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Evokation
  
 
Index
  

 

A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

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

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

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

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

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

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

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

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

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

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

Searching out patterns is a pure delight.

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

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

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

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

A message in the bottle of time"

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

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

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

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

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

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

 

 

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

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

 

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

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

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

 

 

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

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
9
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

 

The Upside Down of the Downside Up

 

 

 

 

 

-
-
-
-
-
AHIMOTUVWXY
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
AHIMOTUVWXY
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
1
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
8
-
-
1
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
9
-
-
-
-
3
-
-
-
-
-
9
M
=
4
-
1
M
13
4
4
-
4
-
-
-
-
-
4
-
-
-
8
-
O
=
6
-
1
O
15
6
6
-
6
-
-
-
-
-
-
5
6
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
2
-
-
-
-
-
8
-
U
=
3
-
1
U
21
3
3
-
-
3
-
-
-
3
-
-
6
-
-
-
V
=
4
-
1
V
22
4
4
-
-
4
-
-
-
-
4
-
-
7
-
-
W
=
5
-
1
W
23
5
5
-
-
5
-
1
-
-
-
5
-
-
-
-
X
=
6
-
1
X
24
6
6
-
-
6
-
-
-
3
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
55
4
11
AHIMOTUVWXY
181
55
55
4
28
27
4
1
2
3
8
5
12
7
8
9
-
-
5+5
-
1+1
-
1+8+1
5+5
5+5
-
5+5
2+7
-
-
-
-
-
-
1+2
-
-
-
-
-
10
-
2
AHIMOTUVWXY
10
10
10
-
10
9
-
1
2
3
8
3
3
7
5
9
-
-
1+0
-
1+1
-
1+0
1+0
1+0
-
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
AHIMOTUVWXY
1
1
1
-
1
9
-
1
2
3
8
3
3
7
5
9

 

 

-
11
A
H
I
M
O
T
U
V
W
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
6
-
-
-
-
6
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
8
9
-
15
-
-
-
-
24
-
+
=
56
5+6
=
11
1+1
2
=
2
-
11
A
H
I
M
O
T
U
V
W
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
4
-
2
3
4
5
-
7
+
=
26
2+6
=
8
=
8
=
8
-
-
1
-
-
13
-
20
21
22
23
-
25
+
=
125
1+2+5
=
8
1+8
8
=
8
-
11
A
H
I
M
O
T
U
V
W
X
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
8
9
13
15
20
21
22
23
24
25
+
=
181
1+8+1
=
10
1+0
1
=
1
-
-
1
8
9
4
6
2
3
4
5
6
7
+
=
55
55
=
10
1+0
1
=
1
-
11
A
H
I
M
O
T
U
V
W
X
Y
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
4
-
-
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
6
-
-
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
45
11
A
H
I
M
O
T
U
V
W
X
Y
-
-
45
-
-
11
-
55
-
46
4+5
1+1
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
1+1
=
5+5
-
4+6
9
2
A
H
I
M
O
T
U
V
W
X
Y
-
-
9
-
-
2
-
10
-
10
-
-
1
8
9
4
6
2
3
4
5
6
7
-
-
-
-
-
-
-
1+0
-
1+0
9
2
A
H
I
M
O
T
U
V
W
X
Y
-
-
9
-
-
2
-
1
-
1

 

THE SPEAR OF DESTINY

 

 

I

THAT

AM ALWAYS AM

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

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

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

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

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

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

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

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

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

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

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

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

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

AN IMPORTANT POSTSCRIPT

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

Page 206

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

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

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

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

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

Page 207

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

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

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

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

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

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

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

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

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

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

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

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

 

 

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

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

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

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

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

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

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

 

 

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

 

 

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

 

 

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

 

 

HOW YOU HAVE FALLEN FROM EVEN O LUCIFER BRIGHT SON OF THE MORNING

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Midway this way of life we're bound upon

I woke to find myself in a dark wood,

Where the right road was wholly lost and gone."

 

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

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

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

Even as a wheel moves equal, free from jars,

Already my heart and will were wheeled by love,

The Love that moves the sun and other stars."

 

 

ADVENT 1004 ADVENT

 

 

IN SEARCH OF EXTRA TERRESTRIALS

Unsolved UFO sightings... strange secrets of the moon... new evidence that alien astronauts are exploring the earth

Alan Landsburg 1976

Page 79

The words of J. B. S. Haldane came back to haunt me. He once wrote, "Now my suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I suspect that there are more things in heaven and earth than are dreamed of in any philosophy. That is the reason why I have no philosophy myself, and must be my excuse for dreaming.

 

 

WHATEVER WHENEVER WENNEFER WENNEFER WHENEVER WHATEVER

 

 

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

 

 

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

 

 

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

 

 

SIGNS IN THE SKY

OPENING THE STARGATE

Adrian Gilbert 2000

Annu Heliopolis

Page 160

"Although the original Benben stone disappeared at about the time the pyramids were built, it bequeathed its name to the pyramidions that sat on the top of the pyramids, and also the pyramidal tips of obelisks.12 There was therefore a close etymological linkage between the Benben stone of the early Dynastic Age, the pyramids of the Old Kingdom and the obelisks of the Middle and New Kingdoms. It was tempting to think that in all cases the pyrarnidions represented the same thirig: the 'seed' or semen of Atum, the cosmic creator, made manifest as his offspring Osiris and sent to earth to carry out his mission of civilizing humankind. This being the case the Benben, like the pyramids, was emblematic of Osiris and therefore somehow linked to the stellar religion of Orion.
It was this essentially Osirian theory for the origins and meaning of the Benben that we presented in The Orion Mystery. Yet this interpretation, plausible as it is, is clearly not the whole story. In ancient Egypt, hand in hand with the Osirian cult of the dead, there was a solar cult of the living. The west bank of the Nile, and in particular the pyramid fields, represented the land of the dead, the kingdom of Osiris. However, the east bank, where Heliopolis stood, symbolized the world of the living under the ever-watchful eye of Re, the sun god. Thus while the pyramids symbolized Orion, the star form of Osiris and his place of ascension in the sky, Heliopolis was connected with the worship of the sun god under his varied names of Atum, Re-Heracte and Khepera. When we wrote The Orion Mystery we had neither time nor space to go into all of this in a book that was essentially about the stellar cult of the Old Kingdom. Yet it was clear to me even then that it would eventually be necessary to address the question of the solar aspects of the Egyptian religion too if we were ever to obtain a holistic view. For while Osiris/Orion is clearly of great esoteric interest, the solar focus of most of the temples used by the living, and indeed of the obelisks, is clear for all to see.

 

 

-
18
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
-
-
-
--
-
--
-
-
-
-
-
8
-
-
-
9
-
-
8
-
6
-
-
-
8
-
-
8
6
-
-
1
+
=
54
5+4
=
9
-
9
=
9
-
-
-
8
-
-
-
9
-
-
8
-
15
-
-
-
8
-
-
8
15
-
-
19
+
=
90
9+0
=
9
=
9
=
9
-
18
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
-
-
-
--
-
--
-
-
-
-
2
-
5
-
2
-
9
2
-
-
-
6
-
2
-
5
-
-
-
9
3
-
+
=
45
4+5
=
9
-
9
=
9
-
-
20
-
5
-
2
-
18
20
-
-
-
6
-
20
-
5
-
-
-
18
21
-
+
=
135
1+3+5
=
9
=
9
=
9
-
18
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
-
-
-
--
-
--
-
-
-
-
20
8
5
-
2
9
18
20
8
-
15
6
-
20
8
5
-
8
15
18
21
19
+
=
225
2+2+5
=
9
=
9
=
9
-
-
2
8
5
-
2
9
9
2
8
-
6
6
-
2
8
5
-
8
6
9
3
1
+
=
99
9+9
=
18
1+8
9
=
9
-
18
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
-
-
-
--
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
8
-
-
-
-
-
-
8
occurs
x
4
=
32
3+2
5
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
18
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
34
-
-
18
-
99
-
36
1+1
1+8
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
3+4
-
-
1+8
-
9+9
-
3+6
2
9
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
7
-
-
9
-
18
-
9
-
-
2
8
5
-
2
9
9
2
8
-
6
6
-
2
8
5
-
8
6
9
3
1
-
-
-
-
-
-
-
1+8
-
-
2
9
T
H
E
-
B
I
R
T
H
-
O
F
-
T
H
E
-
H
O
R
U
S
-
-
7
-
-
9
-
9
-
9

