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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 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

 

 

 

 

 

 

 

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

 

 

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

 

 

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"

 

 

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

 

 

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.' "

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 granduncle. He used to work in a Yokohama bank, and you couldn't see his fingers / Page 69 / when he was going at speed"

 

 

I

SAY

THREAD THAT THREAD

THREAD READ DEATH DEATH READ THREAD

THREAD R DEATH DEATH R THREAD

THREAD READ DEAR DAERHT

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

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

Circa 1900

FOURTH EDITION

Page 1472

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

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

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

FOURTH EDITION

Circa 1900

Page 1472

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

 

 

lisle thread: lisle thread

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

 

 

Definition - of Lisle from Dictionary.net

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

 

 

CASSELL'S ENGLISH DICTIONARY

1974

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

 

 

KARMAS GODS THREAD ALWAYS ALWAYS THREAD GODS KARMAS

DIVINE CREATORS CREATORS DIVINE

GODS IMMORTAL THOUGHT IMMORTAL GODS

THAT THAT THAT

ISISIS

THAT

I

AM

THAT THOU ART THOU ART THAT

 

 

I

ME

ALWAYS

QUESTION I ME I ME I QUESTION

ALWAYS THE WAY THE WAY ALWAYS

THAT

WAY

ISISIS ISISIS

THAT

WAY

ALWAYS THE WAY THE WAY ALWAYS

 

 

4
WHAT
52
16
7
2
IS
28
10
1
2
IS
28
10
1
8
Add to Reduce
108
36
9
-
Reduce to Deduce
1+0+8
3+6
-
8
Essence of Number
9
9
9

 

 

THE

DAWNING OF THE AGE OF AQUARIUS

 

 

Hair Soundtrack Lyrics, Lyrics - Aquarius Lyrics. ... The age of Aquarius Aquarius!Aquarius! Harmony and understanding
Sympathy and trust abounding ... www.stlyrics.com/lyrics/hair/Aquarius.htm - 9k

 

 

When the moon is in the Seventh House
And Jupiter aligns with Mars
Then peace will guide the planets
And love will steer the stars

This is the dawning of the age of Aquarius
The age of Aquarius
Aquarius!
Aquarius!

Harmony and understanding
Sympathy and trust abounding
No more falsehoods or derisions
Golden living dreams of visions
Mystic crystal revelation
And the mind's true liberation
Aquarius!
Aquarius!

When the moon is in the Seventh House
And Jupiter aligns with Mars
Then peace will guide the planets
And love will steer the stars

This is the dawning of the age of Aquarius
The age of Aquarius
Aquarius!
Aquarius!

 

 

 

 

ADVENT 877 ADVENT

 

 

IS, UNIVERSAL, MIND, THE, MIND, OF, HUMANKIND
UNIVERSAL, MIND, IS, THE, MIND, OF, HUMANKIND
HAPPY BIRTHDAY
GOD, GO, DO, GOOD
GOD GO DO GOOD
THREE SIX
FORTY FIVE, FIFTY FOUR
FORTY FIVE
FORTY FIVE
FORTY SIX
FORTYSIX,
FIFTY FOUR, FORTY FIVE
FIFTY FOUR
FIFTY FOUR
FIFTY FOUR
SIXTY THREE
SIXTY THREE
EIGHTY ONE
EIGHTY ONE
ONE TWO SIX
ONE TWO SIX
FORTY FIVE, FIFTY FOUR, SIXTY THREE, EIGHTY ONE
EIGHTEEN THIRTY SIX
EIGHTEEN THIRTY SIX
THE, MERRY, GO, ROUND
NINETEEN
ARCHIMEDES, A, R, CH, I, ME, DE, S
ARCHIMEDES
TIME EMIT
KINETIC, KINETICS
ENERGIES
KINETIC ENERGIES
WEIGHED, IN, THE, BALANCE, AND, FOUND, WANTING
CUNICULUS
CUNICULUS
UNIFIED, FIELD, THEORY
THE, GOVERNMENT, OF, THE, PEOPLE, BY, THE,
PEOPLE
FIVE, SENSES
SIX, SENSES
FIVE, SIX
SELF, CONSCIOUS, CONSCIOUSNESS
HUMAN, INTELLIGENCE
HUMAN, CREATIVITY
I, DEAL, THE, CARDS, AND, HERE, IS, AN, ACE
KARMAS DIVINE LAW
SYNCHRONICITY
SYNCHRONISED

 

 

QUESTION ON I QUEST QUEST I ON QUESTION

?

 

2
IS
28
19
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
189
90
18
3+3
Add to Reduce
1+8+9
9+0
1+8
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

ANSWERING I SAY READING THAT I ME THAT ME I THAT SAY I READING ANSWERING

THE

QUESTION

I

SAY

 

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

 

 

ISISIS

ZERO ONE ONE ZERO

NINE NINE NINE

ONE TWO SIX SIX TWO ONE

THREE FOUR FIVE FIVE FOUR THREE

FIVE FIVE FIVE

FIFTY FOUR FOUR FIFTY

THREE SIX NINE NINE SIX THREE

EIGHTEEN EIGHTEEN

THIRTY SIX SIX SIX THIRTY

EIGHTEEN THIRTY SIX SIX THIRTY EIGHTEEN

 

 

ZEROOREZ

ONEENO TWOOWT THREEEERHT FOURROUF

FIVEEVIF

SIXXIS SEVENNEVES EIGHTTHGIE NINEENIN

 

 

D
=
4
-
4
DARK
34
16
7
M
=
4
-
6
MATTER
77
23
5
M
=
4
-
4
MIND
40
22
4
L
=
3
-
5
LIGHT
56
29
2
-
-
15
-
19
First Total
207
90
18
-
-
1+5
-
1+9
Add to Reduce
2+0+7
9+0
1+8
-
-
6
-
10
Second Total
9
9
9
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
6
-
1
Essence of Number
9
9
9

 

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

H
=
8
-
5
HAPPY
66
30
3
B
=
2
-
5
BIRTH
57
30
3
D
=
4
-
3
DAY
30
12
3
-
-
14
-
13
First Total
153
72
9
-
-
1+4
-
1+3
Add to Reduce
1+5+3
7+2
-
-
-
5
-
4
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
5
-
4
Essence of Number
9
9
9

 

HAPPY BIRTH DAY DEAR ANDREW HAPPY BIRTH DAY TO YOU

 

A
1
-
6
ANDREW
-
-
-
-
-
-
1
A
1
1
1
-
-
-
1
N
14
5
5
-
-
-
1
D
4
4
4
-
-
-
1
R
18
9
9
-
-
-
1
E
5
5
5
-
-
-
1
W
23
5
5
A
1
-
6
ANDREW
65
29
29
-
-
-
-
-
6+5
2+9
2+9
A
1
-
6
ANDREW
11
11
11
-
-
-
-
-
1+1
1+1
1+1
A
1
-
6
ANDREW
2
2
2

 

 

HAPPY BIRTH DAY DEAR REDBECK MAN

MAGIC IS AS MAGIC DOES

THANK YOU FOR YOUR WORK ON BEHALF OF THE ALL AND SUNDRY OF PLANET EARTH

RA IN BOW GOOD WISHES

LOVING THE LIGHT AND YOU R OF THE LIGHT

DAVE D HEREIN THE I'M DENISON DIMENSION

 

 

R
9
-
7
REDBECK
-
-
-
-
-
-
1
R
18
9
9
-
-
-
1
E
5
5
5
-
-
-
1
D
4
4
4
-
-
-
1
B
2
2
2
-
-
-
1
E
5
5
5
-
-
-
1
C
3
3
3
-
-
-
1
K
11
2
2
R
9
-
7
REDBECK
48
30
30
-
-
-
-
-
4+8
3+0
3+0
R
9
-
7
REDBECK
12
3
3
-
-
-
-
-
1+2
-
-
R
9
-
7
REDBECK
3
3
3

 

 

-
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
9
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
=
7
-
-
8
-
-
-
-
-
-
9
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
=
7
-
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
7
7
7
-
2
-
9
2
-
-
4
1
7
+
=
47
4+7
=
11
1+1
2
=
2
=
2
-
-
-
1
16
16
25
-
2
-
18
20
-
-
4
1
25
+
=
128
1+2+8
=
11
1+1
2
=
2
=
2
-
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
1
16
16
25
-
2
9
18
20
8
-
4
1
25
+
=
153
1+5+3
=
9
=
9
=
9
=
9
-
-
8
1
7
7
7
-
2
9
9
2
8
-
4
1
7
+
=
72
4+4
=
9
=
9
=
9
=
9
-
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
-
-
-
-
-
-
7
7
7
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
4
=
28
2+8
10
1+0
1
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
=
7
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
=
9
14
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
31
-
-
9
-
72
-
36
-
27
1+4
1+3
-
-
7
7
7
-
-
-
-
-
-
-
-
-
7
-
-
3+1
-
-
-
-
7+2
-
3+6
-
2+7
5
4
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
4
-
-
9
-
9
-
9
-
9
-
-
8
1
7
7
7
-
2
9
9
2
8
-
4
1
7
-
-
-
-
-
-
-
-
-
-
-
-
5
4
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
4
-
-
9
-
9
-
9
-
9

 

 

13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
-
9
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
=
7
-
8
-
-
-
-
-
-
9
-
-
8
-
-
-
-
+
=
25
2+5
=
7
=
7
=
7
=
7
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
7
7
7
-
2
-
9
2
-
-
4
1
7
+
=
47
4+7
=
11
1+1
2
=
2
=
2
-
-
1
16
16
25
-
2
-
18
20
-
-
4
1
25
+
=
128
1+2+8
=
11
1+1
2
=
2
=
2
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
8
1
16
16
25
-
2
9
18
20
8
-
4
1
25
+
=
153
1+5+3
=
9
=
9
=
9
=
9
-
8
1
7
7
7
-
2
9
9
2
8
-
4
1
7
+
=
72
4+4
=
9
=
9
=
9
=
9
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
=
2
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
=
4
-
-
-
7
7
7
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
4
=
28
2+8
10
1+0
1
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
=
7
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
=
9
13
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
31
-
-
9
-
72
-
36
-
27
1+3
-
-
7
7
7
-
-
-
-
-
-
-
-
-
7
-
-
3+1
-
-
-
-
7+2
-
3+6
-
2+7
4
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
4
-
-
9
-
9
-
9
-
9
-
8
1
7
7
7
-
2
9
9
2
8
-
4
1
7
-
-
-
-
-
-
-
-
-
-
-
-
4
H
A
P
P
Y
-
B
I
R
T
H
-
D
A
Y
-
-
4
-
-
9
-
9
-
9
-
9

.....

