align with the Earth's magnetic field. But the atoms change this settled orientation if they are placed in an external magnetic field. The degree to which they align with the field is known as the salt's "magnetic susceptibility".

Ghosh and his colleagues examined how the susceptibility of the salt varied with temperature. They expected it would decrease as the temperature rose, because the extra energy at higher temperatures disrupts the atoms' ability to maintain the optimum alignment. And it did. But at very low temperatures, the atoms were aligned to a greater degree than would be expected if they had normal quantum energy levels (Graphic omitted). The team believe that quantum entanglement between the atoms is the only explanation for this phenomenon.

It's a big shock: it shows that the quantum phenomenon of entanglement, whose power was thought to be confined to the infinitesimal world of subatomic particles, can produce effects that remain measurable on macroscopic scales.

Ghosh and his colleagues also showed that entanglement affects the salt's heat capacity, defined as the amount of heat needed to change the temperature of a kilogram of substance by 1 kelvin. Throw in some heat, and you can only determine exactly how far the salt's temperature will rise if you take entanglement between atoms into account.

According to Vlatko Vedral, a theoretical physicist at Imperial College in London, these discoveries are highly important. Vedral was one of the team that first predicted the effect, three years ago (Physical Review Letters, vol 87, p 017901). The fact that the prediction has been borne out by experiment catapults the mystery of entanglement into the list of big unanswered questions that scientists need to address, he says.

That's partly because physicists can no longer content themselves with using the quantum and classical energy level descriptions of a material if they want to determine and understand its properties. The effects of entanglement now have to be included as an integral part of any accurate calculation.

But the results also suggest that, if we knew where to look, we might find entanglement causing significant effects in other materials. "It's not just magnetic salts - this should be a more universal thing," Vedral says.

The best place to look first, he believes, might be the enigmatic phenomenon of high-temperature superconductivity. Vedral points out that superconductors contain pairs of electrons whose quantum descriptions, or wave functions, appear to be entangled. "The wave function describing the pair is not equal to the product of two wave functions," he says. "Mathematically, I can see there is entanglement."

So should entanglement be considered as a possible cause of high-temperature superconductivity? Might it show us how to make materials that are superconducting at room temperature? At this stage, it is too early to say: the effects of entanglement on Ghosh's magnetic salt only become noticeable below 1 kelvin. "That is almost absolute zero," Vedral admits. "What would be really interesting would be to find a material that exhibits the effects of entanglement at higher temperatures." Eventually, he thinks, we might well find such a material at room temperature. "I don't think it's going to be a very easy search, but I can't think of anything that would rule this out on the basis of fundamental theory. It doesn't look impossible to me."

While this might seem hopelessly optimistic at first glance, other recent discoveries about entanglement are suggesting otherwise. Entanglements at room temperature appear to be an everyday part of the universe. Reznik, for instance, has shown that all of empty space - what physicists refer to as the vacuum - is filled with pairs of particles that are entangled. "It's an unusual idea," says Reznik. "It was quite hard to get our first paper on this accepted." His paper was finally published last year in Foundations of Physics (vol 33, p 167).

Thomas Durt of Vrije University in Brussels also believes entanglement is everywhere. He has recently shown, from the basic equations that Schrödinger considered, that almost all quantum interactions produce entanglement, whatever the conditions. "When you see light coming from a faraway star, the photon is almost certainly entangled with the atoms of the star and the atoms encountered along the way," he says. And the constant interactions between electrons in the atoms that make up your body are no exception. According to Durt, we are a mass of entanglements.

Curiouser and curiouser

Of course, that is no guarantee we can use them. Reznik says he doesn't think you can take his vacuum entanglement and use it to perform feats such as teleportation. Indeed, he is not even sure how to demonstrate that this entanglement exists. Though the equations of quantum field theory show that it is present, he is still working out how to perform an experiment that makes vacuum entanglement more than a theoretical result.

These are all tantalising revelations, because they suggest that something priceless is within our grasp. But how do we reach it?

We certainly need to find a better handle on practical entanglement: at the moment, the only forms of it we have learned to use are somewhat constraining. The entangled photons used for cryptography and teleportation are produced by firing a photon into a "non-linear" crystal, such as beta barium borate. The optical properties of a non-linear crystal depend on its orientation, and a photon fired in at the correct angle will split into two entangled photons. But the entanglement between the photon pair is an artefact of the internal properties of the original photon - its path and polarisation (Link New Scientist, 30 October 1999, p 32. omitted). So entangled photons from a non-linear crystal effectively remain just one quantum system, rather than being the result of two distinct particles meeting and interacting. "It's a kind of entanglement, but not quite the same as between different quantum systems," Vedral says.

What physicists would dearly like, the resource that would open the way for the best experiments, is an unlimited source of pure two-particle entanglements. Despite the recent progress, this rich source of quantum magic has eluded them so far. So how do we take things forward? Schrödinger first discovered entanglement through analysing the mathematical descriptions of quantum theory, so perhaps mathematicians should be the pioneers. The trouble with this is that entanglement gives mathematicians a severe headache - especially when the entanglement is between anything more than two particles.

In theory, just bouncing particles off an entangled pair will establish another entanglement link that can then be put to work, but it's much easier said than done. Experimental physicists John Rarity and Paul Tapster were the first to entangle three photons, in their laboratory at the UK Defence Evaluation and Research Agency in Malvern, Worcestershire, five years ago. But no one has ever managed to work out how to describe the properties of such a system. For the most part, theorists can't even look at a given quantum state and tell if it is entangled - it is only possible in a few special cases. "Although I can define what it means to be entangled, that is, I can write down a state that's entangled and a state that's not, if you give me a state and ask whether it's entangled, then I have no efficient way of telling you that," says Vedral. In other words, he knows how to formulate the calculation, but it is so difficult that no computer can actually perform it.