 

 

THE

AWAKENING

HUMANKIND IS THAT HORUS OF HOURS THAT IS HUMANKIND

THE

CHRISTOS

 

 

I

RA

RE

ATUM

ATUM A234 432A MUTA

ATUM 1234 MUTA 4321

ATUM A234 432A MUTA

ATUM 1234 MUTA 4321

BEN BEN STONE ENOTS NEB NEB

BEN = BEN

STONE

I

THOUGHT FIVE FIVE I THOUGHT

B EN B EN STO NE EN OTS NE B NE B

BB STO OTS BB

22 126 621 22

EN EN NE EN NE NE

55 55 55 55 55 55

NEBO O BEN NEB O OBEN

RE NEW WEN ER

95 555 555 59

555 59 95 555

WEN ER RE NEW

RA ATUM MUTA AR

91 1234 4321 19

ATOMS ARE ERA SMOTA

12641 195 591 14621

ATUM RA ATOM

ARE RE RE RA ARE

R

ARE

I

THAT AM THAT

RARE ARE RED RA RARE RA RED ARE RARE

READ RA RARE THAT RARE RA READ

AZ R ARE AZ WHITE RABBITZ R ARE R RABBITZ WHITE AZ R ARE AZ

THAT I ME YOU R R YOU ME I THAT

R ARE AZ R ARE AZ R ARE

AZ

THAT

THAT IS RARE AZ RARE AZ THAT IS RARE

 

 

"Exalted Earth". A primeval Egyptian earth-god who represents the mound (or hill) that arose from the primordial water. He is represented with the horns of ... www.pantheon.org/articles/t/tatenen.html

Encyclopedia Mythica

 

TATENEN

by Micha F. Lindemans

"Exalted Earth". A primeval Egyptian earth-god who represents the mound (or hill) that arose from the primordial water. He is represented with the horns of a ram and wearing a crown with feathers. At Memphis he was connected to Ptah (Ptah-Tenen) in his aspect as a creator god, and also with Horus. As a vegetation god, he could be portrayed with green skin.

 

 

THE

PATH OF PTAH

 

 

TatenenAs his name The Risen Land indicates Tatenen was the earth of the beginning, the primeval hill, which had risen out of the primeval waters. ... www.reshafim.org.il/ad/egypt/religion/tatenen.htm

TATENEN

As his name The Risen Land indicates Tatenen was the earth of the beginning, the primeval hill, which had risen out of the primeval waters. And every year he emerged from the waters of the inundation ready to bear fruit and nourish mankind.

Tatenen... from whom have proceeded all things in the shape of food and viands, divine offers, all good things

C. J. Bleeker: Historia Religionum I, p.68

He was venerated at Memphis and came to be identified with Ptah. Ramses II called him father of the gods and saw himself as his successor, as the ruler of the earth

Utterance of the divine king, Lord of the Two Lands, lord of the form of Khepri, in whose limbs is Re, who came forth from Re, whom Ptah-Tatenen begat, King Ramses II, given life; to his father, from whom he came forth, Tatenen, father of the gods

J. H. Breasted: Ancient Records of Egypt, Part Three, § 411

 

 

-
PRIMEVAL MOUND
-
-
-
7
TATENEN
-
-
-
-
T+A+T
41
5
5
-
E
5
5
5
-
N
14
5
5
-
E
5
5
5
-
N
14
5
5
7
TATENEN
-
-
-
-
-
-
-
-
-
-
-
-
-
13
PRIMEVAL MOUND
163
64
1
7
TATENEN
79
25
7

 

 

-
7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
5
-
5
+
=
26
2+6
=
8
-
8
-
8
-
-
-
-
-
-
14
-
14
+
=
26
2+6
=
8
-
8
-
8
-
7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
-
2
1
2
5
-
5
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
20
1
20
5
-
5
-
+
=
91
9+1
=
10
1+0
1
-
1
-
7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
-
20
1
20
5
14
5
14
+
=
117
1+1+7
=
9
-
9
-
9
-
-
2
1
2
5
5
5
5
+
=
45
4+5
=
9
-
9
-
9
-
7
T
A
T
E
N
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
``-
2
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
5
5
5
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
37
7
T
A
T
E
N
E
N
-
-
8
-
-
11
-
45
-
36
3+7
-
-
-
-
-
-
-
-
-
-
-
-
-
1+1
-
4+5
-
3+6
10
7
T
A
T
E
N
E
N
-
-
8
-
-
2
-
9
-
9
1+0
-
2
1
2
5
5
5
5
-
-
-
-
-
-
-
-
-
-
9
7
T
A
T
E
N
E
N
-
-
8
-
-
2
-
9
-
9

 

 

7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
5
+
=
26
2+6
=
8
-
8
-
8
-
-
-
-
-
14
-
14
+
=
26
2+6
=
8
-
8
-
8
7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
2
1
2
5
-
5
-
+
=
19
1+9
=
10
1+0
1
-
1
-
20
1
20
5
-
5
-
+
=
91
9+1
=
10
1+0
1
-
1
7
T
A
T
E
N
E
N
-
-
-
-
-
--
-
-
-
-
-
20
1
20
5
14
5
14
+
=
117
1+1+7
=
9
-
9
-
9
-
2
1
2
5
5
5
5
+
=
45
4+5
=
9
-
9
-
9
7
T
A
T
E
N
E
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
``-
2
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
5
5
5
5
-
-
5
occurs
x
4
=
20
2+0
2
7
T
A
T
E
N
E
N
-
-
8
-
-
11
-
45
-
36
-
-
-
-
-
-
-
-
-
-
-
-
-
1+1
-
4+5
-
3+6
7
T
A
T
E
N
E
N
-
-
8
-
-
2
-
9
-
9
-
2
1
2
5
5
5
5
-
-
-
-
-
-
-
-
-
-
7
T
A
T
E
N
E
N
-
-
8
-
-
2
-
9
-
9

 

I

LOVETH MERITATEN MERITATEN LOVETH

I

 

 

5
NETER
62
26
8
5
ENTER
62
26
8
5
ENTERS
62
26
8
6
NETERS
81
27
9
5
NETERIT
62
26
8
5
ENTER IT
62
26
8

 

 

6
NETHER
70
34
7
5
WORLD
72
27
9

 

 

11
NETHERWORLD
142
61
7
1
I
9
9
9
12
NEITHERWORLD
151
70
16
1+2
-
1+5+1
7+0
1+6
3
NEITHERWORLD
7
7
7

 

 

-
6
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
-
1
+
=
6
-
=
6
=
6
=
6
-
-
14
-
-
-
-
19
+
=
33
3+3
=
6
=
6
=
6
-
6
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
2
5
9
-
+
=
21
2+1
=
3
=
3
=
3
-
-
-
5
20
5
18
-
+
=
48
4+8
=
12
1+2
3
=
3
-
6
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
14
5
20
5
18
19
+
=
81
8+1
=
9
=
9
=
9
-
-
5
5
2
5
9
1
+
=
27
2+7
=
9
=
9
=
9
-
6
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
5
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
28
6
N
E
T
E
R
S
-
-
17
-
-
6
-
27
-
18
2+8
-
-
-
-
-
9
-
-
-
1+7
-
-
-
-
2+7
-
1+8
10
6
N
E
T
E
R
S
-
-
8
-
-
6
-
9
-
9
1+0
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
1
6
N
E
T
E
R
S
-
-
8
-
-
6
-
9
-
9

 

 
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
5
-
-
-
-
1
+
=
6
-
=
6
=
6
=
6
-
14
-
-
-
-
19
+
=
33
3+3
=
6
=
6
=
6
6
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
5
2
5
9
-
+
=
21
2+1
=
3
=
3
=
3
-
-
5
20
5
18
-
+
=
48
4+8
=
12
1+2
3
=
3
6
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
14
5
20
5
18
19
+
=
81
8+1
=
9
=
9
=
9
-
5
5
2
5
9
1
+
=
27
2+7
=
9
=
9
=
9
6
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
5
5
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
6
N
E
T
E
R
S
-
-
17
-
-
6
-
27
-
18
-
-
-
-
-
9
-
-
-
1+7
-
-
-
-
2+7
-
1+8
6
N
E
T
E
R
S
-
-
8
-
-
6
-
9
-
9
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
6
N
E
T
E
R
S
-
-
8
-
-
6
-
9
-
9