 

 

....

 

-
3
G
O
D
-
-
-
-
-
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
3
G
O
D
-
-
-
-
-
-
-
-
-
-
7
-
4
+
=
11
1+1
=
2
=
2
-
-
7
-
4
+
=
11
1+1
=
2
=
2
-
3
G
O
D
-
-
-
-
-
-
-
-
-
-
7
15
4
+
=
26
2+6
=
8
=
8
-
-
7
6
4
+
=
17
1+7
=
8
=
8
-
3
G
O
D
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
23
3
G
O
D
-
-
22
-
-
3
-
17
2+3
-
-
-
-
-
-
2+2
-
-
-
-
1+7
5
3
G
O
D
-
-
4
-
-
3
-
8
-
-
7
6
4
-
-
-
-
-
-
-
-
5
3
G
O
D
-
-
4
-
-
3
-
8

 

 

3
G
O
D
-
-
-
-
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
15
-
+
=
15
1+5
=
6
=
6
3
G
O
D
-
-
-
-
-
-
-
-
-
7
-
4
+
=
11
1+1
=
2
=
2
-
7
-
4
+
=
11
1+1
=
2
=
2
3
G
O
D
-
-
-
-
-
-
-
-
-
7
15
4
+
=
26
2+6
=
8
=
8
-
7
6
4
+
=
17
1+7
=
8
=
8
3
G
O
D
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
6
-
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
7
occurs
x
1
=
7
3
G
O
D
-
-
22
-
-
3
-
17
-
-
-
-
-
-
2+2
-
-
-
-
1+7
3
G
O
D
-
-
4
-
-
3
-
8
-
7
6
4
-
-
-
-
-
-
-
-
3
G
O
D
-
-
4
-
-
3
-
8

 

 

3
GOD
26
17
8
1
O
15
6
6
3
GOD
26
17
8
7
First Total
67
40
22
-
Add to Reduce
6+7
4+0
2+2
7
Second Total
13
4
4
-
Reduce to Deduce
1+3
-
-
7
Essence of Number
4
4
4

 

 

-
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
-
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
15
-
-
15
-
-
15
-
+
=
45
4+5
=
9
=
9
=
9
-
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
-
4
-
-
-
7
-
4
+
=
22
2+2
=
4
=
4
=
4
-
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
15
4
-
15
-
7
15
4
+
=
67
6+7
=
13
1+3
4
=
4
-
-
7
6
4
-
6
-
7
6
4
+
=
40
4+0
=
4
=
4
=
4
-
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
7
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
28
7
G
O
D
-
O
-
G
O
D
-
-
17
-
-
7
-
40
-
22
2+8
-
-
6
-
-
6
-
-
6
-
-
-
1+7
-
-
-
-
4+0
-
2+2
10
7
G
O
D
-
O
-
G
O
D
-
-
8
-
-
7
-
4
-
8
1+0
-
7
6
4
-
6
-
7
6
4
-
-
-
-
-
-
-
-
-
-
1
7
G
O
D
-
O
-
G
O
D
-
-
8
-
-
7
-
4
-
4

 

 

11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
-
+
=
18
1+8
=
9
=
9
=
9
`-
-
15
-
-
15
-
-
15
-
+
=
45
4+5
=
9
=
9
=
9
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
-
4
-
-
-
7
-
4
+
=
22
2+2
=
4
=
4
=
4
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
15
4
-
15
-
7
15
4
+
=
67
6+7
=
13
1+3
4
=
4
-
7
6
4
-
6
-
7
6
4
+
=
40
4+0
=
4
=
4
=
4
11
G
O
D
-
O
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
6
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
7
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
7
G
O
D
-
O
-
G
O
D
-
-
17
-
-
7
-
40
-
22
-
-
6
-
-
6
-
-
6
-
-
-
1+7
-
-
-
-
4+0
-
2+2
7
G
O
D
-
O
-
G
O
D
-
-
8
-
-
7
-
4
-
8
-
7
6
4
-
6
-
7
6
4
-
-
-
-
-
-
-
-
-
-
7
G
O
D
-
O
-
G
O
D
-
-
8
-
-
7
-
4
-
4

 

.....

 

-
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
1
1
+
=
14
14
1+4
5
=
5
=
5
-
-
-
15
-
-
-
15
-
-
-
19
19
+
=
68
6+8
=
14
1+4
5
=
5
-
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
4
-
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
-
-
7
-
4
-
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
-
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
7
15
4
-
7
15
4
4
5
19
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
6
4
-
7
6
4
4
5
1
1
+
=
63
6+3
=
9
=
9
=
9
-
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
4
4
-
-
-
-
-
4
occurs
x
3
=
12
=
3
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
=
3
-
-
7
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
=
5
8
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
22
10
G
O
D
-
G
O
D
D
E
S
S
-
-
23
-
-
10
-
45
-
18
2+2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+3
-
-
1+0
-
4+5
-
1+8
4
10
G
O
D
-
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9
-
-
7
6
4
-
7
6
4
4
5
1
1
-
-
-
-
-
-
-
-
-
-
4
10
G
O
D
-
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9

 

 

10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
1
1
+
=
14
14
1+4
5
=
5
=
5
-
-
15
-
-
-
15
-
-
-
19
19
+
=
68
6+8
=
14
1+4
5
=
5
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
7
-
4
-
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
-
7
-
4
-
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
7
15
4
-
7
15
4
4
5
19
19
+
=
99
9+9
=
18
1+8
9
=
9
-
7
6
4
-
7
6
4
4
5
1
1
+
=
63
6+3
=
9
=
9
=
9
10
G
O
D
-
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
4
-
-
-
4
4
-
-
-
-
-
4
occurs
x
3
=
12
=
3
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
=
3
-
7
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
=
5
10
G
O
D
-
G
O
D
D
E
S
S
-
-
23
-
-
10
-
45
-
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+3
-
-
1+0
-
4+5
-
1+8
10
G
O
D
-
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9
-
7
6
4
-
7
6
4
4
5
1
1
-
-
-
-
-
-
-
-
-
-
10
G
O
D
-
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9

 

 

10
G
O
D
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
1
1
+
=
14
14
1+4
5
=
5
=
5
-
-
15
-
-
15
-
-
-
19
19
+
=
68
6+8
=
14
1+4
5
=
5
10
G
O
D
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
7
-
4
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
-
7
-
4
7
-
4
4
5
-
-
+
=
31
3+1
=
4
=
4
=
4
10
G
O
D
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
7
15
4
7
15
4
4
5
19
19
+
=
99
9+9
=
18
1+8
9
=
9
-
7
6
4
7
6
4
4
5
1
1
+
=
63
6+3
=
9
=
9
=
9
10
G
O
D
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
4
-
-
4
4
-
-
-
-
-
4
occurs
x
3
=
12
=
3
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
=
3
-
7
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
=
5
10
G
O
D
G
O
D
D
E
S
S
-
-
23
-
-
10
-
45
-
18
-
-
-
-
-
-
-
-
-
-
-
-
-
2+3
-
-
1+0
-
4+5
-
1+8
10
G
O
D
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9
-
7
6
4
7
6
4
4
5
1
1
-
-
-
-
-
-
-
-
-
-
10
G
O
D
G
O
D
D
E
S
S
-
-
5
-
-
1
-
9
-
9

 

 

-
7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
1
1
+
=
8
-
=
8
=
8
-
-
-
15
-
-
-
19
19
+
=
53
5+3
=
8
=
8
-
7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
7
-
4
4
5
-
-
+
=
20
2+0
=
2
=
2
-
-
7
-
4
4
5
-
-
+
=
20
2+0
=
2
=
2
-
7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
7
15
4
4
5
19
19
+
=
73
7+3
=
10
1+0
1
-
-
7
6
4
4
5
1
1
+
=
28
2+8
=
10
1+0
1
-
10
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
2
-
-
-
-
``-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
4
-
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
``-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
22
7
G
O
D
D
E
S
S
-
-
23
-
-
7
-
28
2+2
-
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+8
4
7
G
O
D
D
E
S
S
-
-
5
-
-
7
-
10
-
-
7
6
4
4
5
1
1
-
-
-
-
-
-
-
1+0
4
7
G
O
D
D
E
S
S
-
-
5
-
-
7
-
1

 

GODDESS OF GOODNESS IS O IS GOODNESS OF GODDESS

 

7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
6
-
-
-
1
1
+
=
8
-
=
8
=
8
-
-
15
-
-
-
19
19
+
=
53
5+3
=
8
=
8
7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
7
-
4
4
5
-
-
+
=
20
2+0
=
2
=
2
-
7
-
4
4
5
-
-
+
=
20
2+0
=
2
=
2
7
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
7
15
4
4
5
19
19
+
=
73
7+3
=
10
1+0
1
-
7
6
4
4
5
1
1
+
=
28
2+8
=
10
1+0
1
10
G
O
D
D
E
S
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
occurs
x
2
=
2
-
-
-
4
4
-
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
7
G
O
D
D
E
S
S
-
-
23
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+8
7
G
O
D
D
E
S
S
-
-
5
-
-
7
-
10
-
7
6
4
4
5
1
1
-
-
-
-
-
-
-
1+0
7
G
O
D
D
E
S
S
-
-
5
-
-
7
-
1

 

 

2
GO
22
13
4
2
DO
19
10
1
4
GO-OD
41
23
5
8
First Total
82
46
10
-
Add to Reduce
8+2
4+6
1+0
8
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
8
Essence of Number
1
1
1

 

.....