But these problems may be nothing compared to the bombshell that Caslav Brukner of the University of Vienna has just dropped. As if our current understanding of entanglement between widely separated particles were not sketchy enough, Brukner, working with Vedral and two other Imperial College researchers, has uncovered a radical twist. They have shown that moments of time can become entangled too (link omitted).

They achieved this through a thought experiment that examines how quantum theory links successive measurements of a single quantum system. Measure a photon's polarisation, for example, and you will get a particular result. Do it again some time later, and you will get a second result. What Brukner and Vedral have found is a strange connection between the past and the future: the very act of measuring the photon polarisation a second time can affect how it was polarised earlier on. "It's really surprising," says Vedral.

This entanglement between moments in time is so bizarre that it could expose a hole in the very fabric of quantum theory, the researchers believe. The formulation does not allow messages to be sent back in time, but it still means that quantum mechanics seems to be bending the laws of cause and effect. On top of that, entanglement in time puts space and time on an equal footing in quantum theory, and that goes sharply against the grain.

Space and time have always been very different in quantum theory. A location in space is an "observable" - like momentum or spin, spatial coordinates are just another property any quantum particle can have. The passing of time, on the other hand, has always been part of the backdrop. An electron can have a particular value of spin, or momentum or location, but it cannot have a particular time.

But if time can become entangled, it should be considered as an observable, and there is no way to write that into quantum theory. "People have tried, but something in quantum mechanics always has to be violated if you want a proper time-observable," Vedral says. "So it could be that something in quantum mechanics has to be reformulated."

In other words, Brukner's result suggests that we might be missing something important in our understanding of how the world works. Maybe that shouldn't surprise us. After all, entanglement between two spatially separated objects already tells us that space doesn't really have the form that classical physics says it does: instantaneous cause and effect across cosmological distances is not something that any theory of the universe can cope with. And now Brukner's result seems to extend this "impossibility" to events separated in time as well.

It's not cause for despair, though. We know that relativity and quantum theory have to be meshed together if we are to create a "final" theory of how the universe works. It is too early to read much into Brukner's result, but maybe it is a clue about how to produce such a theory.

In the meantime, Vedral thinks he's identified an equally significant project to pursue. If, as Ghosh's result suggests, entanglement can produce macroscopic effects, is it such a stretch to reason that quantum entanglement might be the key to understanding life?

We know that quantum mechanics describes how atoms combine into molecules, and so underpins chemistry. And chemical processes underpin all biological processes, including the metabolic cycle and replication. So could entanglement support the emergent, macroscopic characteristic of chemistry that we call life? Reznik and Durt's revelations - that entanglements exist around us and inside us all the time - can only add to the intrigue. "I think it's a speculation worth making," Vedral says. "There may be some experiments in biology or biochemistry where we can see more of these effects, interpret some of the results in a different light. It would be a very exciting find."

Couple that with the ability to create materials that exploit our unfolding understanding of entanglement, and we might one day even gain the ability to use entanglement to create new forms of life. Now that is a spooky thought.

Michael Brooks

 

7
QUANTUM
107
26
8
12
ENTANGLEMENT
130
49
4

 

 

3
THE
33
15
6
6
SPOOKY
101
29
2
6
EFFECT
45
27
9

 

 

6
ELECTRO
78
33
6
8
MAGNETIC
72
36
9
12
ENTANGLEMENT
130
49
4
26
First Total
280
118
19
2+6
Add to Reduce
2+8+0
1+1+8
1+9
8
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
8
Essence of Number
1
1
1

 

 

-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
+
=
15
1+5
=
6
-
6
-
6
-
-
-
14
-
-
14
-
-
-
-
-
14
-
+
=
42
4+2
=
6
-
6
-
6
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
+
=
88
8+8
=
16
1+6
7
-
7
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
+
=
130
1+3+0
=
4
-
4
-
4
-
-
5
5
2
1
5
7
3
5
4
5
5
2
+
=
49
4+9
=
13
1+3
4
-
4
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
22
-
-
12
-
49
-
22
2+3
1+2
5
5
-
-
5
-
-
5
-
5
5
-
-
-
2+2
-
-
1+2
-
4+9
-
2+2
5
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
13
-
4
-
-
5
5
2
1
5
7
3
5
4
5
5
2
-
-
-
-
-
-
-
1+3
-
-
5
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
4
-
4

 

 

12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
+
=
15
1+5
=
6
-
6
-
6
-
-
14
-
-
14
-
-
-
-
-
14
-
+
=
42
4+2
=
6
-
6
-
6
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
+
=
34
3+4
=
7
-
7
-
7
-
5
-
20
1
-
7
12
5
13
5
-
20
+
=
88
8+8
=
16
1+6
7
-
7
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
+
=
130
1+3+0
=
4
-
4
-
4
-
5
5
2
1
5
7
3
5
4
5
5
2
+
=
49
4+9
=
13
1+3
4
-
4
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
=
5
5
-
-
5
-
-
5
-
5
5
-
=
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
22
-
-
12
-
49
-
22
1+2
5
5
2
1
5
7
3
5
4
5
5
2
-
-
2+2
-
-
1+2
-
4+9
-
2+2
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
13
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
4
-
4

 

 

-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
1
+
=
16
1+6
=
7
-
7
-
7
-
-
-
14
-
-
14
-
-
-
-
-
14
-
19
+
=
61
6+1
=
7
-
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
-
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
-
+
=
88
8+8
=
16
1+6
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
19
+
=
149
1+4+9
=
14
1+4
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
+
=
50
5+0
=
5
-
5
-
5
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
22
-
-
13
-
50
-
23
2+3
1+3
5
5
-
-
5
-
-
5
-
5
5
-
-
-
-
2+2
-
-
1+3
-
5+0
-
2+3
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5