 

 

6
ENTERS
81
27
9
6
NETERS
81
27
9
12
Add to Reduce
162
54
18
1+2
Reduce to Deduce
1+6+2
5+4
1+8
3
Essence of Number
9
9
9

 

 

-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
-
5
-
-
-
-
1
+
=
12
1+2
=
3
=
3
=
3
-
-
-
14
-
-
-
19
-
14
-
-
-
-
19
+
=
66
6+6
=
12
1+2
3
=
3
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
5
9
-
-
-
5
2
5
9
-
+
=
42
4+2
=
6
=
6
=
6
-
-`
5
-
20
5
18
-
-
-
5
20
5
18
-
+
=
96
9+6
=
15
1+5
6
=
6
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
5
14
20
5
18
19
-
14
5
20
5
18
19
+
=
162
1+6+2
=
9
=
9
=
9
-
-
5
5
2
5
9
1
-
5
5
2
5
9
1
+
=
54
5+4
=
9
=
9
=
9
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
5
-
5
-
-
-
5
5
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
28
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
17
-
-
12
-
54
-
18
2+8
1+2
5
5
-
5
-
-
-
5
5
-
5
-
-
-
-
1+7
-
-
1+2
-
5+4
-
1+8
10
3
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
8
-
-
3
-
9
-
9
1+0
-
5
5
2
5
9
1
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
1
3
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
8
-
-
3
-
9
-
9

 

 

-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
-
5
-
-
-
-
1
+
=
12
1+2
=
3
=
3
=
3
-
-
-
14
-
-
-
19
-
14
-
-
-
-
19
+
=
66
6+6
=
12
1+2
3
=
3
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
5
9
-
-
-
5
2
5
9
-
+
=
42
4+2
=
6
=
6
=
6
-
-`
5
-
20
5
18
-
-
-
5
20
5
18
-
+
=
96
9+6
=
15
1+5
6
=
6
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
5
14
20
5
18
19
-
14
5
20
5
18
19
+
=
162
1+6+2
=
9
=
9
=
9
-
-
5
5
2
5
9
1
-
5
5
2
5
9
1
+
=
54
5+4
=
9
=
9
=
9
-
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
5
5
-
5
-
-
-
5
5
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
28
12
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
17
-
-
12
-
54
-
18
2+8
1+2
5
5
-
5
-
-
-
5
5
-
5
-
-
-
-
1+7
-
-
1+2
-
5+4
-
1+8
10
3
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
8
-
-
3
-
9
-
9
1+0
-
5
5
2
5
9
1
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
1
3
E
N
T
E
R
S
-
N
E
T
E
R
S
-
-
8
-
-
3
-
9
-
9

 

 

6
ENTERS
81
27
9
11
INTERTWINED
141
60
6
6
NETERS
81
27
9
23
Add to Reduce
303
114
24
2+3
Reduce to Deduce
3+0+3
1+1+4
2+4
5
Essence of Number
6
6
6

 

 

-
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
-
9
5
-
-
-
-
-
9
5
-
-
-
5
-
-
-
-
1
+
=
40
4+0
=
4
=
4
=
4
=
4
-
-
-
14
-
-
-
19
-
9
14
-
-
-
-
-
9
14
-
-
-
14
-
-
-
-
19
+
=
112
1+1+2
=
4
=
4
=
4
=
4
-
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
2
5
9
-
-
-
-
2
5
9
2
5
-
-
5
4
-
-
5
2
5
9
-
+
=
74
7+4
=
11
1+1
2
=
2
=
2
-
-`
5
-
20
5
18
-
-
-
-
20
5
18
20
23
-
-
5
4
-
-
5
20
5
18
-
+
=
191
1+2+5
=
2
=
2
=
2
=
2
-
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
14
20
5
18
19
-
9
14
20
5
18
20
23
9
14
5
4
-
14
5
20
5
18
19
+
=
303
3+0+3
=
6
=
6
=
6
=
6
-
-
5
5
2
5
9
1
-
9
5
2
5
9
2
5
9
5
5
4
-
5
5
2
5
9
1
+
=
114
1+1+4
=
6
=
6
=
6
=
6
-
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
4
=
8
=
8
=
8
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
-
5
5
-
5
-
-
-
-
5
-
5
-
-
5
-
5
5
-
-
5
5
-
5
-
-
-
-
5
occurs
x
11
=
55
5+5
10
5+5
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
5
=
45
4+5
9
=
9
24
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
21
-
-
23
-
114
-
33
-
24
2+4
2+3
5
5
-
5
-
-
-
-
5
-
5
-
-
5
-
5
5
-
-
5
5
-
5
-
-
-
-
2+1
-
-
2+3
-
1+1+4
-
3+3
-
2+4
6
5
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
3
-
-
5
-
6
-
6
-
6
-
-
5
5
2
5
9
1
-
9
5
2
5
9
2
5
9
5
5
4
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
-
-
6
5
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
3
-
-
5
-
6
-
6
-
6

 

 

23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
1
-
9
5
-
-
-
-
-
9
5
-
-
-
5
-
-
-
-
1
+
=
40
4+0
=
4
=
4
=
4
=
4
-
-
14
-
-
-
19
-
9
14
-
-
-
-
-
9
14
-
-
-
14
-
-
-
-
19
+
=
112
1+1+2
=
4
=
4
=
4
=
4
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
2
5
9
-
-
-
-
2
5
9
2
5
-
-
5
4
-
-
5
2
5
9
-
+
=
74
7+4
=
11
1+1
2
=
2
=
2
-`
5
-
20
5
18
-
-
-
-
20
5
18
20
23
-
-
5
4
-
-
5
20
5
18
-
+
=
191
1+2+5
=
2
=
2
=
2
=
2
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
14
20
5
18
19
-
9
14
20
5
18
20
23
9
14
5
4
-
14
5
20
5
18
19
+
=
303
3+0+3
=
6
=
6
=
6
=
6
-
5
5
2
5
9
1
-
9
5
2
5
9
2
5
9
5
5
4
-
5
5
2
5
9
1
+
=
114
1+1+4
=
6
=
6
=
6
=
6
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
=
2
-
-
-
2
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
4
=
8
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
5
5
-
5
-
-
-
-
5
-
5
-
-
5
-
5
5
-
-
5
5
-
5
-
-
-
-
5
occurs
x
11
=
55
5+5
10
5+5
1
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
5
=
45
4+5
9
=
9
23
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
21
-
-
23
-
114
-
33
-
24
2+3
5
5
-
5
-
-
-
-
5
-
5
-
-
5
-
5
5
-
-
5
5
-
5
-
-
-
-
2+1
-
-
2+3
-
1+1+4
-
3+3
-
2+4
5
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
3
-
-
5
-
6
-
6
-
6
-
5
5
2
5
9
1
-
9
5
2
5
9
2
5
9
5
5
4
-
5
5
2
5
9
1
-
-
-
-
-
-
-
-
-
-
-
-
5
E
N
T
E
R
S
-
I
N
T
E
R
T
W
I
N
E
D
-
N
E
T
E
R
S
-
-
3
-
-
5
-
6
-
6
-
6

 

 

-
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
9
5
-
-
6
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
-
9
-
8
9
14
-
-
15
-
-
+
=
55
5+5
=
10
1+0
1
=
1
-
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
-
-
-
-
6
-
9
4
+
=
26
2+6
=
8
-
8
=
8
-
-
23
-
20
-
-
-
-
6
-
18
13
+
=
80
8+0
=
8
-
8
=
8
-
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
23
9
20
8
9
14
-
6
15
18
13
+
=
135
1+3+5
=
9
=
9
=
9
-
-
5
9
2
8
9
5
-
6
6
9
4
+
=
63
6+3
=
9
=
9
=
9
-
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
4
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
11
10
W
I
T
H
I
N
-
F
O
R
M
-
-
34
-
-
10
-
63
-
27
1+1
1+0
-
9
-
-
9
-
-
--
--
9
-
-
-
3+4
-
--
1+0
-
6+3
-
2+7
2
1
W
I
T
H
I
N
-
F
O
R
M
-
-
7
-
-
1
-
9
-
9
-
-
5
9
2
8
9
5
-
6
6
9
4
-
-
-
-
-
-
--
-
-
-
2
1
W
I
T
H
I
N
-
F
O
R
M
-
-
7
-
-
1
-
9
-
9