 

3
GOD
26
17
8
2
GO
22
13
4
2
DO
19
10
1
4
GOOD
41
23
5
11
Add to Reduce
108
63
18
1+1
Reduce to Deduce
1+0+8
6+3
1+7
2
Essence of Number
9
9
9

 

 

-
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
6
-
+
=
24
2+3
=
6
=
6
=
6
-
`-
-
15
-
-
15
-
-
15
15
-
+
=
60
6+0
=
6
1+2
6
=
6
-
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
-
-
4
-
-
7
-
-
4
+
=
22
2+2
=
4
=
4
=
4
-
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
15
-
4
15
-
7
15
15
4
+
=
82
8+2
=
10
1+0
1
=
1
-
-
7
6
-
4
6
-
7
6
6
4
+
=
46
4+6
=
10
1+0
1
=
1
-
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
``-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
``-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
``-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
6
-
-
6
occurs
x
4
=
24
2+4
6
-
-
7
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
``-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
28
8
G
O
-
D
O
-
G
O
O
D
-
-
17
-
-
8
-
46
-
19
2+8
-
-
6
6
-
-
-
6
-
-
6
-
-
1+7
-
-
-
-
4+6
-
1+9
10
8
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
8
-
9
-
10
1+0
-
7
6
-
4
6
-
7
6
6
4
-
-
-
-
-
-
-
-
-
1+0
1
8
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
8
-
9
-
1

 

 

8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
6
-
+
=
24
2+3
=
6
=
6
=
6
`-
-
15
-
-
15
-
-
15
15
-
+
=
60
6+0
=
6
1+2
6
=
6
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
-
-
4
-
-
7
-
-
4
+
=
22
2+2
=
4
=
4
=
4
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
15
-
4
15
-
7
15
15
4
+
=
82
8+2
=
10
1+0
1
=
1
-
7
6
-
4
6
-
7
6
6
4
+
=
46
4+6
=
10
1+0
1
=
1
8
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
6
6
-
-
-
6
-
-
6
-
-
6
occurs
x
4
=
24
2+4
6
-
7
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
G
O
-
D
O
-
G
O
O
D
-
-
17
-
-
8
-
46
-
19
-
-
6
6
-
-
-
6
-
-
6
-
-
1+7
-
-
-
-
4+6
-
1+9
8
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
8
-
9
-
10
-
7
6
-
4
6
-
7
6
6
4
-
-
-
-
-
-
-
-
-
1+0
8
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
8
-
9
-
1

 

 

THE

HOURS OF HORUS

HAVE

ARRIVED

HURRAH FOR RAH FOR RAH HURRAH

AMEN THAT NAME GODS NAME AMEN

RA IN BOW LIGHT GODS LIGHT RA IN BOW

THE LIGHT IS RISEN NOW RISEN IS THE LIGHT

 

 

3
GOD
26
17
8
2
GO
22
13
4
2
DO
19
10
1
4
GOOD
41
23
5
11
Add to Reduce
108
63
18
1+1
Reduce to Deduce
1+0+8
6+3
1+7
2
Essence of Number
9
9
9

 

 

-
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
-
6
6
-
+
=
30
3+0
=
3
=
3
=
3
-
`-
-
15
-
-
-
15
-
-
15
-
-
15
15
-
+
=
75
7+5
=
12
1+2
3
=
3
-
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
-
4
-
7
-
-
4
-
-
7
-
-
4
+
=
33
3+3
=
6
=
6
=
6
-
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
`-
7
15
4
-
7
15
-
4
15
-
7
15
15
4
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
6
4
-
7
6
-
4
6
-
7
6
6
4
+
=
63
6+3
=
9
=
9
=
9
-
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
3
=
12
1+2
3
5
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
-
6
6
-
-
-
6
occurs
x
5
=
30
3+0
3
-
-
7
-
-
-
7
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
28
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
17
-
-
11
-
63
-
9
2+8
1+1
-
6
-
-
-
6
-
-
6
-
-
6
6
-
-
-
1+7
-
-
1+1
-
6+3
-
-
10
2
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
2
-
9
-
9
1+0
-
7
6
4
-
7
6
-
4
6
-
7
6
6
4
-
-
-
-
-
-
-
-
-
-
1
2
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
2
-
9
-
9

 

 

11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
6
-
-
6
6
-
+
=
30
3+0
=
3
=
3
=
3
`-
-
15
-
-
-
15
-
-
15
-
-
15
15
-
+
=
75
7+5
=
12
1+2
3
=
3
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
-
4
-
7
-
-
4
-
-
7
-
-
4
+
=
33
3+3
=
6
=
6
=
6
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
`-
7
15
4
-
7
15
-
4
15
-
7
15
15
4
+
=
108
1+0+8
=
9
=
9
=
9
-
7
6
4
-
7
6
-
4
6
-
7
6
6
4
+
=
63
6+3
=
9
=
9
=
9
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
3
=
12
1+2
3
-
-
6
-
-
-
6
-
-
6
-
-
6
6
-
-
-
6
occurs
x
5
=
30
3+0
3
-
7
-
-
-
7
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
11
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
17
-
-
11
-
63
-
9
1+1
-
6
-
-
-
6
-
-
6
-
-
6
6
-
-
-
1+7
-
-
1+1
-
6+3
-
-
2
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
2
-
9
-
9
-
7
6
4
-
7
6
-
4
6
-
7
6
6
4
-
-
-
-
-
-
-
-
-
-
2
G
O
D
-
G
O
-
D
O
-
G
O
O
D
-
-
8
-
-
2
-
9
-
9

 

.....

 

36 = 3+6 = 9 9 = 6 +3 = 63

 

-
-
-
THREE SIX
-
-
-
3
-
5
THREE
56
29
2
6
-
3
SIX
52
25
7
9
-
8
THREE SIX
108
54
9
-
-
-
-
1+0+8
5+4
-
9
-
8
THREE SIX
9
9
9

 

 

9
FORTYFIVE
126
54
9
9
FIFTYFOUR
126
54
9
18
-
252
108
18
1+8
-
2+5+2
1+0+8
1+8
9
-
9
9
9

 

45 = 4+5 = 9 9 = 5 + 4 = 54

 

9
FORTYFIVE
126
54
9
9
FIFTYFOUR
126
54
9
18
-
252
108
18
1+8
-
2+5+2
1+0+8
1+8
9
-
9
9
9

 

54 5+4 = 9 9 = 4 + 5 = 45

 

9
FIFTY FOUR
126
54
45
9

 

45 = 4+5 = 9 9 = 5 + 4 = 54

 

9
FORTY FIVE
126
54
45
9

 

 

-
FORTY FIVE
-
-
-
2
F+O
21
12
3
1
R
18
9
9
2
T+Y
45
9
9
1
F
6
6
6
1
I
9
9
9
2
V+E
27
9
9
9
FORTY FIVE
126
54
45
-
-
1+2+6
5+4
4+5
9
FORTY FIVE
9
9
9

 

 

9
FORTYFIVE
126
54
45
9

 

 

--
9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
-
9
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
9
-
-
+
=
24
2+4
=
6
=
6
=
6
--
9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
2
7
-
6
-
4
5
+
=
39
3+9
=
12
1+2
3
=
3
-
-
6
-
18
20
25
-
6
-
22
5
+
=
102
1+0+2
=
3
=
3
=
3
--
9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
6
15
18
20
25
-
6
9
22
5
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
6
9
2
7
-
6
9
4
5
+
=
54
5+4
=
9
=
9
=
9
-
9
F
O
R
T
Y
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
--
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
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
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
9
F
O
R
T
Y
-
F
I
V
E
-
-
33
-
-
9
-
54
-
36
1+2
-
6
6
-
-
-
-
6
-
-
-
-
-
3+3
-
-
-
-
5+4
-
3+6
3
9
F
O
R
T
Y
-
F
I
V
E
-
-
6
-
-
9
-
9
-
9
-
-
6
6
9
2
7
--
6
9
4
5
-
-
-
-
-
-
-
-
-
-
3
9
F
O
R
T
Y
-
F
I
V
E
-
-
6
-
-
9
-
9
-
9

 

 

9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
-
9
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
15
-
-
-
-
-
9
-
-
+
=
24
2+4
=
6
=
6
=
6
9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
6
-
9
2
7
-
6
-
4
5
+
=
39
3+9
=
12
1+2
3
=
3
-
6
-
18
20
25
-
6
-
22
5
+
=
102
1+0+2
=
3
=
3
=
3
9
F
O
R
T
Y
--
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
6
15
18
20
25
-
6
9
22
5
+
=
126
1+2+6
=
9
=
9
=
9
-
6
6
9
2
7
-
6
9
4
5
+
=
54
5+4
=
9
=
9
=
9
9
F
O
R
T
Y
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
--
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
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
occurs
x
1
=
7
=
7
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
F
O
R
T
Y
-
F
I
V
E
-
-
33
-
-
9
-
54
-
36
-
6
6
-
-
-
-
6
-
-
-
-
-
3+3
-
-
-
-
5+4
-
3+6
9
F
O
R
T
Y
-
F
I
V
E
-
-
6
-
-
9
-
9
-
9
-
6
6
9
2
7
--
6
9
4
5
-
-
-
-
-
-
-
-
-
-
9
F
O
R
T
Y
-
F
I
V
E
-
-
6
-
-
9
-
9
-
9

 

 

8
FORTY SIX
136
46
1

 

46 = 4+6 =10 = 1+0 = 1 1 = 1+0 = 10 = 6+0 = 64

 

-
FORTY SIX
-
-
-
2
F+O
21
12
3
1
R
18
9
9
2
T+Y
45
9
9
1
S
19
1
1
1
I
9
9
9
1
X
24
6
6
8
FORTY SIX
136
46
37
-
-
1+3+6
4+6
3+7
8
FORTY SIX
10
10
10
-
-
1+0
1+0
1+0
8
FORTY SIX
1
1
1

 

 

-
FORTY SIX
-
-
-
2
FORTY
84
30
3
1
SIX
52
16
7
8
FORTY SIX
136
46
10
-
-
1+3+6
4+6
1+0
8
FORTYSIX
10
10
1
-
-
1+0
1+0
1+0
8
FORTYSIX
1
1
1

 

 

8
FORTYSIX
136
46
1

 

 