 

 

-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
1
+
=
16
1+6
=
7
-
7
-
7
-
-
-
14
-
-
14
-
-
-
-
-
14
-
19
+
=
61
6+1
=
7
-
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
-
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
-
+
=
88
8+8
=
16
1+6
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
19
+
=
149
1+4+9
=
14
1+4
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
+
=
50
5+0
=
5
-
5
-
5
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
22
-
-
13
-
50
-
23
2+3
1+3
5
5
-
-
5
-
-
5
-
5
5
-
-
-
-
2+2
-
-
1+3
-
5+0
-
2+3
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5

 

 

I

ME

YOU

ENTANGLEMENTS

MENTAL ANGLE ANGEL ANGLE MENTAL

ENTANGLE MENTALLY MENTALLY ENTANGLE

KARMAS THOUGHT ENTANGLEMENT THOUGHT KARMAS

0123456789 REAL REALITY REVEALED REALITY REAL 9876543210

0987654321 GODS REAL REALITY REAL GODS 1234567890

ONE GOD ONE I ONE ME ONE YOU ONE EVERYTHING GODS

INTO THE WITHIN OF THE WITHOUT THAT IS UNIVERSAL MIND OF DIVINE THOUGHT

 

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

 

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

 

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

 

 

ATOMIC ENERGY

 

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

 

 

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

 

 

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

 

 

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

 

LETTERS REARRANGED NUMERICALLY

 

ATOMIC NUMBERS

 

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

 

 

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

 

LETTERS REARRANGED NUMERICALLY

 

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

 

 

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

 

 

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

 

 

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

 

 

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

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

Higgs boson
Subatomic particle

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

Composition: Elementary particle

Classification: Boson

Symbol: H°

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

Electric charge: 0 e

Discovered: Large Hadron Collider (2011–2013)

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

 

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

 

 

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

 

 

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

 

 

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

 

LETTERS RE-ARRANGED IN NUMERICAL ORDER

 

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

 

 

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

 

 

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

 

 

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

 

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

 

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

 

 

Hydrogen line - Wikipedia

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

 

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

 

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

 

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

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

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

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

Discovery?[edit]

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

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

In radio astronomy?[edit]

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

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

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

In cosmology?[edit]

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

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

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


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

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

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

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

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

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

 

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

 

 

TWENTY ONE CENTIMETER LINE

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

 

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

 

TWENTY ONE CENTIMETER LINE

 

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

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

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

 

TWENTY ONE CENTIMETER LINE

 

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

 

TWENTY ONE CENTIMETER LINE

 

-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
G
=
7
-
7
GRAVITY
102
39
3
G
=
7
-
4
GODS
45
27
9
R
=
9
-
2
RA
19
10
1
V
=
4
-
8
VITALITY
118
37
1
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-
-
2+7
-
2+1
-
2+8+4
1+1+3
1+4
-
-
9
-
3
GRAVITY GODS RA VITALITY
14
5
5
-
-
-
-
-
-
1+4
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
5
5
5

 

 

-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-3
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-3
-
-
-
GRAVITY
-
-3
-
-
-
-
-
-
-
-
-
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
1
=
9
5
1
1
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-3
39
-
7
GRAVITY
102
39
39
-
-
-
-
-
-
-
-
-
-
-
-3
-
-
-
GODS
-
-3
-
-
-
-
-
-
-
-
-
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
9
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-3
18
-
4
GODS
45
27
18
-
-
-
-
-
-
-
-
-
-
-
-3
-
-
-
RA
-
-3
-
-
-
-
-
-
-
-
-
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
13
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-3
10
-
2
RA
19
10
10
-
-
-
-
-
-
-
-
-
-
-
-3
-
-
-
VITALITY
-
-3
-
-
-
-
-
-
-
-
-
-
-
V
=
4
14
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
1
=
9
15
1
1
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
18
1
L
21
3
3
-
-
-
3
-
-
-
-
-
-
1
=
9
19
1
1
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
37
-
8
VITALITY
118
37
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
6
3
12
5
6
28
8
45
-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-
-
-
-
1+2
-
-
2+8
-
4+5
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
3
5
6
10
8
9
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
1+0
-
-
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
1
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
-
2+8+4
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
14
5
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
5
5
5
-
4
6
3
3
5
6
1
8
9

 

 