 

 

10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
9
-
8
9
5
-
-
6
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
9
-
8
9
14
-
-
15
-
-
+
=
55
5+5
=
10
1+0
1
=
1
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
5
-
2
-
-
-
-
6
-
9
4
+
=
26
2+6
=
8
-
8
=
8
-
23
-
20
-
-
-
-
6
-
18
13
+
=
80
8+0
=
8
-
8
=
8
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
23
9
20
8
9
14
-
6
15
18
13
+
=
135
1+3+5
=
9
=
9
=
9
-
5
9
2
8
9
5
-
6
6
9
4
+
=
63
6+3
=
9
=
9
=
9
10
W
I
T
H
I
N
-
F
O
R
M
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
10
W
I
T
H
I
N
-
F
O
R
M
-
-
34
-
-
10
-
63
-
27
1+0
-
9
-
-
9
-
-
--
--
9
-
-
-
3+4
-
--
1+0
-
6+3
-
2+7
1
W
I
T
H
I
N
-
F
O
R
M
-
-
7
-
-
1
-
9
-
9
-
5
9
2
8
9
5
-
6
6
9
4
-
-
-
-
-
-
--
-
-
-
1
W
I
T
H
I
N
-
F
O
R
M
-
-
7
-
-
1
-
9
-
9

 

 

-
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
6
-
-
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
-
9
-
8
15
-
-
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
-
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
-
-
3
2
-
6
-
9
4
+
=
31
3+1
=
4
-
4
=
4
-
-
23
-
20
-
-
21
20
-
6
-
18
13
+
=
121
1+2+1
=
4
-
4
=
4
-
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
23
9
20
8
15
21
20
-
6
15
18
13
+
=
168
1+6+8
=
6
=
6
=
6
-
-
5
9
2
8
6
3
2
-
6
6
9
4
+
=
60
6+0
=
6
=
6
=
6
-
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
8
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
37
-
-
10
-
60
-
42
-
1+1
-
9
-
-
--
-
-
-
--
--
9
-
-
-
3+7
-
--
1+0
-
6+0
-
4+2
8
8
W
I
T
H
O
U
T
-
F
O
R
M
-
-
10
-
-
1
-
6
-
6
-
-
5
9
2
8
6
3
2
-
6
6
9
4
-
-
1+0
-
-
-
--
-
-
-
8
8
W
I
T
H
O
U
T
-
F
O
R
M
-
-
1
-
-
1
-
6
-
6

 

 

11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
-
9
-
8
6
-
-
-
-
6
-
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
9
-
8
15
-
-
-
-
15
-
-
+
=
47
4+7
=
11
1+1
2
=
2
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
5
-
2
-
-
3
2
-
6
-
9
4
+
=
31
3+1
=
4
-
4
=
4
-
23
-
20
-
-
21
20
-
6
-
18
13
+
=
121
1+2+1
=
4
-
4
=
4
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
--
-
-
-
-
-
23
9
20
8
15
21
20
-
6
15
18
13
+
=
168
1+6+8
=
6
=
6
=
6
-
5
9
2
8
6
3
2
-
6
6
9
4
+
=
60
6+0
=
6
=
6
=
6
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
11
W
I
T
H
O
U
T
-
F
O
R
M
-
-
37
-
-
10
-
60
-
42
1+1
-
9
-
-
--
-
-
-
--
--
9
-
-
-
3+7
-
--
1+0
-
6+0
-
4+2
8
W
I
T
H
O
U
T
-
F
O
R
M
-
-
10
-
-
1
-
6
-
6
-
5
9
2
8
6
3
2
-
6
6
9
4
-
-
1+0
-
-
-
--
-
-
-
8
W
I
T
H
O
U
T
-
F
O
R
M
-
-
1
-
-
1
-
6
-
6

 

 

-
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
-
9
5
1
9
-
-
-
6
-
-
1
9
-
-
+
=
40
4+0
=
4
-
4
-
4
-
-
9
14
19
9
-
-
-
15
-
-
19
9
-
-
+
=
94
9+4
=
13
1+3
4
-
4
-
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
4
5
-
-
3
2
-
-
4
5
+
=
23
2+3
=
5
-
5
-
5
-
-
-
-
-
-
4
5
-
-
21
20
-
-
4
5
+
=
59
5+9
=
14
1+4
5
-
5
-
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
-
9
14
19
9
4
5
-
15
21
20
19
9
4
5
+
=
153
1+5+3
=
9
-
9
-
9
-
-
9
5
1
9
4
5
-
6
3
2
1
9
4
5
+
=
63
6+3
=
9
-
9
-
9
-
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
--
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
7
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
30
-
-
13
-
63
-
36
1+5
1+3
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
1+3
-
6+3
-
3+6
6
4
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9
-
-
9
5
1
9
4
5
-
6
3
2
1
9
4
5
-
-
-
-
-
-
-
-
-
-
6
4
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9

 

 

3
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
9
5
1
9
-
-
-
6
-
-
1
9
-
-
+
=
40
4+0
=
4
-
4
-
4
-
9
14
19
9
-
-
-
15
-
-
19
9
-
-
+
=
94
9+4
=
13
1+3
4
-
4
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
4
5
-
-
3
2
-
-
4
5
+
=
23
2+3
=
5
-
5
-
5
-
-
-
-
-
4
5
-
-
21
20
-
-
4
5
+
=
59
5+9
=
14
1+4
5
-
5
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
9
14
19
9
4
5
-
15
21
20
19
9
4
5
+
=
153
1+5+3
=
9
-
9
-
9
-
9
5
1
9
4
5
-
6
3
2
1
9
4
5
+
=
63
6+3
=
9
-
9
-
9
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
--
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
30
-
-
13
-
63
-
36
1+3
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
1+3
-
6+3
-
3+6
4
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9
-
9
5
1
9
4
5
-
6
3
2
1
9
4
5
-
-
-
-
-
-
-
-
-
-
4
I
N
S
I
D
E
-
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9

 

 

3
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
9
5
1
9
-
-
6
-
-
1
9
-
-
+
=
40
4+0
=
4
-
4
-
4
-
9
14
19
9
-
-
15
-
-
19
9
-
-
+
=
94
9+4
=
13
1+3
4
-
4
13
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
4
5
-
3
2
-
-
4
5
+
=
23
2+3
=
5
-
5
-
5
-
-
-
-
-
4
5
-
21
20
-
-
4
5
+
=
59
5+9
=
14
1+4
5
-
5
13
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
-
-
-
--
-
-
-
-
-
9
14
19
9
4
5
15
21
20
19
9
4
5
+
=
153
1+5+3
=
9
-
9
-
9
-
9
5
1
9
4
5
6
3
2
1
9
4
5
+
=
63
6+3
=
9
-
9
-
9
13
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
--
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
5
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
9
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
30
-
-
13
-
63
-
36
1+3
9
-
-
9
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
1+3
-
6+3
-
3+6
4
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9
-
9
5
1
9
4
5
6
3
2
1
9
4
5
-
-
-
-
-
-
-
-
-
-
4
I
N
S
I
D
E
O
U
T
S
I
D
E
-
-
3
-
-
4
-
9
-
9

 

 

--
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
--
8
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
--
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
5
1
9
2
-
-
6
-
9
5
-
1
-
9
-
5
1
2
5
9
+
=
69
6+9
=
15
1+5
6
=
6
-
-
5
1
18
20
-
-
6
-
18
5
-
1
-
18
-
23
1
20
5
18
+
=
159
1+5+9
=
15
1+5
6
=
6
--
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
5
1
18
20
8
-
6
9
18
5
-
1
9
18
-
23
1
20
5
18
+
=
185
1+8+5
=
14
1+4
5
=
5
-
-
5
1
9
2
8
-
6
9
9
5
-
1
9
9
-
5
1
2
5
9
+
=
95
9+5
=
14
1+4
5
=
5
-
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
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
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
9
9
-
-
-
9
9
-
-
-
-
-
9
-
-
9
occurs
x
6
=
36
3+6
9
14
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
31
-
-
17
-
95
-
32
1+4
1+7
-
-
9
-
-
-
-
9
9
-
-
-
9
9
-
-
-
-
-
9
-
-
3+1
-
-
1+7
-
9+5
-
3+2
5
8
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
4
-
-
8
-
14
-
5
-
-
5
1
9
2
8
-
6
9
9
5
-
1
9
9
-
5
1
2
5
9
-
-
-
-
-
-
-
1+4
-
3+2
5
8
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
4
-
-
8
-
5
-
5