--
8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
1
9
6
+
=
22
2+2
=
4
=
4
=
4
-
-
-
15
-
-
-
-
19
9
24
+
=
67
6+7
=
13
1+3
4
=
4
--
8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
2
7
-
-
-
-
+
=
24
2+4
=
6
1+2
6
=
6
-
-
6
-
18
20
25
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
--
8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
6
15
18
20
25
-
19
9
24
+
=
136
1+3+6
=
10
1+0
1
=
1
-
-
6
6
9
2
7
-
1
9
6
+
=
46
4+6
=
10
1+0
1
=
1
-
8
F
O
R
T
Y
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
--
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
--
-
-
-
--
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
7
--
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
20
8
F
O
R
T
Y
-
S
I
X
-
-
25
-
-
9
-
46
-
36
2+0
-
6
6
-
-
-
-
-
9
-
-
-
2+5
-
-
-
-
4+6
-
3+6
2
8
F
O
R
T
Y
-
S
I
X
-
-
7
-
-
9
-
10
-
9
-
-
6
6
9
2
7
--
1
9
6
-
-
-
-
-
-
-
-
-
-
2
8
F
O
R
T
Y
-
S
I
X
-
-
7
-
-
9
-
9
-
9

 

 

8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
6
-
-
-
-
1
9
6
+
=
22
2+2
=
4
=
4
=
4
-
-
15
-
-
-
-
19
9
24
+
=
67
6+7
=
13
1+3
4
=
4
8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
6
-
9
2
7
-
-
-
-
+
=
24
2+4
=
6
1+2
6
=
6
-
6
-
18
20
25
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
8
F
O
R
T
Y
--
S
I
X
-
-
-
-
-
--
-
-
-
-
-
6
15
18
20
25
-
19
9
24
+
=
136
1+3+6
=
10
1+0
1
=
1
-
6
6
9
2
7
-
1
9
6
+
=
46
4+6
=
10
1+0
1
=
1
8
F
O
R
T
Y
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
--
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
6
6
-
-
-
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
7
--
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
8
F
O
R
T
Y
-
S
I
X
-
-
25
-
-
9
-
46
-
36
-
6
6
-
-
-
-
-
9
-
-
-
2+5
-
-
-
-
4+6
-
3+6
8
F
O
R
T
Y
-
S
I
X
-
-
7
-
-
9
-
10
-
9
-
6
6
9
2
7
--
1
9
6
-
-
-
-
-
-
-
-
-
-
8
F
O
R
T
Y
-
S
I
X
-
-
7
-
-
9
-
9
-
9

 

 

45 = 4+5 = 9 9 = 5 + 4 = 54

 

9
FORTYFIVE
126
54
9
9
FIFTYFOUR
126
54
9
18
-
252
108
18
1+8
-
2+5+2
1+0+8
1+8
9
-
9
9
9

 

54 5+4 = 9 9 = 4 + 5 = 45

 

9
FIFTY FOUR
126
54
45
9

 

 

-
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
T+Y
45
9
9
1
F
6
6
6
2
OUR
54
18
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

9
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
TY
45
9
9
1
F
6
6
6
2
OU
36
9
9
1
R
18
9
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

9
FIFTYFOUR
126
54
45
9

 

 

--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
--
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
--
-
--
-
-
-
-
5
-
-
-
-
-
-
-
-
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
7
--
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
--
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
18
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
1+8
-
6
-
6
-
-
-
6
6
-
-
-
-
2+7
-
-
-
-
5+4
-
2+7
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
-
6
9
6
2
7
--
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

 

9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
--
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
7
--
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
-
6
-
6
-
-
-
6
6
-
-
-
-
2+7
-
-
-
-
5+4
-
2+7
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
6
9
6
2
7
--
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

5+4 = 9 9 = 4 + 5

 

9
FIFTYFOUR
126
54
9
9
FORTYFIVE
126
54
9
18
-
252
108
18
1+8
-
2+5+2
1+0+8
1+8
9
-
9
9
9

 

3 + 6 = 9 9 = 6 + 3

 

-
-
-
THREE SIX
-
-
-
3
-
5
THREE
56
29
2
6
-
3
SIX
52
25
7
9
-
8
THREE SIX
108
54
9
-
-
-
-
1+0+8
5+4
-
9
-
8
THREE SIX
9
9
9

 

63 = 6 + 3 = 9 9 = 3 + 6 = 36

 

-
SIXTY THREE
-
-
-
5
SIXTY
97
34
7
5
THREE
56
29
2
10
SIXTY THREE
153
63
9
1+0
-
1+5+3
6+3
-
1
SIXTY THREE
9
9
9

 

 

-
SIXTY THREE
-
-
-
4
S+I+X+T
72
27
9
2
Y+T
45
9
9
1
H
8
8
8
1
R
18
9
9
2
E+E
10
1
1
10
SIXTY THREE
153
54
36
1+0
-
1+5+3
5+4
3+6
1
SIXTY THREE
9
9
9

 

 

10
SIXTYTHREE
153
54
36
9

 

 

-
10
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
-
1
9
6
-
-
-
-
8
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
9
24
-
-
-
-
8
-
-
-
+
=
60
6+0
=
6
=
6
=
6
-
10
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
2
7
-
2
-
9
5
5
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
20
25
-
20
-
18
5
5
+
=
93
9+3
=
12
1+2
3
=
3
-
-
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
-
19
9
24
20
25
-
20
8
18
5
5
+
=
153
1+5+3
=
8
=
8
=
8
-
-
1
9
6
2
7
-
2
8
9
5
5
+
=
54
5+4
=
9
=
9
=
9
-
10
S
I
X
T
Y
-
T
H
R
E
E
-
-
-
-
--
-
-
-
-
-
--
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
--
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
--
--
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
7
10
S
I
X
T
Y
-
T
H
R
E
E
-
-
38
-
-
10
-
54
-
36
-
1+0
-
9
-
-
-
-
-
-
9
-
-
-
-
3+8
-
-
1+0
-
5+4
-
3+6
7
1
S
I
X
T
Y
-
T
H
R
E
E
-
-
11
-
-
1
-
9
-
9
-
-
1
9
6
2
7
-
2
8
9
5
5
-
-
1+1
-
-
-
-
-
-
-
7
1
S
I
X
T
Y
-
T
H
R
E
E
-
-
2
-
-
1
-
9
-
9

 

 

0
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
1
9
6
-
-
-
-
8
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
19
9
24
-
-
-
-
8
-
-
-
+
=
60
6+0
=
6
=
6
=
6
10
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
-
-
-
2
7
-
2
-
9
5
5
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
20
25
-
20
-
18
5
5
+
=
93
9+3
=
12
1+2
3
=
3
-
S
I
X
T
Y
-
T
H
R
E
E
-
--
-
-
-
-
-
-
-
-
-
19
9
24
20
25
-
20
8
18
5
5
+
=
153
1+5+3
=
8
=
8
=
8
-
1
9
6
2
7
-
2
8
9
5
5
+
=
54
5+4
=
9
=
9
=
9
10
S
I
X
T
Y
-
T
H
R
E
E
-
-
-
-
--
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
2
-
-
2
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
9
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
S
I
X
T
Y
-
T
H
R
E
E
-
-
38
-
-
10
-
54
-
36
1+0
-
9
-
-
-
-
-
-
9
-
-
-
-
3+8
-
-
1+0
-
5+4
-
3+6
1
S
I
X
T
Y
-
T
H
R
E
E
-
-
11
-
-
1
-
9
-
9
-
1
9
6
2
7
-
2
8
9
5
5
-
-
1+1
-
-
-
-
-
-
-
1
S
I
X
T
Y
-
T
H
R
E
E
-
-
2
-
-
1
-
9
-
9

 

 

9
EIGHTY ONE
108
54
9

 

81 = 8+1 = 9 9 = 1+8 = 18

 

-
EIGHTYONE
-
-
-
1
E
5
5
5
1
I
9
9
9
2
G+H
15
15
6
2
T+Y
45
9
9
3
ONE
34
16
7
9
EIGHTY ONE
108
54
36
-
-
1+0+8
5+4
3+6
9
EIGHTY ONE
9
9
9

 

 

-
EIGHTY ONE
-
-
-
7
EIGHTYO
89
44
8
2
N+E
19
10
1
9
EIGHTY ONE
108
54
9
-
-
1+0+8
5+4
-
9
EIGHTY ONE
9
9
9

 

 

8
+
6
EIGHTY
74
38
2
1
+
3
ONE
34
16
7
9
-
9
Add to Reduce
108
54
9
-
-
-
Reduce to Deduce
1+0+8
5+4
-
9
+
9
Essence of Number
9
9
9

 

 

9
EIGHTYONE
108
54
9

 

 

-
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
+
6
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
9
-
8
-
-
-
15
14
-
+
=
46
4+6
=
10
1+0
1
=
1
-
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
-
7
-
2
7
+
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
5
-
7
-
20
25
+
-
-
5
+
=
62
6+2
=
8
=
8
=
8
-
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
--
-
-
-
-
-
-
5
9
7
8
20
25
+
15
14
5
+
=
108
1+0+8
=
9
=
9
=
9
-
-
5
9
7
8
2
7
+
6
5
5
+
=
54
5+4
=
9
=
9
=
9
-
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
+
-
-
-
+
=
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
+
-
5
5
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
+
6
-
-
+
=
6
occurs
x
1
=
6
=
6
-
-
-
-
7
-
-
7
+
-
-
-
+
=
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
8
-
-
+
-
-
-
+
=
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
9
E
I
G
H
T
Y
+
O
N
E
+
+
37
-
-
9
-
54
-
36
-
-
5
-
-
-
-
-
+
-
5
5
-
-
3+7
-
-
-
-
5+4
-
3+6
8
-
E
I
G
H
T
Y
-
O
N
E
-
-
10
-
-
9
-
9
-
9
-
-
-
9
7
8
2
7
+
6
5
5
+
+
1+0
-
-
-
-
-
-
8
9
E
I
G
H
T
Y
+
O
N
E
+
+
2
-
-
9
-
9
-
9

 

 