-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-3
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
1
=
9
5
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
T
=
2
6
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
O
=
6
9
1
O
15
6
6
-
-
-
-
-
5
6
-
8
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
5
-
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
5
-
-
8
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
A
=
1
13
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
V
=
4
14
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
1
=
9
15
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
T
=
2
16
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
L
=
3
18
1
L
21
3
3
-
-
-
3
-
5
-
-
8
-
1
=
9
19
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
T
=
2
20
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
-
-
-
-
-
-
-
-
-
-
4
6
3
12
5
6
28
8
45
-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-
-
-
-
1+2
-
-
2+8
-
4+5
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
3
5
6
10
8
9
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
1+0
-
-
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
1
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
-
2+8+4
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
14
5
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
5
5
5
-
4
6
3
3
5
6
1
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-3
1
2
3
4
5
6
7
8
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
5
-
-
8
-
A
=
1
13
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
5
-
-
8
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
5
-
-
8
-
L
=
3
18
1
L
21
3
3
-
-
-
3
-
5
-
-
8
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
5
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
V
=
4
14
1
V
22
4
4
-
-
-
-
4
5
-
-
8
-
O
=
6
9
1
O
15
6
6
-
-
-
-
-
5
6
-
8
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
5
-
7
8
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
5
-
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
1
=
9
5
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
5
-
-
8
9
1
=
9
15
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
1
=
9
19
1
1
9
9
9
-
-
-
-
-
5
-
-
8
9
-
-
-
-
-
-
-
-
-
-
4
6
3
12
5
6
28
8
45
-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-
-
-
-
1+2
-
-
2+8
-
4+5
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
3
5
6
10
8
9
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
1+0
-
-
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
5
6
1
8
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-
4
6
3
3
5
6
1
8
9
-
-
2+7
-
2+1
-
2+8+4
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
14
5
5
-
4
6
3
3
5
6
1
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
5
5
5
-
4
6
3
3
5
6
1
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-3
1
2
3
4
6
7
9
G
=
7
-
7
GRAVITY
102
39
3
-
-
-
-
-
-
-
-
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
-
-
R
=
9
-
2
RA
19
10
1
-
-
-
-
-
-
-
-
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-3
1
2
3
4
6
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
A
=
1
13
1
A
1
1
1
-
1
-
-
-
-
-
-
A
=
1
17
1
A
1
1
1
-
1
-
-
-
-
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
L
=
3
18
1
L
21
3
3
-
-
-
3
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
V
=
4
14
1
V
22
4
4
-
-
-
-
4
-
-
-
O
=
6
9
1
O
15
6
6
-
-
-
-
-
6
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
7
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
-
-
7
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
7
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
7
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
9
1
=
9
5
1
1
9
9
9
-
-
-
-
-
-
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
9
1
=
9
15
1
1
9
9
9
-
-
-
-
-
-
-
9
1
=
9
19
1
1
9
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4
6
3
12
6
28
45
-
-
-
-
21
GRAVITY GODS RA VITALITY
-
-
-
-
-
-
-
1+2
-
2+8
4+5
G
=
7
-
7
GRAVITY
102
39
3
-
4
6
3
3
6
10
9
G
=
7
-
4
GODS
45
27
9
-
-
-
-
-
-
1+0
-
R
=
9
-
2
RA
19
10
1
-
4
6
3
3
6
1
9
V
=
4
-
8
VITALITY
118
37
1
-
-
-
-
-
-
-
-
-
-
27
-
21
GRAVITY GODS RA VITALITY
284
113
14
-
4
6
3
3
6
1
9
-
-
2+7
-
2+1
-
2+8+4
1+1+3
1+4
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
14
5
5
-
4
6
3
3
6
1
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
GRAVITY GODS RA VITALITY
5
5
5
-
4
6
3
3
6
1
9

 

BREATHE ON ME BREATH OF GOD

 

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

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

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 


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

 


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

 

 

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

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

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

– Niels Bohr

 

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

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

 

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

 

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

 

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

 

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

 

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

ENERGY ENERGIES ENERGISE ENERGISES ENERGISED ENERGISING

 

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

 

 

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

 

 

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

 

ENERGYENERGIESENERGISEENERGISESENERGISEDENERGISING

LETTERS TRANSPOSED INTO NUMBER REARRANGED INTO NUMERICAL ORDER

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

-
-
-
-
11

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

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

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

GLORIA IN EXCELSIS
1
1
1

 

 

-
-
-
-
15

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

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

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

SOLVING PROBLEMS
1
9
9

 

 

-
-
-
-
15

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

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

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

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

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

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

 

 

-
-
-
-
15

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

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

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

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

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

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

 

 

-
-
-
-
15

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

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

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

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

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

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

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

 

ABCDEFGHIJKLMNOPQRSTUVWXYZ WELCOME

HERO

WELCOME ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

 

-
REAL
-
-
-
1
R
18
9
9
3
E+A+L
18
9
9
4
REAL
36
18
18
-
-
3+6
1+8
1+8
4
REAL
9
9
9

 

 

-
REALITY
-
-
-
1
R
18
9
9
3
E+A+L
18
9
9
1
I
9
9
9
2
T+Y
45
9
9
7
REALITY
90
36
36
-
-
9+0
3+6
3+6
7
REALITY
9
9
9

 

 

-
REVEALED
-
-
-
1
R
18
9
9
2
E+V
27
9
9
3
E+A+L
18
9
9
2
E+D
9
9
9
8
REVEALED
72
36
36
-
-
7+2
3+6
3+6
8
REVEALED
9
9
9

 

 

-
REAL
-
-
-
1
R
18
9
9
3
E+A+L
18
9
9
-
REALITY
-
-
-
1
R
18
9
9
3
E+A+L
18
9
9
1
I
9
9
9
2
T+Y
45
9
9
-
REVEALED
-
-
-
1
R
18
9
9
2
E+V
27
9
9
3
E+A+L
18
9
9
2
E+D
9
9
9
19
First Total
198
90
36
1+9
Add to Reduce
1+9+8
9+0
3+6
10
Second Total
18
9
9
1+0
Reduce to Deduce
1+8
-
-
1
Essence of Number
9
9
9

 

 

-
-
-
-
-
REAL REALITY
-
-
-
R
=
9
9
9
REAL
36
18
9
R
=
9
9
9
REALITY
90
36
9
-
-
-
-
-
REAL REALITY
126
54
18
-
-
-
-
-
-
1+2+6
5+4
1+8
R
=
9
9
-
REAL REALITY
9
9
9

 

 

REAL REALITY REVEALED HAVE I MENTIONED GODS DIVINE THOUGHT HAVE I MENTIONED

THAT

 