 

 

17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
--
8
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
5
1
9
2
-
-
6
-
9
5
-
1
-
9
-
5
1
2
5
9
+
=
69
6+9
=
15
1+5
6
=
6
-
5
1
18
20
-
-
6
-
18
5
-
1
-
18
-
23
1
20
5
18
+
=
159
1+5+9
=
15
1+5
6
=
6
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
--
-
-
-
-
-
5
1
18
20
8
-
6
9
18
5
-
1
9
18
-
23
1
20
5
18
+
=
185
1+8+5
=
14
1+4
5
=
5
-
5
1
9
2
8
-
6
9
9
5
-
1
9
9
-
5
1
2
5
9
+
=
95
9+5
=
14
1+4
5
=
5
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
--
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
=
4
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
9
9
-
-
-
9
9
-
-
-
-
-
9
-
-
9
occurs
x
6
=
36
3+6
9
17
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
31
-
-
17
-
95
-
32
1+7
-
-
9
-
-
-
-
9
9
-
-
-
9
9
-
-
-
-
-
9
-
-
3+1
-
-
1+7
-
9+5
-
3+2
8
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
4
-
-
8
-
14
-
5
-
5
1
9
2
8
-
6
9
9
5
-
1
9
9
-
5
1
2
5
9
-
-
-
-
-
-
-
1+4
-
3+2
8
E
A
R
T
H
-
F
I
R
E
-
A
I
R
-
W
A
T
E
R
-
-
4
-
-
8
-
5
-
5

 

 

5
NORTH
75
30
3
5
SOUTH
83
20
2
4
EAST
45
9
9
4
WEST
67
13
4
18
Add
270
72
18
1+8
Reduce
2+7+0
7+2
1+8
9
Deduce
9
9
9

 

 

-
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
5
6
-
-
8
-
1
6
-
-
8
-
-
-
1
-
-
-
-
1
-
+
=
36
2+6
=
8
=
8
-
8
-
-
14
15
-
-
8
-
19
15
-
-
8
-
-
-
19
-
-
-
-
19
-
+
=
117
1+1+7
=
8
=
8
-
8
-
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
2
-
-
-
-
3
2
-
-
5
1
-
2
-
5
5
-
2
+
=
36
1+5+9
=
15
1+5
6
-
6
-
-
-
-
18
20
-
-
-
-
21
20
-
-
5
1
-
20
-
23
5
-
20
+
=
153
1+5+3
=
15
1+5
6
-
6
-
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
14
15
18
20
8
-
19
15
21
20
8
-
5
1
19
20
-
23
5
19
20
+
=
270
2+7+0
=
9
=
9
-
9
-
-
5
6
9
2
8
-
1
6
3
2
8
-
5
1
1
2
-
5
5
1
2
+
=
117
1+1+7
=
9
=
9
-
9
-
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
-
4
-
-
-
-
-
2
-
-
-
-
-
2
--
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
4
=
8
-
8
-
-
-
-
-
-
-
-
--
-
3
--
-
-
-
--
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
6
-
-
-
-
-
6
--
-
--
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
9
11
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
34
-
-
18
-
72
-
36
1+1
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+4
-
-
1+8
-
7+2
-
3+6
2
9
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
7
-
-
9
-
9
-
9
-
-
5
6
9
2
8
-
1
6
3
2
8
-
5
1
1
2
-
5
5
1
2
-
-
-
-
-
-
-
-
-
-
2
9
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
7
-
-
9
-
9
-
9

 

 

18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
5
6
-
-
8
-
1
6
-
-
8
-
-
-
1
-
-
-
-
1
-
+
=
36
2+6
=
8
=
8
-
8
-
14
15
-
-
8
-
19
15
-
-
8
-
-
-
19
-
-
-
-
19
-
+
=
117
1+1+7
=
8
=
8
-
8
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
-
9
2
-
-
-
-
3
2
-
-
5
1
-
2
-
5
5
-
2
+
=
36
1+5+9
=
15
1+5
6
-
6
-
-
-
18
20
-
-
-
-
21
20
-
-
5
1
-
20
-
23
5
-
20
+
=
153
1+5+3
=
15
1+5
6
-
6
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
14
15
18
20
8
-
19
15
21
20
8
-
5
1
19
20
-
23
5
19
20
+
=
270
2+7+0
=
9
=
9
-
9
-
5
6
9
2
8
-
1
6
3
2
8
-
5
1
1
2
-
5
5
1
2
+
=
117
1+1+7
=
9
=
9
-
9
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
-
4
-
-
-
-
2
-
-
-
-
-
2
--
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
4
=
8
-
8
-
-
-
-
-
-
-
--
-
3
--
-
-
-
--
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
6
--
-
--
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
9
18
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
34
-
-
18
-
72
-
36
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+4
-
-
1+8
-
7+2
-
3+6
9
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
7
-
-
9
-
9
-
9
-
5
6
9
2
8
-
1
6
3
2
8
-
5
1
1
2
-
5
5
1
2
-
-
-
-
-
-
-
-
-
-
9
N
O
R
T
H
-
S
O
U
T
H
-
E
A
S
T
-
W
E
S
T
-
-
7
-
-
9
-
9
-
9

 

 

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

 

 

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

 

 

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

 

EARTH HEART THERA TERAH

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT I

PLANETS STARS AND LIFE

Page 24

"A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "
Page 24 / 25
"A manifestly artificial signal- even if it were as boring as lists of prime numbers, or the digits of 'pi' - would imply that 'intelli- gence' wasn't unique to the Earth and had evolved elsewhere. The nearest potential sites are so far away that signals would take many years in transit. For this reason alone, transmission would be primarily one-way. There would be time to send a measured response, but no scope for quick repartee!
Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.)
Clearly, alien beings wouldn't use metres, kilograms or seconds. But we could exchange information about the ratios of two masses (such as thc ratio of proton and electron masses) or of two lengths, which are 'pure numbers' that don't depend on what units are used: the statement that one rod is ten times as long as another is true (or false) whether we measure lengths / in feet or metres or some alien units"

 

"A proton is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'"

 

 

E
=
5
-
8
EIGHTEEN
73
46
1
T
=
2
-
9
THIRTYSIX
152
53
8
-
-
7
4
17
First Total
225
99
9
-
-
-
-
1+7
Add to Reduce
2+2+5
9+9
-
Q
-
7
-
8
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
Q
-
7
-
8
Essence of Number
9
9
9

 

 

WHY SMASH ATOMS

A. K. Solomon 1940

VAN DE GRAAFF GENERATOR

Page 77

"Once the fairy tale hero has penetrated the ring of fire round the magic mountain he is free to woo the heroine in her castle on the mountain top."

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

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

Page 15

The Nine Billion Names of God

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

Page16

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

 

 

I = 9 9 = I

R = 9 9 = R

 

 

OF

T9ME AND STA9S

A9thu9 C. Cla9ke,1972

Page 15

THE N9NE B9LL9ON NAMES OF GOD

'Th9s 9s a sl9ghtly unusual 9equest,'sa9d D9 Wagne9, w9th what he hoped was commendable 9est9a9nt.' As fa9 as 9 know, 9t's the f99st t9me anyone's been asked to supply a T9betan monaste9y with an Automat9c Sequence Compute9. 9 don't w9sh to be 9nqu9s9t9ve, but 9 should ha9dly have thought that you9- ah - establ9shment had much use for such a mach9ne.Could you expla9n just what you 9ntend to do w9th 9t?'