9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
+
6
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
9
-
8
-
-
-
15
14
-
+
=
46
4+6
=
10
1+0
1
=
1
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
5
-
7
-
2
7
+
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
5
-
7
-
20
25
+
-
-
5
+
=
62
6+2
=
8
=
8
=
8
9
E
I
G
H
T
Y
+
O
N
E
-
-
-
-
--
-
-
-
-
-
5
9
7
8
20
25
+
15
14
5
+
=
108
1+0+8
=
9
=
9
=
9
-
5
9
7
8
2
7
+
6
5
5
+
=
54
5+4
=
9
=
9
=
9
9
E
I
G
H
T
Y
-
O
N
E
-
-
-
-
-
-
-
-
-
-
+
-
-
-
-
2
-
+
-
-
-
+
=
2
occurs
x
1
=
2
=
2
+
5
-
-
-
-
-
+
-
5
5
+
=
5
occurs
x
3
=
15
1+5
6
+
-
-
-
-
-
-
+
6
-
-
+
=
6
occurs
x
1
=
6
=
6
+
-
-
7
-
-
7
+
-
-
-
+
=
7
occurs
x
2
=
14
1+4
5
+
-
-
-
8
-
-
+
-
-
-
+
=
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
E
I
G
H
T
Y
+
O
N
E
+
+
37
-
-
9
-
54
-
36
-
5
-
-
-
-
-
+
-
5
5
-
-
3+7
-
-
-
-
5+4
-
3+6
-
E
I
G
H
T
Y
-
O
N
E
-
-
10
-
-
9
-
9
-
9
-
-
9
7
8
2
7
+
6
5
5
+
+
1+0
-
-
-
-
-
-
9
E
I
G
H
T
Y
+
O
N
E
+
+
2
-
-
9
-
9
-
9

 

 

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

 

 

-
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
6
5
-
-
-
-
6
-
1
9
6
+
=
33
3+3
=
6
-
6
-
6
-
-
15
14
-
-
-
-
15
-
19
9
24
+
=
96
9+6
=
15
1+5
6
-
6
-
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
2
5
-
-
-
-
-
+
=
12
1+2
=
3
-
3
-
3
-
-
-
-
5
-
20
23
-
-
-
-
-
+
=
48
4+8
=
12
1+2
3
-
4
-
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
15
14
5
-
20
23
15
-
19
9
24
+
=
144
1+4+4
=
9
-
9
-
9
-
-
6
5
5
-
2
5
6
-
1
9
6
+
=
45
4+5
=
9
-
9
-
9
-
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
6
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
-
9
22
9
O
N
E
-
T
W
O
-
S
I
X
-
-
23
-
-
9
-
73
-
28
2+2
-
6
-
-
-
-
-
6
-
-
-
6
-
-
2+3
-
-
-
-
7+3
-
2+8
4
9
O
N
E
-
T
W
O
-
S
I
X
-
-
5
-
-
9
-
10
-
10
-
-
6
5
5
-
2
5
6
-
1
9
6
-
-
-
-
-
-
-
1+0
-
1+0
4
9
O
N
E
-
T
W
O
-
S
I
X
-
-
5
-
-
9
-
1
-
1

 

 
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
6
5
-
-
-
-
6
-
1
9
6
+
=
33
3+3
=
6
-
6
-
6
-
15
14
-
-
-
-
15
-
19
9
24
+
=
96
9+6
=
15
1+5
6
-
6
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
2
5
-
-
-
-
-
+
=
12
1+2
=
3
-
3
-
3
-
-
-
5
-
20
23
-
-
-
-
-
+
=
48
4+8
=
12
1+2
3
-
4
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
15
14
5
-
20
23
15
-
19
9
24
+
=
144
1+4+4
=
9
-
9
-
9
-
6
5
5
-
2
5
6
-
1
9
6
+
=
45
4+5
=
9
-
9
-
9
9
O
N
E
-
T
W
O
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
6
-
-
-
-
-
6
-
-
-
6
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
-
9
9
O
N
E
-
T
W
O
-
S
I
X
-
-
23
-
-
9
-
73
-
28
-
6
-
-
-
-
-
6
-
-
-
6
-
-
2+3
-
-
-
-
7+3
-
2+8
9
O
N
E
-
T
W
O
-
S
I
X
-
-
5
-
-
9
-
10
-
10
-
6
5
5
-
2
5
6
-
1
9
6
-
-
-
-
-
-
-
1+0
-
1+0
9
O
N
E
-
T
W
O
-
S
I
X
-
-
5
-
-
9
-
1
-
1

 

 

F
=
6
-
45
-
9
FORTYFIVE
126
54
9
F
=
6
-
54
-
9
FIFTYFOUR
126
54
9
S
=
1
-
63
-
10
SIXTYTHREE
153
54
9
E
=
5
-
81
-
9
EIGHTYONE
108
54
9
-
-
18
-
243
-
37
Add to Reduce
513
216
36
-
-
1+8
-
2+4+3
-
3+7
Reduce to Deduce
5+1+3
2+1+6
3+6
-
-
9
-
9
-
10
Essence of Number
9
9
9

 

 

T
=
2
-
5
THREE
56
29
2
-
3
F
=
6
-
4
FOUR
60
24
6
-
4
F
=
6
-
4
FIVE
42
24
6
-
5
-
-
14
-
13
First Total
158
77
14
-
12
-
-
1+4
-
1+3
Add to Reduce
1+5+8
7+7
1+4
-
1+2
-
-
5
-
4
Second Total
14
14
5
-
12
-
-
-
-
-
Reduce to Deduce
1+4
1+4
--
-
1+2
-
-
5
-
4
Essence of Number
5
5
5
-
3

 

 

3
-
5
THREE
56
29
2
4
-
4
FOUR
60
24
6
5
-
4
FIVE
42
24
6
12
-
13
First Total
158
77
14
1+2
-
1+3
Add to Reduce
1+5+8
7+7
1+4
3
-
4
Second Total
14
14
5
--
--
-
Reduce to Deduce
1+4
1+4
--
3
-
4
Essence of Number
5
5
5

 

 

-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
+
=
54
5+4
=
9
=
9
=
9
-
-`
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
+
=
126
1+2+6
=
9
=
9
=
9
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
20
8
18
5
5
-
6
6
21
18
-
6
9
22
5
+
=
158
8+6
=
5
=
5
=
5
-
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
+
=
77
4+1
=
14
1+4
5
=
5
-
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
37
-
-
13
-
77
-
41
-
1+3
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+7
-
-
1+3
-
7+7
-
4+1
8
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
10
-
-
4
-
14
-
5
-
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
-
1+0
-
-
-
-
1+4
-
-
8
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
1
-
-
4
-
5
-
5

 

THREE FOUR FIVE FIVE FOUR THREE

 

13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
+
=
32
3+2
=
5
=
5
=
5
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
+
=
54
5+4
=
9
=
9
=
9
-`
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
+
=
126
1+2+6
=
9
=
9
=
9
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
--
-
-
-
-
-
20
8
18
5
5
-
6
6
21
18
-
6
9
22
5
+
=
158
8+6
=
5
=
5
=
5
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
+
=
77
4+1
=
14
1+4
5
=
5
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
37
-
-
13
-
77
-
41
1+3
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+7
-
-
1+3
-
7+7
-
4+1
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
10
-
-
4
-
14
-
5
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
-
1+0
-
-
-
-
1+4
-
-
4
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
-
1
-
-
4
-
5
-
5

 

 

18
-
8
EIGHTEEN
73
46
1
36
-
9
THIRTY SIX
152
62
8
54
-
17
Add to Reduce
225
108
9
5+4
1+7
Reduce to Deduce
2+2+5
1+0+8
-
9
-
8
Essence of Number
9
9
9

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT

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
-
-
-
-
1+7
Reduce to Deduce
-
1+8
-
Q
-
7
-
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

 

3
THE
33
15
6
5
MERRY
79
34
7
2
GO
22
13
4
5
ROUND
72
27
9

 

 

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

 

 

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

 

 

-
8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
5
9
5
-
-
-
-
5
+
=
24
2+4
=
6
=
6
=
6
-
-
14
9
14
-
-
-
-
14
+
=
51
5+1
=
6
=
6
=
6
-
8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
2
5
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
-
-
5
20
5
5
-
+
=
35
3+5
=
8
=
8
=
8
-
8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
14
9
14
5
20
5
5
14
+
=
86
8+6
=
14
1+4
5
=
5
-
-
5
9
5
5
2
5
5
5
+
=
41
4+1
=
5
=
5
=
5
-
8
N
I
N
E
T
E
E
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
5
-
5
5
-
5
5
5
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
29
8
N
I
N
E
T
E
E
N
-
-
16
-
-
8
-
41
-
14
2+9
-
5
-
5
5
-
5
5
5
-
-
1+6
-
-
-
-
4+1
-
1+4
11
8
N
I
N
E
T
E
E
N
-
-
5
-
-
8
-
5
-
5
1+1
-
5
9
5
5
2
5
5
5
-
-
-
-
-
-
-
-
-
-
2
8
N
I
N
E
T
E
E
N
-
-
5
-
-
8
-
5
-
5

 

 

8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
5
9
5
-
-
-
-
5
+
=
24
2+4
=
6
=
6
=
6
-
14
9
14
-
-
-
-
14
+
=
51
5+1
=
6
=
6
=
6
8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
2
5
5
-
+
=
17
1+7
=
8
=
8
=
8
-
-
-
-
5
20
5
5
-
+
=
35
3+5
=
8
=
8
=
8
8
N
I
N
E
T
E
E
N
-
-
-
-
-
--
-
-
-
-
-
14
9
14
5
20
5
5
14
+
=
86
8+6
=
14
1+4
5
=
5
-
5
9
5
5
2
5
5
5
+
=
41
4+1
=
5
=
5
=
5
8
N
I
N
E
T
E
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
5
-
5
5
-
5
5
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
8
N
I
N
E
T
E
E
N
-
-
16
-
-
8
-
41
-
14
-
5
-
5
5
-
5
5
5
-
-
1+6
-
-
-
-
4+1
-
1+4
8
N
I
N
E
T
E
E
N
-
-
5
-
-
8
-
5
-
5
-
5
9
5
5
2
5
5
5
-
-
-
-
-
-
-
-
-
-
8
N
I
N
E
T
E
E
N
-
-
5
-
-
8
-
5
-
5

 

 

-
ARCHIMEDES
-
-
-
1
A
1
1
1
1
R
18
9
9
2
C+H
11
2
2
1
I
9
9
9
2
M+ E
18
9
9
2
D+E
9
9
9
1
S
19
10
1
10
ARCHIMEDES
-
-
-

 

Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.