4
REAL
36
18
9
7
REALITY
90
36
9
8
REVEALED
72
36
9
19
First Total
198
90
27
1+9
Add to Reduce
1+9+8
9+0
2+7
10
Second Total
18
9
9
1+0
Reduce to Deduce
1+8
-
-
1
Essence of Number
9
9
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
R
=
18
=
9
R
18
9
9
--
-
-
-
-
E+A+L
18
9
9
R
=
18
=
9
R
18
9
9
--
-
-
-
-
E+A+L
18
9
9
--
-
-
-
-
I
9
9
9
--
-
-
-
-
T+Y
45
9
9
R
=
18
=
9
R
18
9
9
--
-
-
-
-
E+V
27
9
9
-
-
-
-
-
E+A+L
18
9
9
-
-
-
-
-
E+D
9
9
9
-
-
54
-
27
REAL REALITY REVEALED
-
-
-
-
-
5+4
-
2+7
-
-
-
-
-
-
9
-
9
REAL REALITY REVEALED
-
-
-

 

IT WAS BUT YESTERDAY WE MET IN A DREAM

 

-
-
-
-
19
REAL REALITY REVEALED
198
90
27
R
=
9
-
-
REAL
36
18
9
R
=
9
-
4
REALITY
90
36
9
R
=
9
-
7
REVEALED
72
36
9
-
-
27
-
10
REAL REALITY REVEALED
198
90
27
-
-
2+7
-
1+0
-
1+9+8
9+0
2+7
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
9
-
10
REAL REALITY REVEALED
9
9
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
-3
1
2
3
4
5
6
7
8
9
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REAL
-
-
-
-
1
2
3
4
5
6
7
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
9
REAL
36
18
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
16
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
36
-
7
REALITY
90
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REVEALED
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
3
13
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
13
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
36
-
7
REVEALED
72
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
19
REAL REALITY REVEALED
-
-
-
-
3
2
9
8
25
6
7
8
36
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
2+5
-
-
-
3+6
R
=
9
-
7
REALITY
90
36
9
-
3
2
9
8
7
6
7
8
9
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-
3
2
9
8
7
6
7
8
9
-
-
2+7
-
1+9
-
1+9+8
9+0
2+7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
3
2
9
8
7
6
7
8
9
-
-
-
-
1+0
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
REAL REALITY REVEALED
9
9
9
-
3
2
9
8
7
6
7
8
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
-3
1
2
3
4
5
6
7
8
9
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REAL
-
-
-
-
1
2
3
4
5
6
7
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
-
-
-
-
-
REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
6
-
8
-
Y
=
7
16
1
Y
25
7
7
-
-
-
-
-
-
6
7
8
-
-
-
-
-
-
REVEALED
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
V
=
3
13
1
V
22
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
D
=
4
13
1
D
4
4
4
-
-
-
-
4
-
6
-
8
-
-
-
-
-
-
REVEALED
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
19
REAL REALITY REVEALED
-
-
-
-
3
2
9
8
25
6
7
8
36
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
2+5
-
-
-
3+6
R
=
9
-
7
REALITY
90
36
9
-
3
2
9
8
7
6
7
8
9
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-
3
2
9
8
7
6
7
8
9
-
-
2+7
-
1+9
-
1+9+8
9+0
2+7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
3
2
9
8
7
6
7
8
9
-
-
-
-
1+0
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
REAL REALITY REVEALED
9
9
9
-
3
2
9
8
7
6
7
8
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
-3
1
2
3
4
5
6
7
8
9
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
6
-
8
-
Y
=
7
16
1
Y
25
7
7
-
-
-
-
-
-
6
7
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
V
=
3
13
1
V
22
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
D
=
4
13
1
D
4
4
4
-
-
-
-
4
-
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
19
REAL REALITY REVEALED
-
-
-
-
3
2
9
8
25
6
7
8
36
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
2+5
-
-
-
3+6
R
=
9
-
7
REALITY
90
36
9
-
3
2
9
8
7
6
7
8
9
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-
3
2
9
8
7
6
7
8
9
-
-
2+7
-
1+9
-
1+9+8
9+0
2+7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
3
2
9
8
7
6
7
8
9
-
-
-
-
1+0
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
REAL REALITY REVEALED
9
9
9
-
3
2
9
8
7
6
7
8
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
-3
1
2
3
4
5
6
7
8
9
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-3
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
6
-
8
-
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
6
-
8
-
V
=
3
13
1
V
22
4
4
-
-
-
-
4
-
6
-
8
-
D
=
4
13
1
D
4
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
Y
=
7
16
1
Y
25
7
7
-
-
-
-
-
-
6
7
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
19
REAL REALITY REVEALED
-
-
-
-
3
2
9
8
25
6
7
8
36
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
2+5
-
-
-
3+6
R
=
9
-
7
REALITY
90
36
9
-
3
2
9
8
7
6
7
8
9
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-
3
2
9
8
7
6
7
8
9
-
-
2+7
-
1+9
-
1+9+8
9+0
2+7
-
-
-
-
-
-
-
-
-
-
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
3
2
9
8
7
6
7
8
9
-
-
-
-
1+0
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
REAL REALITY REVEALED
9
9
9
-
3
2
9
8
7
6
7
8
9

 

 

-
-
-
-
-
REAL REALITY REVEALED
-
-
-
-3
1
2
3
4
5
7
9
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
-
-
-
R
=
9
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-3
1
2
3
4
5
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
T
=
2
15
1
T
20
2
2
-
-
2
-
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
L
=
3
13
1
L
12
3
3
-
-
-
3
-
-
-
-
V
=
3
13
1
V
22
4
4
-
-
-
-
4
-
-
-
D
=
4
13
1
D
4
4
4
-
-
-
-
4
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
Y
=
7
16
1
Y
25
7
7
-
-
-
-
-
-
7
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
19
REAL REALITY REVEALED
-
-
-
-
3
2
9
8
25
7
36
R
=
9
-
4
REAL
36
18
9
-
-
-
-
-
2+5
-
3+6
R
=
9
-
7
REALITY
90
36
9
-
3
2
9
8
7
7
9
R
=
9
-
8
REVEALED
72
36
9
-
-
-
-
-
-
-
-
-
-
27
-
19
REAL REALITY REVEALED
198
90
27
-
3
2
9
8
7
7
9
-
-
2+7
-
1+9
-
1+9+8
9+0
2+7
-
-
-
-
-
-
-
-
-
-
9
-
10
REAL REALITY REVEALED
18
9
9
-
3
2
9
8
7
7
9
-
-
-
-
1+0
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
REAL REALITY REVEALED
9
9
9
-
3
2
9
8
7
7
9