'Gladly,' 9epl9ed the lama, 9eadjust9ng h9s s9lk 9obes and ca9efully putting away the sl9de 9ule he had been us9ng fo9 cu99ency conve9s9ons. 'You9 Ma9k V Compute9 can ca99y out any 9out9ne mathemat9cal ope9at9on 9nvolv9ng up to ten d9g9ts. Howeve9, for ou9 work we are 9nte9ested 9n lette9s, not numbe9s. As we w9sh you to mod9fy the output c9rcu9ts,the mach9ne w9ll be p99nt9ng wo9ds not columns of f9gu9es.'

'9 dont qu9te unde9stand…'

'Th9s 9s a p9oject on wh9ch we have been work9ng fo9 the last th9ee centu99es - s9nce the lamase9y was founded, 9n fact.9t 9s somewhat al9en to you9 way of thought, so9 hope you w9ll l9sten with an open m9nd wh9le 9 expla9n 9t

'Natu9ally.'

'9t 9s 9eally qu9te s9mple.We have been comp9l9ng a l9st wh9ch shall conta9n all the poss9ble names of God'

'9 beg you9 pa9don?' / Page16 / 'We have 9eason to bel9eve' cont9nued the lama 9mpe9tu9bably, ' that all such names can be w99tten with not mo9e than n9ne lette9s 9n an alphabet we have dev9sed,'

'And you have been do9ng th9s for three centu99es?

'Yes: we expected9t would take us about f9fteen thousand years to complete the task.'

'Oh, Dr Wagne9 looked a l9ttle dazed. 'Now9 see why you wanted to h99e one of ou9 mach9nes. But what exactly9s the pu9pose of th9s p9oject ?

'The lama hes9tated fo9 a f9act9on of a second, and Wagne9 wonde9ed9f he had offended h9m.9f so the9e was no t9ace of annoyance9n the 9eply.

'Call9t 99tual, 9f you l9ke, but 9t's a fundamental pa9t of ou9 bel9ef. All the many names of the Sup9eme Be9ng - God , Jehova , Allah , and so on - they a9e only man made labels. The9e 9s a ph9losoph9cal p9oblem of some d9ff9culty he9e, wh9ch9 do not p9opose to d9scuss, but somewhe9e among all the poss9ble comb9nat9ons of lette9s that can occu9 a9e what one may call the 9eal names of God. By systemat9c pe9mutat9on of lette9s, we have been t9y9ng to l9st them all'

9 see. You've been sta9t9ng at AAAAAAA… and wo9k-9ng up to ZZZZZZZZ …'

'Exactly - though we use a spec9al alphabet of ou9 own. Mod9fy9ng the elect9omat9c typew99te9s to deal w9th th9s 9s of cou9se t99v9al. A 9athe9 mo9e 9nte9est9ng p9oblem 9s that of dev9s9ng su9table c99cu9ts to el9m9nate 9 9d9culous comb9nat9ons. Fo9 example, no lette9 must occu9 mo9e than th9ee t9mes 9n sucess9on.'

'Th9ee? Su9ely you mean two.'

'Th9ee 9s co99ect; 9 am af9a9d 9t would take too long to expla9n why , even 9f you unde9stood ou9 language.'/ Page 17 / '9'm su9e 9t would,' sa9d Wagne9 hast9ly. 'Go on.'

'Luck9ly, 9t w9ll be a s9mple matte9 to adapt you9 Automat9c Sequence Compute9 fo9 th9s wo9k, s9nce once 9t has been p9og9ammed p9ope9ly 9t w9ll pe9mute each lette9 9n tu9n and p99nt the 9esult. What would have taken us f9fteen thousand years 9t w9ll be able to do 9n a hund9ed days.'

'Dr Wagne9 was sca9cely consc9ous of the fa9nt sounds f9om the Manhatten st9eets fa9 below. He was 9n a d9ffe9ent wo9ld, a wo9ld of natu9al, not man-made mounta9ns. H9gh up 9n the99 9emote ae99es these monks had been pat9ently at wo9k gene9at9on afte9 gene9at9on, comp9l9ng the99 l9sts of mean9ngless wo9ds. Was the9e any l9m9ts to the foll9es of mank9nd ? St9ll, he must g9ve no h9nt of h9s 9nne9 thoughts. The custome9 was always 99ght…"

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

Page 68

Into the Comet


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

 

 

DECIPHER

MANKIND HAD 1200 YEARS YEARS

TO CRACK THE CODE WE HAVE

ONE WEEK LEFT

Stel Pavlou

Page 357

24 hours

"We live in a universe of patterns. Every night the stars move in circles across the sky. The seasons cycle at yearly inter vals. No two snowflakes are ever exactly the same, but the all have sixfold symmetry. Tigers and zebras are covered in patterns of stripes; leopards and hyenas are covered in pat terns of spots. Intricate trains of waves march across the oceans; very similar trains of sand dunes march across the desert . . . By using mathematics... we have discovered great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes."

Ian Stewart, Nature's Numbers, 1995

 

 

2061

ODYSSEY THREE

Arthur C. Clarke 1987

Page 13 (number 0mitted)

"THE MAGIC MOUNTAIN"

 

 

THE LOST WORLDS OF 2001

Arthur C.Clarke

1972

"Sorry to interrupt the festivities, but we have a problem."
(HAL 9000, during Frank Poole's birthday party)


"Houston, we've had a problem." (Jack Swigert, shortly after playing the

Zarathustra

theme to his TV audience, aboard Apollo 13 Command Module Odyssey)

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1924

Page 706 /716 (inclusive)

THE

THUNDERBOLT

Page 716

"FINIS OPERIS"

 

 

THE DIE IS NOW CAST NOW CAST IS THE DIE

 

 

CITIZENS OF PLANET EARTH

WE HOLD THESE TRUTHS TO BE SELF EVIDENT

THAT

ALL

HUMAN BEINGS

ARE CREATED EQUAL THAT THEY ARE ENDOWED BY THEIR

CREATOR

WITH CERTAIN UNALIENABLE RIGHTS THAT AMONG THESE ARE

LIFE

LIBERTY AND THE PURSUIT OF HAPPINESS

 

 

GODS

PEACE BE UNTO

YOU

CHILDREN OF THE RAINBOW LIGHT

SALUTATIONS AND GOODWILL

THOUGHTS

OF

LIGHT AND LOVE GODS LOVE AND LIGHT

UPON YOU AND UPON ALL SENTIENT BEINGS

 

 

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
11
TERRESTRIAL
145
55
1
16
EXTRATERRESTRIAL
213
78
6
3
AND
19
10
1
9
CELESTIAL
86
32
5
2
AM
14
5
5
1
I
9
9
9
49
First Total
558
216
45
4+9
Add to Reduce
5+5+8
2+1+6
4+5
13
Second Total
18
9
9
1+3
Reduce to Deduce
1+8
-
-
4
Essence of Number
9
9
9

 

 

GOD ONE GOD

AND ONE CHOSEN RACE THE HUMAN RACE

 

 

HOLY BIBLE

Scofield References

C 1 V 16

THE ACTS OF THE APOSTLES

Page 1148 (Part quoted)

"MEN AND BRETHREN THIS SCRIPTURE MUST NEEDS HAVE BEEN FULFILLED

WHICH THE HOLY GHOST BY THE MOUTH OF DAVID SPAKE"

 

 

 

 

SECRETS OF THE PYRAMIDS REVEALED

Robert K. Moffett 1976

Page 153

"Maat can be defined loosely as Truth (definately capitalized) or "right order"

"Maat"

"Maat"

Page 154

"In the pursuit of Maat,"

 

9

I

AM AT

MAAT

AM AT MAAT MAAT AM AT

MAAT ISISIS ISISIS MAAT

ISISIS

IS GODS LAW GODS IS

I

AM AT TA MA

AM MAAT AT

AM

I

9

 

 

 

I

ME

REAL REALITY REAL

LAW IS MAAT IS MAAT IS LAW

THAT

ISISIS

THE

CREATORS R PERFECT R CREATORS

BALANCING ALWAYS BALANCING

I AM MAAT AT AM AT MAAT AM I

R DIVINE CREATORS R CREATORS DIVINE R

 

 