 

A
=
1
-
10
ARCHIMEDES
85
58
4
O
=
6
-
2
OF
21
12
3
S
=
1
-
8
SYRACUSE
111
48
3
-
-
8
4
20
First Total
217
118
10
-
-
-
-
2+0
Add to Reduce
1+8+7
1+1+8
1+0
Q
-
8
-
2
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
Q
-
8
-
2
Essence of Number
1
1
1

 

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
-
-
-
-
-
8
4
20
First Total
217
118
10
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
6
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
49
-
10
ARCHIMEDES
85
58
49
-
-
-
-
-
-
-
-
-
-
-
-
-
-
OF
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
11
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
-
12
-
-
OF
21
12
12
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SYRACUSE
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
14
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
15
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
16
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
C
=
3
17
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
18
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
48
-
-
SYRACUSE
111
48
48
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
2
9
8
15
12
7
8
27
A
=
1
-
10
ARCHIMEDES
85
58
4
-
-
-
-
-
1+5
1+2
7
-
2+7
O
=
6
-
2
OF
21
12
3
-
5
2
9
8
6
3
-
8
9
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
7
-
-
-
-
8
4
20
First Total
217
118
10
-
5
2
9
8
6
3
7
8
9
-
-
-
-
2+0
Add to Reduce
1+8+7
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Second Total
10
10
1
-
5
2
9
8
6
3
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Essence of Number
1
1
1
-
5
2
9
8
6
3
7
8
9

 

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
-
-
-
-
-
8
4
20
First Total
217
118
10
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
-
-
-
9
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
O
=
6
11
1
O
15
6
6
-
-
2
-
-
-
6
-
-
-
F
=
6
12
1
F
6
6
6
-
-
2
-
-
-
6
-
-
-
S
=
1
13
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
Y
=
7
14
1
Y
25
7
7
-
-
2
-
-
-
-
7
-
-
R
=
9
15
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
A
=
1
16
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
C
=
3
17
1
C
3
3
3
-
-
2
3
-
-
-
-
-
-
U
=
3
18
1
U
21
3
3
-
-
2
3
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
-
48
-
-
SYRACUSE
111
48
48
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
2
9
8
15
12
7
8
27
A
=
1
-
10
ARCHIMEDES
85
58
4
-
-
-
-
-
1+5
1+2
7
-
2+7
O
=
6
-
2
OF
21
12
3
-
5
2
9
8
6
3
-
8
9
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
7
-
-
-
-
8
4
20
First Total
217
118
10
-
5
2
9
8
6
3
7
8
9
-
-
-
-
2+0
Add to Reduce
1+8+7
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Second Total
10
10
1
-
5
2
9
8
6
3
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Essence of Number
1
1
1
-
5
2
9
8
6
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
O
=
6
-
2
OF
21
12
3
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
-
-
-
-
-
8
4
20
First Total
217
118
10
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
2
-
-
-
-
-
-
-
A
=
1
16
1
A
1
1
1
-
1
2
-
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
-
-
-
-
C
=
3
17
1
C
3
3
3
-
-
2
3
-
-
-
-
-
-
U
=
3
18
1
U
21
3
3
-
-
2
3
-
-
-
-
-
-
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
2
-
-
5
-
-
-
-
O
=
6
11
1
O
15
6
6
-
-
2
-
-
-
6
-
-
-
F
=
6
12
1
F
6
6
6
-
-
2
-
-
-
6
-
-
-
Y
=
7
14
1
Y
25
7
7
-
-
2
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
-
-
8
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
-
-
-
9
R
=
9
15
1
R
18
9
9
-
-
2
-
-
-
-
-
-
9
-
48
-
-
SYRACUSE
111
48
48
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
2
9
8
15
12
7
8
27
A
=
1
-
10
ARCHIMEDES
85
58
4
-
-
-
-
-
1+5
1+2
7
-
2+7
O
=
6
-
2
OF
21
12
3
-
5
2
9
8
6
3
-
8
9
S
=
1
-
8
SYRACUSE
111
48
3
-
-
-
-
-
-
-
7
-
-
-
-
8
4
20
First Total
217
118
10
-
5
2
9
8
6
3
7
8
9
-
-
-
-
2+0
Add to Reduce
1+8+7
1+1+8
1+0
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Second Total
10
10
1
-
5
2
9
8
6
3
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
Q
-
8
-
2
Essence of Number
1
1
1
-
5
2
9
8
6
3
7
8
9

 

 

Wikipedia
https://en.wikipedia.org › wiki › Archimedes
archimedes from en.wikipedia.org
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.
Known for: List: Archimedes' principle; Archim...
Born: c. 287 BC; Syracuse?, ?Sicily?
Died: c. 212 BC (aged approximately 75); Syra...
Fields: Mathematics; ?Physics?; ?Astronomy?; ?Mec...?
?Archimedes' screw · ?Archimedes Palimpsest · ?Archimedes' principle · ?Eureka (word)

Archimedes of Syracuse (/???rk?'mi?di?z/, ARK-ihm-EE-deez;[2][a] c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.[3] Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,[4] Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems.[5][6] These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.[7][8]

Archimedes' other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever,[9] the widespread use of the concept of center of gravity,[10] and the enunciation of the law of buoyancy or Archimedes' principle.[11] He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his mathematical discoveries.

Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the

 

S
-
49
4
10
ARCHIMEDES
85
58
49
-
-
4+9
S
1+0
-`
8+5
5+8
4+9
S
-
13
4
1
ARCHIMEDES
13
13
13
-
-
1+3
-
-
-`
1+3
1+3
1+3
-
-
4
-
1
ARCHIMEDES
4
4
4

 

 

A
=
1
-
8
ARCHIMEDES
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
8
ARCHIMEDES
91
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
6
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
-
49
4
10
ARCHIMEDES
85
58
49
-
2
2
3
8
10
6
7
8
18
-
-
4+9
S
1+0
-`
8+5
5+8
4+9
-
-
-
-
-
1+0
-
-
-
1+8
S
-
13
4
1
ARCHIMEDES
13
13
13
-
2
2
8
4
1
6
7
8
9
-
-
1+3
-
-
-`
1+3
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
ARCHIMEDES
4
4
4
-
2
2
8
4
1
6
7
8
9

 

 

A
=
1
-
8
ARCHIMEDES
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
8
ARCHIMEDES
91
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
6
7
-
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
6
7
-
9
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
6
7
8
-
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
6
7
-
9
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
6
7
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
6
7
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
6
7
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
6
7
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
-
49
4
10
ARCHIMEDES
85
58
49
-
2
2
3
8
10
6
7
8
18
-
-
4+9
S
1+0
-`
8+5
5+8
4+9
-
-
-
-
-
1+0
-
-
-
1+8
S
-
13
4
1
ARCHIMEDES
13
13
13
-
2
2
8
4
1
6
7
8
9
-
-
1+3
-
-
-`
1+3
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
ARCHIMEDES
4
4
4
-
2
2
8
4
1
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

A
=
1
-
8
ARCHIMEDES
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
8
ARCHIMEDES
91
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
6
7
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
6
7
-
-
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
6
7
-
-
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
6
7
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
6
7
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
6
7
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
6
7
8
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
6
7
-
9
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
6
7
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
-
49
4
10
ARCHIMEDES
85
58
49
-
2
2
3
8
10
6
7
8
18
-
-
4+9
S
1+0
-`
8+5
5+8
4+9
-
-
-
-
-
1+0
-
-
-
1+8
S
-
13
4
1
ARCHIMEDES
13
13
13
-
2
2
8
4
1
6
7
8
9
-
-
1+3
-
-
-`
1+3
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
ARCHIMEDES
4
4
4
-
2
2
8
4
1
6
7
8
9

 

 

A
=
1
-
8
ARCHIMEDES
-
-
-
-
1
3
4
5
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
8
ARCHIMEDES
91
37
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
3
4
5
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
3
-
-
-
-
M
=
4
6
1
M
13
4
4
-
-
-
4
-
-
-
D
=
4
8
1
D
4
4
4
-
-
-
4
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
5
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
5
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S
-
49
4
10
ARCHIMEDES
85
58
49
-
2
3
8
10
8
18
-
-
4+9
S
1+0
-`
8+5
5+8
4+9
-
-
-
-
1+0
-
1+8
S
-
13
4
1
ARCHIMEDES
13
13
13
-
2
8
4
1
8
9
-
-
1+3
-
-
-`
1+3
1+3
1+3
-
-
-
-
-
-
-
-
-
4
-
1
ARCHIMEDES
4
4
4
-
2
8
4
1
8
9

 

 

-
10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
1
+
=
18
1+8
=
9
-
9
-
9
-
-
-
-
-
8
9
-
-
-
-
19
+
=
36
3+6
=
9
-
9
-
9
-
10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
-
-
1
9
3
-
-
4
5
4
5
-
+
=
31
3+1
=
4
-
4
=
4
-
`-
1
18
3
-
-
13
5
4
5
-
+
=
49
4+9
=
13
1+3
4
-
4
-
10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
-
`-
1
18
3
8
9
13
5
4
5
19
+
=
85
8+5
=
13
1+3
4
-
4
-
-
1
9
3
8
9
4
5
4
5
1
+
=
49
4+9
=
13
1+3
4
-
4
-
10
A
R
C
H
I
M
E
D
E
S
T
-
-
-
-
-
-
-
-
-
-
--
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
4
-
4
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
--
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
15
10
A
R
C
H
I
M
E
D
E
S
-
-
30
-
-
10
-
49
-
31
1+5
1+0
-
9
-
-
9
-
-
-
-
-
-
-
3+0
-
-
1+0
-
4+9
-
3+1
6
1
A
R
C
H
I
M
E
D
E
S
-
-
3
-
-
1
-
13
-
4
-
-
1
9
3
8
9
4
5
4
5
1
-
-
-
-
-
-
-
1+3
-
-
6
1
A
R
C
H
I
M
E
D
E
S
-
-
3
-
-
1
-
4
9
4

 

 

10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
9
-
-
-
-
1
+
=
18
1+8
=
9
-
9
-
9
-
-
-
-
8
9
-
-
-
-
19
+
=
36
3+6
=
9
-
9
-
9
10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
-
1
9
3
-
-
4
5
4
5
-
+
=
31
3+1
=
4
-
4
=
4
`-
1
18
3
-
-
13
5
4
5
-
+
=
49
4+9
=
13
1+3
4
-
4
10
A
R
C
H
I
M
E
D
E
S
-
-
-
-
-
--
-
-
-
-
`-
1
18
3
8
9
13
5
4
5
19
+
=
85
8+5
=
13
1+3
4
-
4
-
1
9
3
8
9
4
5
4
5
1
+
=
49
4+9
=
13
1+3
4
-
4
10
A
R
C
H
I
M
E
D
E
S
T
-
-
-
-
-
-
-
-
-
--
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
4
-
4
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
--
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
9
-
-
9
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
A
R
C
H
I
M
E
D
E
S
-
-
30
-
-
10
-
49
-
31
1+0
-
9
-
-
9
-
-
-
-
-
-
-
3+0
-
-
1+0
-
4+9
-
3+1
1
A
R
C
H
I
M
E
D
E
S
-
-
3
-
-
1
-
13
-
4
-
1
9
3
8
9
4
5
4
5
1
-
-
-
-
-
-
-
1+3
-
-
1
A
R
C
H
I
M
E
D
E
S
-
-
3
-
-
1
-
4
9
4

 

ARCHIMEDES - PRINCIPLE

 

Archimede's Principle states that a body immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced, and this is fundamental to the equilibrium of a body floating in still water. A body floating freely in still water experiences a downward force acting on it due to gravity.