 

 

7
REALITY
90
36
9
6
LIVING
73
37
1
3
THE
33
15
6
4
MYTH
66
21
3
20
First Total
262
109
19
2+0
Add to Reduce
2+6+2
1+0+9
1+9
2
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
2
Essence of Number
1
1
1
-
-
-
-
-
-
-
-
-
-
7
REALITY
90
36
9
3
THE
33
15
6
6
LIVING
73
37
1
4
MYTH
66
21
3
20
First Total
262
109
19
2+0
Add to Reduce
2+6+2
1+0+9
1+9
2
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
2
Essence of Number
1
1
1

 

 

7
MANKIND
66
30
3
5
WOMAN
66
21
3
4
MYTH
66
21
3
16
First Total
198
72
9
1+6
Add to Reduce
1+9+8
7+2
-
7
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
7
Essence of Number
9
9
9

 

 

1
I
11
2
9
2
ME
18
9
9
3
EGO
27
18
9
4
OGRE
45
27
9
10
EGOCENTRIC
99
54
9
10
CONSCIENCE
90
45
9

 

 

-
1
I
-
-
-
I
-
--
-
-
-
-
9
+
=
9
-
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
3
I
-
-
-
I
-
-
-
-
-
-
9
+
=
9
-
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
-
-
-
I
-
-
-
-
-
-
9
+
=
9
-
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
T
-
0
ZERO
-
-
-
0
1
-
-
-
-
1
ONE
-
-
-
1
2
-
-
-
-
2
TWO
-
-
-
2
3
-
-
-
-
3
THREE
-
-
-
3
4
-
-
-
-
4
FOUR
-
-
-
4
5
--
-
-
-
5
FIVE
-
-
-
5
6
-
-
-
-
6
SIX
-
-
-
6
7
-
-
-
-
7
SEVEN
-
-
-
7
8
-
-
-
-
8
EIGHT
-
-
-
8
-
-
9
-
-
9
NINE
x
1
=
9
36
1
I
-
-
36
-
-
1
-
9
3+6
-
9
-
-
3+6
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9
-
-
9
-
-
-
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9

 

 

-
1
I
-
-
-
-
-
--
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
3
I
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
T
-
-
-
-
-
-
-
1
-
-
-
-
1
--
-
-
-
1
2
-
-
-
-
2
--
-
-
-
2
3
-
-
-
-
3
-
-
-
-
3
4
-
-
-
-
4
--
-
-
-
4
5
--
-
-
-
5
--
-
-
-
5
6
-
-
-
-
6
--
-
-
-
6
7
-
-
-
-
7
--
-
-
-
7
8
-
-
-
-
8
--
-
-
-
8
-
-
9
-
-
9
occurs
x
1
=
9
36
1
I
-
-
36
-
-
1
-
9
3+6
-
9
-
-
3+6
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9
-
-
9
-
-
-
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9

 

 

-
1
I
-
-
-
-
-
--
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
3
I
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+8
=
9
=
9
-
-
9
+
=
9
-
=
9
=
9
-
1
I
T
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
36
1
I
-
-
36
-
-
1
-
9
3+6
-
9
-
-
3+6
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9
-
-
9
-
-
-
-
-
-
-
-
9
1
I
-
-
9
-
-
1
-
9

 

 

-
2
M
E
-
-
-
-
-
--
-
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
-
4
5
+
=
9
-
=
9
=
9
-
2
M
E
-
-
-
-
-
--
-
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
-
4
5
+
=
9
-
=
9
=
9
-
2
M
E
-
-
-
-
-
--
-
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
-
4
5
+
=
9
-
=
9
=
9
-
2
M
E
-
-
-
-
-
-
-
-
1
-
--
--
--
--
1
--
--
--
--
--
2
-
--
--
--
--
2
--
--
--
--
--
3
-
--
--
--
--
3
--
--
--
--
--
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
--
--
--
--
6
--
--
--
--
--
7
-
--
--
--
--
7
--
--
--
--
--
8
-
--
--
--
--
8
--
--
--
--
--
9
-
--
--
--
--
9
--
--
--
--
--
36
2
M
E
-
-
9
-
-
2
-
9
3+6
-
4
5
-
-
-
-
-
-
-
-
9
2
M
E
-
-
9
-
-
2
-
9
-
-
4
5
-
-
-
-
-
-
-
-
9
2
M
E
-
-
9
-
-
2
-
9

 

 

2
M
E
-
-
-
-
-
--
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
4
5
+
=
9
-
=
9
=
9
2
M
E
-
-
-
-
-
--
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
4
5
+
=
9
-
=
9
=
9
2
M
E
-
-
-
-
-
--
-
-
-
13
5
+
=
18
1+8
=
9
=
9
-
4
5
+
=
9
-
=
9
=
9
2
M
E
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
5
-
-
5
occurs
x
1
=
5
2
M
E
-
-
9
-
-
2
-
9
-
4
5
-
-
-
-
-
-
-
-
2
M
E
-
-
9
-
-
2
-
9
-
4
5
-
-
-
-
-
-
-
-
2
M
E
-
-
9
-
-
2
-
9

 

 