-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
9
1
-
-
9
-
9
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
-
-
9
19
-
-
9
-
9
14
-
-
-
-
-
+
=
60
6+0
=
6
=
6
=
6
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
4
1
1
2
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
30
3+0
=
3
=
3
=
3
-
-
13
1
1
20
-
-
-
-
4
-
22
-
-
5
-
12
1
23
+
=
102
1+0+2
=
3
=
3
=
3
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
13
1
1
20
-
9
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
=
9
=
9
-
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
=
9
=
9
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
2+1
2+1
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
3
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
3
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
9
1
-
-
9
-
9
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
-
9
19
-
-
9
-
9
14
-
-
-
-
-
+
=
60
6+0
=
6
=
6
=
6
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
4
1
1
2
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
30
3+0
=
3
=
3
=
3
-
13
1
1
20
-
-
-
-
4
-
22
-
-
5
-
12
1
23
+
=
102
1+0+2
=
3
=
3
=
3
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
13
1
1
20
-
9
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
=
9
=
9
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
=
9
=
9
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
2+1
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

 

-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+7
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

 

HOW GREAT THOU ART MY GOD HOW GREAT THOU ART

 

 

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

 

 

O
=
6
-
3
ONE
34
16
7
T
=
2
-
3
TWO
56
29
2
T
=
2
-
5
THREE
52
16
7
F
=
6
-
4
FOUR
60
24
6
F
=
6
-
4
FIVE
65
20
2
S
=
1
-
3
SIX
42
24
6
S
=
1
-
5
SEVEN
58
13
4
E
=
5
-
5
EIGHT
49
31
4
N
=
5
-
4
NINE
42
24
6
-
-
34
-
36
Total
458
197
44
-
-
3+4
-
3+6
Add
4+5+8
1+9+7
4+4
-
-
7
4
9
 Reduce
17
17
8
-
-
-
-
-
 Deduce
1+7
1+7
-
-
-
7
-
9
 Essence
8
8
8

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

O
=
6
3
ONE
34
16
7
T
=
2
3
TWO
58
13
4
T
=
2
5
THREE
56
29
2
F
=
6
4
FOUR
60
24
6
F
+
6
4
FIVE
42
24
6
S
=
1
3
SIX
52
16
7
S
=
1
5
SEVEN
65
20
2
E
=
5
5
EIGHT
49
31
4
N
=
5
4
NINE
42
24
6
-
-
39
36
-
458
197
44
-
-
3+9
3+6
-
4+5+8
1+9+7
4+4
-
-
12
9
-
17
17
8
-
-
1+2
-
-
-
-
-
-
-
3
9
-
8
8
8

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Page 32

5


To Sorcerers and Magicians number FIVE is the most powerful - five is the mark of the pentacle, a five pointed star drawn by extending the sides of a Pentagon. Five surely is in the possession of the occult. And the Pentagon is the geometric figure in which the golden ratio of classical art and architecture is found most.

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

 

 

O
=
15
-
3
ONE
34
16
7
-
1
T
=
20
-
3
TWO
58
13
4
-
2
T
=
20
-
5
THREE
56
29
2
-
3
F
=
6
-
4
FOUR
60
24
6
-
4
-
-
61
-
15
Add
208
82
19
-
10
-
-
6+1
-
1+5
Reduce
2+0+8
8+2
1+9
-
1+0
-
-
7
-
6
Deduce
10
10
10
-
1
-
-
-
-
-
Produce
1+0
1+0
1+0
-
-
-
-
7
-
6
Essence
1
1
1
-
1

 

 

N
=
14
-
4
NINE
42
24
6
-
9
E
=
5
-
5
EIGHT
49
31
4
-
8
S
=
19
-
5
SEVEN
65
20
2
-
7
S
=
19
-
3
SIX
52
16
7
-
6
-
-
57
-
17
Add
208
91
19
-
30
-
-
5+7
-
1+7
Reduce
2+0+8
9+1
1+9
-
3+0
-
-
12
-
8
Deduce
10
10
10
-
3
-
-
1+2
-
-
Produce
1+0
1+0
1+0
-
-
-
-
3
-
8
Essence
1
1
1
-
3

 

 

4
FIVE
42
24
6

 

1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1

 

15
ONE TWO THREE FOUR
208
82
1
4
FIVE
42
24
6
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

3
ONE
34
16
7
-
3
SIX
52
16
7
3
TWO
58
13
4
-
5
SEVEN
65
20
2
5
THREE
56
29
2
-
5
EIGHT
49
31
4
4
FOUR
60
24
6
-
4
NINE
42
24
6
15
Add
208
82
19
-
17
Add
208
91
19
1+5
Reduce
2+0+8
8+2
1+9
-
1+7
Reduce
2+0+8
9+1
1+9
6
Deduce
10
10
10
-
8
Deduce
10
10
10
-
Produce
1+0
1+0
1+0
-
-
Produce
1+0
1+0
1+0
6
Essence
1
1
1
-
8
Essence
1
1
1

 

 

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

 

 

E
=
5
-
8
EIGHTEEN
73
46
1
A
=
1
-
9
THIRTYSIX
152
53
8
-
-
9
4
17
First Total
225
99
9
-
-
-
-
1+7
Add to Reduce
2+2+5
9+9
-
Q
-
9
-
8
Second Total
9
18
9
-
-
-
-
1+7
Reduce to Deduce
-
1+8
-
Q
-
9
-
8
Essence of Number
9
9
9

 

 

-
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
5
-
-
8
9
-
-
-
1
9
6
+
=
55
5+5
=
10
1+0
1
=
1
-
-
-
9
-
8
-
-
-
14
-
-
8
9
-
-
-
19
9
24
+
=
100
1+0+0
=
1
2+0
1
=
1
-
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
5
-
7
-
2
5
5
-
+
2
-
-
9
2
7
-
-
-
+
=
44
4+4
=
8
=
8
=
8
-
-
5
-
7
-
20
5
5
-
+
20
-
-
18
20
25
-
-
-
+
=
125
1+2+5
=
8
=
8
=
8
-
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
5
9
7
8
20
5
5
14
+
20
8
9
18
20
25
19
9
24
+
=
225
2+2+5
=
9
=
9
=
9
-
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
99
9+9
=
18
=
9
=
9
-
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
1
-
-
+
=
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
+
2
-
-
-
2
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
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
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
+
-
-
9
9
-
-
-
9
-
+
=
9
occurs
x
4
=
36
3+6
9
7
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
38
-
-
17
-
99
-
36
-
1+7
-
9
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
-
-
-
3+8
-
-
1+7
-
9+9
-
3+6
7
8
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
11
-
-
8
-
18
-
9
-
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
1+1
-
-
-
-
1+8
-
-
7
8
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
2
-
-
8
-
9
-
9

 

 

17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
5
-
-
8
9
-
-
-
1
9
6
+
=
55
5+5
=
10
1+0
1
=
1
-
-
9
-
8
-
-
-
14
-
-
8
9
-
-
-
19
9
24
+
=
100
1+0+0
=
1
2+0
1
=
1
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
5
-
7
-
2
5
5
-
+
2
-
-
9
2
7
-
-
-
+
=
44
4+4
=
8
=
8
=
8
-
5
-
7
-
20
5
5
-
+
20
-
-
18
20
25
-
-
-
+
=
125
1+2+5
=
8
=
8
=
8
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
-
5
9
7
8
20
5
5
14
+
20
8
9
18
20
25
19
9
24
+
=
225
2+2+5
=
9
=
9
=
9
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
99
9+9
=
18
=
9
=
9
17
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
1
-
-
+
=
1
occurs
x
1
=
1
=
1
+
-
-
-
-
2
-
-
-
+
2
-
-
-
2
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
+
5
-
-
-
-
5
5
5
+
-
-
-
-
-
-
-
-
-
+
=
5
occurs
x
4
=
20
2+0
2
+
-
-
-
-
-
-
-
-
+
-
-
-
-
-
-
-
-
6
+
=
6
occurs
x
1
=
6
-
6
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
+
-
9
-
-
-
-
-
-
+
-
-
9
9
-
-
-
9
-
+
=
9
occurs
x
4
=
36
3+6
9
17
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
38
-
-
17
-
99
-
36
1+7
-
9
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
-
-
-
3+8
-
-
1+7
-
9+9
-
3+6
8
E
I
G
H
T
E
E
N
-
T
H
I
R
T
Y
S
I
X
-
-
11
-
-
8
-
18
-
9
-
5
9
7
8
2
5
5
5
+
2
8
9
9
2
7
1
9
6
+
=
1+1
-
-
-
-
1+8
-
-
8
E
I
G
H
T
E
E
N
+
T
H
I
R
T
Y
S
I
X
+
=
2
-
-
8
-
9
-
9