 

A
=
1
-
10
ARCHIMEDES
85
58
4
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
7
4
19
First Total
187
106
7
-
-
-
-
1+9
Add to Reduce
1+8+7
1+0+6
-
Q
-
7
-
10
Second Total
16
7
7
-
-
-
-
1+0
Reduce to Deduce
1+6
-
-
Q
-
7
-
1
Essence of Number
7
7
7

 

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
-
-
-
-
-
-
-
7
4
19
First Total
187
106
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-ARCHIMEDES
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
6
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
49
-
7
-ARCHIMEDES
85
58
49
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PRINCIPLE
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
11
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
16
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
p
=
7
17
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
18
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
48
-
-
PRINCIPLE
102
48
48
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
10
ARCHIMEDES
85
58
4
-
2
2
9
8
20
6
14
8
45
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
2+0
-
1+4
-
4+5
-
-
7
4
19
First Total
187
106
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+9
Add to Reduce
1+8+7
1+0+6
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
10
Second Total
16
7
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+0
Reduce to Deduce
1+6
-
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
1
Essence of Number
7
7
7
-
2
2
9
8
2
6
5
8
9

 

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
-
-
-
-
-
-
-
7
4
19
First Total
187
106
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-ARCHIMEDES
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
6
-
-
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
6
-
-
9
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
6
-
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
6
-
8
-
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
6
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
66
-
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
6
-
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
6
-
-
-
P
=
7
11
1
P
16
7
7
-
-
2
-
-
-
6
7
-
-
R
=
9
12
1
R
18
9
9
-
-
2
-
-
-
6
-
-
9
I
=
9
13
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
N
=
5
14
1
N
14
5
5
-
-
2
-
-
5
6
-
-
-
C
=
3
15
1
C
3
3
3
-
-
2
3
-
-
6
-
-
-
I
=
9
16
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
p
=
7
17
1
P
16
7
7
-
-
2
-
-
-
6
7
-
-
L
=
3
18
1
L
12
3
3
-
-
2
3
-
-
6
-
-
-
E
=
5
19
1
E
5
5
5
-
-
2
-
-
5
6
-
-
-
-
-
-
-
PRINCIPLE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
10
ARCHIMEDES
85
58
4
-
2
2
9
8
20
6
14
8
45
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
2+0
-
1+4
-
4+5
-
-
7
4
19
First Total
187
106
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+9
Add to Reduce
1+8+7
1+0+6
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
10
Second Total
16
7
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+0
Reduce to Deduce
1+6
-
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
1
Essence of Number
7
7
7
-
2
2
9
8
2
6
5
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
2
3
4
5
6
7
8
9
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
-
-
-
-
-
-
-
7
4
19
First Total
187
106
7
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-ARCHIMEDES
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
2
-
-
-
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
6
-
-
-
C
=
3
3
1
C
3
3
3
-
-
2
3
-
-
6
-
-
-
C
=
3
15
1
C
3
3
3
-
-
2
3
-
-
6
-
-
-
L
=
3
18
1
L
12
3
3
-
-
2
3
-
-
6
-
-
-
M
=
4
6
1
M
13
4
4
-
-
2
-
4
-
6
-
-
-
D
=
4
8
1
D
4
4
4
-
-
2
-
4
-
6
-
-
-
E
=
5
7
1
E
5
5
5
-
-
2
-
-
5
66
-
-
-
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
2
-
-
5
6
-
-
-
E
=
5
19
1
E
5
5
5
-
-
2
-
-
5
6
-
-
-
P
=
7
11
1
P
16
7
7
-
-
2
-
-
-
6
7
-
-
p
=
7
17
1
P
16
7
7
-
-
2
-
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
2
-
-
-
6
-
8
-
R
=
9
2
1
R
18
9
9
-
-
2
-
-
-
6
-
-
9
I
=
9
5
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
R
=
9
12
1
R
18
9
9
-
-
2
-
-
-
6
-
-
9
I
=
9
13
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
I
=
9
16
1
I
9
9
9
-
-
2
-
-
-
6
-
-
9
-
-
-
-
PRINCIPLE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
10
ARCHIMEDES
85
58
4
-
2
2
9
8
20
6
14
8
45
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
2+0
-
1+4
-
4+5
-
-
7
4
19
First Total
187
106
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+9
Add to Reduce
1+8+7
1+0+6
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
10
Second Total
16
7
7
-
2
2
9
8
2
6
5
8
9
-
-
-
-
1+0
Reduce to Deduce
1+6
-
-
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
1
Essence of Number
7
7
7
-
2
2
9
8
2
6
5
8
9

 

 

A
=
1
-
10
ARCHIMEDES
85
58
4
-
1
3
4
5
7
8
9
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
-
-
-
-
-
-
7
4
19
First Total
187
106
7
-
1
3
4
5
7
8
9
-
-
-
-
-ARCHIMEDES
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
3
-
-
-
-
-
C
=
3
15
1
C
3
3
3
-
-
3
-
-
-
-
-
L
=
3
18
1
L
12
3
3
-
-
3
-
-
-
-
-
M
=
4
6
1
M
13
4
4
-
-
-
4
-
-
-
-
D
=
4
8
1
D
4
4
4
-
-
-
4
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
5
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
5
-
-
-
E
=
5
19
1
E
5
5
5
-
-
-
-
5
-
-
-
P
=
7
11
1
P
16
7
7
-
-
-
-
-
7
-
-
p
=
7
17
1
P
16
7
7
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
9
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
12
1
R
18
9
9
-
-
-
-
-
-
-
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
9
I
=
9
16
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
-
-
PRINCIPLE
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
10
ARCHIMEDES
85
58
4
-
2
9
8
20
14
8
45
P
=
7
-
9
PRINCIPLE
102
48
3
-
-
-
-
2+0
1+4
-
4+5
-
-
7
4
19
First Total
187
106
7
-
2
9
8
2
5
8
9
-
-
-
-
1+9
Add to Reduce
1+8+7
1+0+6
-
-
-
-
-
-
-
-
-
Q
-
7
-
10
Second Total
16
7
7
-
2
9
8
2
5
8
9
-
-
-
-
1+0
Reduce to Deduce
1+6
-
-
-
-
-
-
-
-
-
-
Q
-
7
-
1
Essence of Number
7
7
7
-
2
9
8
2
5
8
9

 

 

-
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
+
=
18
1+8
=
9
-
9
=
9
-
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
4
5
-
5
4
-
2
+
=
22
2+2
=
4
-
4
-
4
-
-
20
-
13
5
-
5
13
-
20
+
=
76
7+6
=
13
1+3
4
-
4
-
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
-
20
9
13
5
-
5
13
9
20
+
=
94
9+4
=
13
1+3
4
-
4
-
-
2
9
4
5
-
5
4
9
2
+
=
40
4+0
=
4
-
4
-
4
-
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
5
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
25
8
T
I
M
E
-
E
M
I
T
-
-
20
-
-
8
-
40
-
22
2+5
-
-
9
-
-
-
-
-
9
-
-
-
2+0
-
-
-
-
4+0
-
2+2
7
8
T
I
M
E
-
E
M
I
T
-
-
2
-
-
8
-
4
-
4
-
-
2
9
4
5
-
5
4
9
2
-
-
-
-
-
-
-
-
-
-
7
8
T
I
M
E
-
E
M
I
T
-
-
2
-
-
8
-
4
-
4

 

 

8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
-
-
9
-
+
=
18
1+8
=
9
-
9
=
9
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
2
-
4
5
-
5
4
-
2
+
=
22
2+2
=
4
-
4
-
4
-
20
-
13
5
-
5
13
-
20
+
=
76
7+6
=
13
1+3
4
-
4
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
--
-
-
-
-
-
20
9
13
5
-
5
13
9
20
+
=
94
9+4
=
13
1+3
4
-
4
-
2
9
4
5
-
5
4
9
2
+
=
40
4+0
=
4
-
4
-
4
8
T
I
M
E
-
E
M
I
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
-
4
-
-
-
4
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
5
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
8
T
I
M
E
-
E
M
I
T
-
-
20
-
-
8
-
40
-
22
-
-
9
-
-
-
-
-
9
-
-
-
2+0
-
-
-
-
4+0
-
2+2
8
T
I
M
E
-
E
M
I
T
-
-
2
-
-
8
-
4
-
4
-
2
9
4
5
-
5
4
9
2
-
-
-
-
-
-
-
-
-
-
8
T
I
M
E
-
E
M
I
T
-
-
2
-
-
8
-
4
-
4

 

 

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

 

 

-
KINETICS
--
-
-
-
-
--
-
-
-
-
-
-
-
KINETICS
--
-
-
-
-
1
K
11
2
2
-
2
1
I
9
9
9
9
-
3
N+E+T
39
12
3
-
3
1
I
9
9
9
9
-
2
C+S
22
4
4
-
4
8
KINETICS
-
-
-
-
-

 

 

K
=
2
-
-
KINETICS
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
-
-
-
-
1
S
19
10
1
K
=
2
Q
8
KINETICS
90
45
36
-
-
-
-
-
-
9+0
4+5
3+6
K
=
2
Q
8
KINETICS
9
9
9