-
3
E
G
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
E
G
O
-
-
-
-
-
--
-
-
-
-
5
7
-
+
=
12
1+2
=
3
=
3
-
3
E
G
O
-
-
-
-
-
--
-
-
-
-
5
7
15
+
=
27
2+7
=
9
=
9
-
-
5
7
6
+
=
18
1+8
=
9
=
9
-
3
E
G
O
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
-
7
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
27
3
E
G
O
-
-
18
-
-
3
-
18
2+7
-
-
-
-
-
-
1+8
-
-
-
-
1+8
9
3
E
G
O
-
-
9
-
-
3
-
9
-
-
5
7
6
-
-
-
-
-
-
-
-
9
3
E
G
O
-
-
9
-
-
3
-
9

 

 

3
E
G
O
-
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
E
G
O
-
-
-
-
-
--
-
-
-
5
7
-
+
=
12
1+2
=
3
=
3
3
E
G
O
-
-
-
-
-
--
-
-
-
5
7
15
+
=
27
2+7
=
9
=
9
-
5
7
6
+
=
18
1+8
=
9
=
9
3
E
G
O
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
7
occurs
x
1
=
7
3
E
G
O
-
-
18
-
-
3
-
18
-
-
-
-
-
-
1+8
-
-
-
-
1+8
3
E
G
O
-
-
9
-
-
3
-
9
-
5
7
6
-
-
-
-
-
-
-
-
3
E
G
O
-
-
9
-
-
3
-
9

 

 

11
4
O
G
R
E
-
-
-
-
--
-
-
-
-
6
-
-
-
+
=
6
-
=
6
=
6
-
-
15
-
-
-
+
=
15
1+5
=
6
=
6
11
4
O
G
R
E
-
-
-
-
-
--
-
-
-
-
-
7
9
5
+
=
21
2+1
=
3
=
3
-
-
-
7
18
5
+
=
30
3+0
=
3
=
3
11
4
O
G
R
E
-
-
-
-
-
--
-
-
-
-
15
7
18
5
+
=
45
4+5
=
9
=
9
-
-
6
7
9
5
+
=
27
2+7
=
9
=
9
11
4
O
G
R
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
3
-
--
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
18
4
O
G
R
E
-
-
27
-
-
4
-
27
1+8
-
-
-
9
-
-
-
2+7
-
-
-
-
2+7
9
4
O
G
R
E
-
-
9
-
-
4
-
9
-
-
6
7
9
5
-
-
-
-
-
-
-
-
9
4
O
G
R
E
-
-
9
-
-
4
-
9

 

 

4
O
G
R
E
-
-
-
-
--
-
-
-
6
-
-
-
+
=
6
-
=
6
=
6
-
15
-
-
-
+
=
15
1+5
=
6
=
6
4
O
G
R
E
-
-
-
-
-
--
-
-
-
-
7
9
5
+
=
21
2+1
=
3
=
3
-
-
7
18
5
+
=
30
3+0
=
3
=
3
4
O
G
R
E
-
-
-
-
-
--
-
-
-
15
7
18
5
+
=
45
4+5
=
9
=
9
-
6
7
9
5
+
=
27
2+7
=
9
=
9
4
O
G
R
E
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
9
-
-
-
9
occurs
x
1
=
9
4
O
G
R
E
-
-
27
-
-
4
-
27
-
-
-
9
-
-
-
2+7
-
-
-
-
2+7
4
O
G
R
E
-
-
9
-
-
4
-
9
-
6
7
9
5
-
-
-
-
-
-
-
-
4
O
G
R
E
-
-
9
-
-
4
-
9

 

 

--
EGO CENTRIC
-
-
-
3
EGO
27
18
9
7
CENTRIC
72
36
9
10
EGO CENTRIC
99
54
18
1+0
-
9+9
5+4
1+8
1
EGO CENTRIC
18
9
9
-
-
1+8
-
-
1
EGO CENTRIC
9
9
9

 

 

11
INSTINCT
-
-
-
1
I
9
9
9
3
NST
53
17
8
1
I
9
9
9
3
NCT
37
1
1
8
INSTINCT
108
36
27
-
-
1+0+8
3+6
2+7
8
INSTINCT
9
9
9

 

 

11
INSTINCT
-
-
-
1
I
9
9
9
3
NST
-
17
8
1
I
9
9
9
3
NCT
-
1
1
8
INSTINCT
-
36
45

 

 

11
INSTINCT
-
-
-
1
I
9
9
9
3
NST
53
17
8
1
I
9
9
9
3
NCT
37
1
1
8
INSTINCT
108
36
45

 

 

8
INSTINCT
108
36
9

 

 

11
INSTINCTIVE
-
-
-
1
I
9
9
9
3
NST
53
8
8
1
I
9
9
9
3
NCT
37
10
1
1
I
9
9
9
2
VE
27
9
9
11
INSTINCTIVE
144
54
45
1+1
-
1+4+4
5+4
4+5
11
INSTINCTIVE
9
9
9

 

 

11
INSTINCTIVE
-
-
-
1
I
9
9
9
3
NST
-
-
-
1
I
9
9
9
3
NCT
-
-
-
1
I
9
9
9
2
VE
-
-
-
11
INSTINCTIVE
144
54
45

 

 

11
INSTINCTIVE
-
-
-
1
I
-
-
-
3
NST
53
8
8
1
I
-
-
-
3
NCT
37
10
1
1
I
-
-
-
2
VE
27
9
9
11
INSTINCTIVE
144
54
45

 

 

EVOLVE LOVE EVOLVE

LOVES SOLVE LOVES

EVOLVE LOVE EVOLVE

 

Algorithm - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Algorithm

In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and ...