 

 

E
=
5
-
8
EIGHTEEN
73
46
1
A
=
1
-
9
THIRTYSIX
152
53
8
-
-
9
4
17
First Total
225
99
9
-
-
-
-
1+7
Add to Reduce
2+2+5
9+9
-
Q
-
9
-
8
Second Total
9
18
9
-
-
-
-
1+7
Reduce to Deduce
-
1+8
-
Q
-
9
-
8
Essence of Number
9
9
9

 

 

 

 

9
9
T
H
E
-
F
A
M
I
L
Y
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
-
-
9
-
-
+
=
17
1+7
=
8
-
8
-
-
-
8
-
-
-
-
-
9
-
-
+
=
17
1+7
=
8
-
8
9
9
T
H
E
-
F
A
M
I
L
Y
-
-
-
-
-
--
-
-
-
-
2
-
5
-
6
1
4
9
3
7
+
=
28
2+8
=
10
1+0
1
-
-
20
-
5
-
6
1
13
9
12
25
+
=
82
8+2
=
10
1+0
1
9
9
T
H
E
-
F
A
M
I
L
Y
-
-
-
-
-
--
-
-
-
-
20
8
5
-
6
1
13
9
12
25
+
=
99
9+9
=
18
1+8
9
-
-
2
8
5
-
6
1
4
9
3
7
+
=
45
4+5
=
9
-
9
9
9
T
H
E
-
F
A
M
I
L
Y
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
2
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
8
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
45
9
T
H
E
-
F
A
M
I
L
Y
-
-
45
-
-
9
-
45
4+5
-
-
-
-
-
-
-
-
9
-
-
-
-
4+5
-
-
-
-
4+5
9
9
T
H
E
-
F
A
M
I
L
Y
-
-
9
-
-
9
-
9
-
-
2
8
5
-
6
1
4
9
3
7
-
-
-
-
-
--
-
-
9
9
T
H
E
-
F
A
M
I
L
Y
-
-
9
-
-
9
-
9

 

 

4
GODS
45
18
9
7
IMAGERS
5
5
9
8
CREATORS
99
36
9
-
-
-
-
-
-
-
-
-
-
8
THE ENNEA
72
36
9

 

 

 

FIRST CONTACT

 

 

-
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
-
-
-
6
5
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
-
9
-
19
-
-
-
15
14
-
-
-
-
+
=
57
5+7
=
12
1+2
3
=
3
-
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
6
-
9
-
2
-
3
-
-
2
1
3
2
+
=
28
2+8
=
10
1+0
1
=
1
-
-
6
-
18
-
20
-
3
-
-
20
1
3
20
+
=
91
9+1
=
10
1+0
1
=
1
-
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
6
9
18
19
20
-
3
15
14
20
1
3
20
+
=
148
1+4+8
=
13
1+3
4
=
4
-
-
6
9
9
1
2
-
3
6
5
2
1
3
2
+
=
58
5+8
=
13
1+3
4
=
4
-
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
19
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
26
-
-
12
-
49
-
31
1+9
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
1+2
-
4+9
-
3+1
10
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
8
-
-
3
-
13
-
4
1+0
-
6
9
9
1
2
-
3
6
5
2
1
3
2
-
-
-
-
-
-
-
1+3
-
-
1
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
8
-
-
3
-
4
-
4

 

 
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
-
-
-
6
5
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-
9
-
19
-
-
-
15
14
-
-
-
-
+
=
57
5+7
=
12
1+2
3
=
3
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
6
-
9
-
2
-
3
-
-
2
1
3
2
+
=
28
2+8
=
10
1+0
1
=
1
-
6
-
18
-
20
-
3
-
-
20
1
3
20
+
=
91
9+1
=
10
1+0
1
=
1
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
6
9
18
19
20
-
3
15
14
20
1
3
20
+
=
148
1+4+8
=
13
1+3
4
=
4
-
6
9
9
1
2
-
3
6
5
2
1
3
2
+
=
58
5+8
=
13
1+3
4
=
4
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
2
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
26
-
-
12
-
49
-
31
-
-
9
9
-
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
1+2
-
4+9
-
3+1
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
8
-
-
3
-
13
-
4
-
6
9
9
1
2
-
3
6
5
2
1
3
2
-
-
-
-
-
-
-
1+3
-
-
5
F
I
R
S
T
-
C
O
N
T
A
C
T
-
-
8
-
-
3
-
4
-
4

 

 

 

 

 

 

 

`-
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
9
5
-
1
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
-
-
-
-
14
-
-
-
-
-
-
-
-
9
14
-
19
+
=
56
5+6
=
11
1+1
2
=
2
`-
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
6
9
1
2
5
9
-
1
3
-
7
9
5
5
2
-
-
3
-
+
=
71
7+1
=
71
=
8
=
8
-
-
6
18
1
20
5
18
-
1
12
-
7
18
5
5
20
-
-
3
-
+
=
143
1+4+3
=
143
1+4+3
8
=
8
`-
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
6
18
1
20
5
18
14
1
12
-
7
18
5
5
20
9
14
7
19
+
=
199
1+9+9
=
19
1+9
10
=
1
-
-
6
9
1
2
5
9
5
1
3
-
7
9
5
5
2
9
5
7
17
+
=
91
9+1
=
19
=
1
=
1
-
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
--
--
--
2
--
--
--
--
--
-
--
--
--
--
2
--
--
--
--
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
5
5
-
-
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
9
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
12
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
33
-
-
18
-
91
-
37
1+2
1+8
-
-
-
-
5
-
5
-
-
-
-
-
5
5
-
-
5
-
-
-
-
3+3
-
-
1+8
-
9+1
-
3+7
3
9
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
6
-
-
9
-
10
-
10
-
-
6
9
1
2
5
9
5
1
3
-
7
9
5
5
2
9
5
7
-
-
-
-
-
-
-
-
1+0
-
1+0
3
9
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
6
-
-
9
-
1
-
1

 

 

18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
9
5
-
1
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
-
-
-
14
-
-
-
-
-
-
-
-
9
14
-
19
+
=
56
5+6
=
11
1+1
2
=
2
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
6
9
1
2
5
9
-
1
3
-
7
9
5
5
2
-
-
3
-
+
=
71
7+1
=
71
=
8
=
8
-
6
18
1
20
5
18
-
1
12
-
7
18
5
5
20
-
-
3
-
+
=
143
1+4+3
=
143
1+4+3
8
=
8
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
6
18
1
20
5
18
14
1
12
-
7
18
5
5
20
9
14
7
19
+
=
199
1+9+9
=
19
1+9
10
=
1
-
6
9
1
2
5
9
5
1
3
-
7
9
5
5
2
9
5
7
17
+
=
91
9+1
=
19
=
1
=
1
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
--
--
--
2
--
--
--
--
--
-
--
--
--
--
2
--
--
--
--
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
5
-
5
-
-
-
-
-
5
5
-
-
5
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
9
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
18
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
33
-
-
18
-
91
-
37
1+8
-
-
-
-
5
-
5
-
-
-
-
-
5
5
-
-
5
-
-
-
-
3+3
-
-
1+8
-
9+1
-
3+7
9
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
6
-
-
9
-
10
-
10
-
6
9
1
2
5
9
5
1
3
-
7
9
5
5
2
9
5
7
-
-
-
-
-
-
-
-
1+0
-
1+0
9
F
R
A
T
E
R
N
A
L
-
G
R
E
E
T
I
N
G
S
-
-
6
-
-
9
-
1
-
1

 

 

F
=
6
9
FRATERNAL
95
41
5
G
=
7
9
GREETINGS
104
50
5
C
=
3
8
CHILDREN
73
46
1
O
=
6
2
OF
21
12
3
T
=
2
3
THE
33
15
6
R
=
9
7
RAINBOW
82
37
1
L
=
3
5
LIGHT
56
29
2
-
-
36
43
First Total
464
230
23
-
-
3+6
4+3
Add to Reduce
4+6+4
2+3+0
2+3
Q
-
9
7
Second Total
14
5
5
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
9
7
Essence of Number
5
5
5

 

 

 

 
 
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