 

 

-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
25
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
2+5
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

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

 

 

-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
2+3
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

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

 

 

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

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
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
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
18
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+8
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

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

 

 

7
WEIGHED
61
43
7
2
IN
23
14
5
3
THE
33
15
6
7
BALANCE
38
20
2
3
AND
19
10
1
5
FOUND
60
24
6
7
WANTING
88
34
7
34
Add to Reduce
322
160
34
3+4
Reduce to Deduce
3+2+2
1+6+0
3+4
7
Essence of Number
7
7
7

 

 

6
RABBIT
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
CUNICULUS
-
-
-
-
-
1
C
3
3
3
-
3
1
U
21
3
3
-
3
1
N
14
5
5
-
-
1
I
9
9
9
-
-
1
C
3
3
3
-
3
1
U
21
3
3
-
3
1
L
12
3
3
-
3
1
U
21
3
3
-
3
1
S
19
10
1
-
-
9
CUNICULUS
123
42
33
-
18
-
-
1+2+3
4+2
3+3
-
1+8
9
CUNICULUS
6
6
6
-
9

 

 

-
9
C
U
N
I
C
U
L
U
S
-
-
-
-
--
-
-
-
-
-
-
-
-
5
9
-
-
-
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
14
9
-
-
-
-
19
+
=
42
4+2
=
6
=
6
=
6
-
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
3
3
3
3
-
+
=
18
1+8
=
9
=
9
=
9
-
-
3
21
-
-
3
21
12
21
-
+
=
81
8+1
=
9
=
9
=
9
-
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
21
14
9
3
21
12
21
19
+
=
123
1+2+3
=
6
=
6
=
6
-
-
3
3
5
9
3
3
3
3
1
+
=
33
3+3
=
6
=
6
=
6
-
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
3
3
-
-
3
3
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
27
9
C
U
N
I
C
U
L
U
S
-
-
18
-
-
9
-
33
-
24
2+7
-
3
3
-
-
3
3
3
3
-
-
-
1+8
-
-
-
-
3+3
-
2+4
9
9
C
U
N
I
C
U
L
U
S
-
-
9
-
-
9
-
3
-
6
-
-
3
3
5
9
3
3
3
3
1
-
-
-
-
-
-
-
-
-
-
9
9
C
U
N
I
C
U
L
U
S
-
-
9
-
-
9
-
3
-
6

 

 

9
C
U
N
I
C
U
L
U
S
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
-
-
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
9
-
-
-
-
19
+
=
42
4+2
=
6
=
6
=
6
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
3
3
3
3
-
+
=
18
1+8
=
9
=
9
=
9
-
3
21
-
-
3
21
12
21
-
+
=
81
8+1
=
9
=
9
=
9
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
3
21
14
9
3
21
12
21
19
+
=
123
1+2+3
=
6
=
6
=
6
-
3
3
5
9
3
3
3
3
1
+
=
33
3+3
=
6
=
6
=
6
9
C
U
N
I
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
3
3
-
-
3
3
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
C
U
N
I
C
U
L
U
S
-
-
18
-
-
9
-
33
-
24
-
3
3
-
-
3
3
3
3
-
-
-
1+8
-
-
-
-
3+3
-
2+4
9
C
U
N
I
C
U
L
U
S
-
-
9
-
-
9
-
3
-
6
-
3
3
5
9
3
3
3
3
1
-
-
-
-
-
-
-
-
-
-
9
C
U
N
I
C
U
L
U
S
-
-
9
-
-
9
-
3
-
6

 

 

U
=
3
7
UNIFIED
68
41
5
F
=
6
5
FIELD
36
27
9
T
=
2
6
THEORY
91
37
1
-
-
11
18
First Total
195
105
15
-
-
1+1
1+8
Add to Reduce
1+9+5
1+0+5
1+5
Q
-
2
9
Second Total
15
6
6
-
-
-
-
Reduce to Deduce
1+5
-
-
-
-
2
9
Essence of Number
6
6
6

 

 

3
THE
33
15
6
10
GOVERNMENT
133
52
7
2
OF
21
12
3
3
THE
33
15
6
6
PEOPLE
69
33
6
2
BY
27
9
9
3
THE
33
15
6
6
PEOPLE
69
33
6

 

 

4
FIVE
42
24
6
6
SENSES
81
18
9
10
Add to Reduce
123
42
15
1+0
Reduce to Deduce
1+2+3
4+2
1+5
1
Essence of Number
6
6
6

 

 

3
SIX
52
16
7
6
SENSES
81
18
9

 

 

5
4
FIVE
42
24
6
6
3
SIX
52
16
7

 

 

4
SELF
42
15
6
9
CONSCIOUS
118
37
1
13
CONSCIOUSNESS
57
21
3

 

 

5
HUMAN
57
21
3
12
INTELLIGENCE
115
61
7
17
First Total
172
82
10
1+7
Add to Reduce
1+7+2
8+2
1+0
8
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
8
Essence of Number
1
1
1

 

 

5
HUMAN
57
21
3
10
CREATIVITY
132
51
6
15
First Total
189
72
9
1+5
Add to Reduce
1+8+9
7+2
-
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

1
I
9
9
9
4
DEAL
22
13
4
3
THE
33
15
6
5
CARDS
45
18
9
3
AND
19
10
1
4
HERE
36
27
9
2
IS
28
10
1
2
AN
15
6
6
3
ACE
9
9
9
27
Add to Reduce
216
117
54
2+7
Reduce to Deduce
2+1+6
1+1+7
5+4
9
Essence of Number
9
9
9

 

 

K
=
2
-
6
KARMAS
63
18
9
D
=
4
-
6
DIVINE
45
18
9
L
=
3
-
3
LAW
36
9
9
-
-
9
-
15
Add to Reduce
162
63
27
-
-
--
-
1+5
Reduce to Deduce
1+6+2
6+3
2+7
-
-
9
-
6
Essence of Number
9
9
9

 

 

-
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
1
-
-
9
-
9
5
-
-
-
-
-
+
=
24
2+4
=
6
-
6
-
6
-
-
-
-
-
-
-
19
-
-
9
-
9
14
-
-
-
-
-
+
=
51
5+1
=
6
-
6
-
6
-
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
2
1
9
4
1
-
-
4
-
4
-
-
5
-
3
1
5
+
=
39
3+9
=
12
1+2
3
-
3
-
-
11
1
18
13
1
-
-
4
-
22
-
-
5
-
12
1
23
+
=
111
1+1+1
=
3
-
3
-
3
-
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
11
1
18
13
1
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
-
9
-
9
-
-
2
1
9
4
1
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
-
9
-
9
-
15
K
A
R
M
A
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
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
2+1
1+5
-
1
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
3
6
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
-
2
1
9
4
1
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
2
6
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
1
-
-
9
-
9
5
-
-
-
-
-
+
=
24
2+4
=
6
-
6
-
6
-
-
-
-
-
-
19
-
-
9
-
9
14
-
-
-
-
-
+
=
51
5+1
=
6
-
6
-
6
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
2
1
9
4
1
-
-
4
-
4
-
-
5
-
3
1
5
+
=
39
3+9
=
12
1+2
3
-
3
-
11
1
18
13
1
-
-
4
-
22
-
-
5
-
12
1
23
+
=
111
1+1+1
=
3
-
3
-
3
15
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
11
1
18
13
1
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
-
9
-
9
-
2
1
9
4
1
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
-
9
-
9
15
K
A
R
M
A
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
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
1+5
-
1
-
-
1
1
-
-
-
-
-
-
-
-
-
1
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
6
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
2
1
9
4
1
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
6
K
A
R
M
A
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

-
13
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
-
8
-
6
5
9
-
9
-
-
+
=
43
4+3
=
7
=
7
=
7
-
-
19
-
14
-
8
-
15
14
9
-
9
-
-
+
=
88
8+8
=
16
1+6
7
=
7
-
13
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
-
9
-
-
-
3
-
2
7
+
=
31
3+1
=
4
-
4
=
4
-
-
-
25
-
3
-
18
-
-
-
3
-
20
25
+
=
94
9+4
=
13
1+3
4
=
4
-
13
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
19
25
14
3
8
18
15
14
9
3
9
20
25
+
=
182
1+8+2
=
11
1+1
2
=
2
-
-
1
7
5
3
8
9
6
5
9
3
9
2
7
+
=
74
7+4
=
11
1+1
2
=
2
-
13
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
9
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
13
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
41
-
-
13
-
74
-
38
-
1+3
-
-
-
-
-
9
-
-
9
-
9
-
-
-
-
4+1
-
-
1+3
-
7+4
-
3+8
4
4
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
5
-
-
4
-
11
-
11
-
-
1
7
5
3
8
9
6
5
9
3
9
2
7
-
-
-
-
-
-
-
1+1
-
1+1
4
4
S
Y
N
C
H
R
O
N
I
C
I
T
Y
-
-
5
-
-
4
-
2
-
2

 

 

-
12
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
-
-
-
-
-
-
-
-
-
-
1
-
5
-
8
-
6
5
9
1
-
-
+
=
35
3+5
=
8
=
8
-
8
-
-
19
-
14
-
8
-
15
14
9
19
-
-
+
=
98
9+8
=
17
1+7
8
-
8
-
12
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
-
9
-
-
-
-
5
4
+
=
28
2+8
=
10
1+0
1
-
1
-
-
-
25
-
3
-
18
-
-
-
-
5
4
+
=
55
5+5
=
10
1+0
1
-
1
-
12
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
-
-
-
-
-
-
-
-
-
-
19
25
14
3
8
18
15
14
9
19
5
4
+
=
153
1+5+3
=
9
-
9
-
9
-
-
1
7
5
3
8
9
6
5
9
1
5
4
+
=
63
6+3
=
9
-
9
-
9
-
12
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
2
12
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
43
-
-
12
-
63
-
45
-
1+2
-
-
-
-
-
9
-
-
9
-
-
-
-
-
4+3
-
-
1+2
-
6+3
-
4+5
2
3
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
7
-
-
3
-
9
-
9
-
-
1
7
5
3
8
9
6
5
9
1
5
4
-
-
-
-
-
-
-
-
-
-
2
3
S
Y
N
C
H
R
O
N
I
S
E
D
-
-
7
-
-
3
-
9
-
9

 

 

 
 
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