 

A
=
1
-
9
ALGORITHM
103
49
4
A
=
1
-
10
ALGORITHMS
122
59
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
-
ALGORITHMS
-
-
-
-
-
-
-
1
A
1
1
1
-
-
-
-
1
L
12
3
3
-
-
-
-
1
G
7
7
7
-
-
-
-
1
O
15
6
6
-
-
-
-
1
R
18
9
9
-
-
-
-
1
I
9
9
9
-
-
-
-
1
T
20
2
2
-
-
-
-
1
H
8
8
8
-
-
-
-
1
M+S
32
14
5
A
=
1
-
10
ALGORITHMS
122
59
50
-
-
-
-
1+0
-
1+2+2
5+9
5+0
A
=
1
-
1
ALGORITHMS
5
14
5
-
-
-
-
-
-
-
1+4
-
A
=
1
-
1
ALGORITHMS
5
5
5

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
T
=
2
-
1
T
20
2
2
L
=
3
-
1
L
12
3
3
M
=
4
-
1
M
13
4
4
5
-
5
-
-
5
-
-
5
O
=
6
-
1
O
15
6
6
G
=
7
-
1
G
7
7
7
H
=
8
-
1
H
8
8
8
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

A
=
1
-
10
ALGORITHMS
122
59
5
A
=
1
-
9
ALGORITHM
103
49
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALGORITHM
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
1
L
12
3
3
G
=
7
-
1
G
7
7
7
O
=
6
-
1
O
15
6
6
R
=
9
-
1
R
18
9
9
I
=
9
-
1
I
9
9
9
T
=
2
-
1
T
20
2
2
H
=
8
-
1
H
8
8
8
M
=
4
-
1
M
13
4
4
-
-
49
-
9
ALGORITHM
103
49
49
-
-
4+9
-
-
-
1+0+3
4+9
4+9
-
-
13
-
9
ALGORITHM
103
13
13
-
-
1+3
-
-
-
-
1+3
1+3
-
-
4
-
9
ALGORITHM
103
4
4

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
5
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
5
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
5
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

M
=
4
-
4
MIND
40
22
4
S
=
1
-
6
SPIRIT
91
37
1
M
=
4
-
6
MATTER
77
23
5
-
-
9
4
16
First Total
208
82
10
-
-
-
-
1+6
Add to Reduce
2+0+8
8+2
1+0
-
-
9
-
7
Second Total
10
10
1
-
-
-
4
-
Reduce to Deduce
1+0
1+0
-
-
-
9
5
7
Essence of Number
1
1
1

 

 

D
=
4
4
DARK
34
16
7
M
=
4
6
MATTER
77
23
5
-
-
8
10
First Total
111
39
12
-
-
-
1+0
Add to Reduce
1+1+1
3+9
1+2
Q
-
8
1
Second Total
3
12
3
-
-
-
-
Reduce to Deduce
-
1+2
-
-
-
8
1
Essence of Number
3
3
3

 

 

D
=
4
4
DARK
34
16
7
L
=
3
5
LIGHT
56
29
2
-
-
7
9
Add to Reduce
90
45
9
-
=
-
-
Reduce to Deduce
9+0
4+5
-
-
-
7
9
Essence of Number
9
9
9

 

 

3
GOD
26
17
8
8
ENERGIES
82
46
1
11
Add to Reduce
108
63
9
1+1
Reduce to Deduce
1+0+8
6+3
-
2
Essence of Number
9
9
9

 

 

3
THE
33
15
6
6
THEORY
91
37
1
2
OF
21
12
3
10
EVERYTHING
133
61
7
2
IS
28
10
1
4
GODS
45
18
9
27
Add to Reduce
351
153
27
2+7
Reduce to Deduce
3+5+1
1+5+3
2+7
9
Essence of Number
9
9
9

 

 

D
=
4
4
DARK
34
16
7
E
=
5
6
ENERGY
74
38
2
-
-
9
10
Add to Reduce
108
54
9
-
=
-
1+0
Reduce to Deduce
1+0+8
5+4
-
-
-
9
1
Essence of Number
9
9
9

 

 

3
THE
33
15
6
7
KINETIC
71
35
8
6
NATURE
79
25
7
2
OF
21
12
3
6
THINGS
77
32
5

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
7
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
K
=
2
-
-
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
30
6
7
8
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
3+0
-
-
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
K
=
2
-
-
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
-
-
-
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
30
6
7
8
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
3+0
-
-
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
4
5
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
-
-
-
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
-
-
-
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
-
-
-
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
-
-
-
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
-
-
-
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
30
6
7
8
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
3+0
-
-
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

K
=
2
Q
7
KINETIC
71
35
35
-
1
2
3
5
7
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
7
Q
15
-
153
90
81
-
1
2
3
5
7
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
-
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
1
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
7
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
3
1
N
14
5
5
-
-
-
-
5
-
-
-
-
-
4
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
8
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
9
1
N
14
5
5
-
-
-
-
5
-
-
-
-
-
10
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
14
1
E
5
5
5
-
-
-
-
5
-
-
-
-
-
12
1
G
7
7
7
-
-
-
-
-
7
-
-
-
-
2
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
6
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
11
1
R
18
9
9
-
-
-
-
-
-
9
-
-
-
13
1
I
9
9
9
-
-
-
-
-
-
9
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
30
7
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
3+0
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
3
7
9

 

 

K
=
2
Q
7
KINETIC
71
35
8
E
=
5
Q
8
ENERGIES
82
55
1
Q
Q
7
Q
15
Add to Reduce
153
90
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
-
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
E
=
5
Q
8
ENERGIES
82
55
46
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

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

AND THE DICE ALL READ A FIVE

LIVING FORM FROM OUT THE IN OF GODS LIVING FORM

 

 

 

 
 
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