1. The document contains a series of calculations involving addition, subtraction, multiplication and division. 2. The numbers become increasingly larger as the calculations progress. 3. The final results are long strings of digits that appear to have no obvious meaning on their own.

1. )19
9
9 1 9
9 2 18
9 3 27
9 4 36
9 5 45
9 6 54
9 7 63
9 8 72
9 9 81
9 10 90
× =
× =
× =
× =
× =
× =
× =
× =
× =
× =
9110
1109
97 9×67379 7 63× =
)
2.
3
3 6 12 24 48 96 192 384 768 1536 3072 ×××
4
1

2. 2 34793×
364568759714955
918358366
48448
10
( )4 2 2× = × ×W W
( )( )( )8 2 2 2× = × × ×W W
)
4682 3484 7528 603638 20304050
)5:
510
5
5 1369×6845136968413696845
2

3. 11:
1 10 11+ =
11
11 1 10× = × + ×W W W
11 2643 1 2643 10 2643× = × + ×
33
3 4 7+ =73
4 6 10+ =736
6 1 2 9+ + =9073
229073
10
)
711
)1
7462423708
)
63523478556082
3

4. )12
12 10 2× = × + +W W W
12 2473 10 2473 2 2473
24730 4946
× = × + ×
= +
24730
04946
29676
332 3 6× =6
( )7 2 3 17× + =7614
( )4 2 7 1 16× + + =
67612
( )2 2 4 1 9= × + + =
9676229676
10412
)21:
21
4

5. 21 2473×
3 2 0+ ×3 =
7 2 3 13+ × =
19=1(4 2 7 1+ × +
11=1(2 2 4 1+ × +
1 2 2+ × +1(5 =
21 4273 51933× =
32 2351×
32 2351 30 2351 2 2351× = × + ×
70530 4702= +
75232=
22
2 5 3 1 13× + × =32
22=2 3 3 5 1× + × +232
2(
2 2 3 3 2 15× + × + =52321(
2 0×2(7 1 2 3= + × +
75232
23
32 41 23 52
345
5

6. (4) 12 4521
(5) 21 5632
(6) 21 23031
(7) 12 37852
(8) 21 12578
(9) 12 23521
×
×
×
×
×
×
)
56389265 6 3 8 9 2 33+ + + + + =3 3 6+ =
9(
12 2351 28212× =
3 1 2 12= + =
2351=( )2 3 5 1 11 2+ + + = =
28212=15 6=
12×2351=28212
3 2 6× =
×
6

7. ≠×
4 5 6 7 8 9
)35672381941
7

8. 1:(
*
*
*
*
*
*
*
*
*
*
35
*
*
*
*
*
*
*
*
*
*
*
3535
1 ‫ح‬2 ‫ح‬
8

9. 2:(
9 ‫ح‬
5 ‫ح‬
9 ‫ح‬
100 ‫ح‬101⊕
⊕⊕
9
4 ‫ح‬
⊕ ⊕⊕ ⊕ ⊕
3 ‫ح‬
⊕ ⊕⊕ ⊕
2 ‫ح‬
⊕ ⊕⊕
1 ‫ح‬
⊕ ⊕
⊕ ⊕⊕ ⊕ ⊕ ⊕
⊕ ⊕⊕ ⊕ ⊕⊕ ⊕ ⊕⊕ ⊕

10. 5 ‫ح‬
6 ‫ح‬
50 ‫ح‬
1.
2.
3.
3:(
11 ‫ح‬
21 ‫ح‬
12 ‫ح‬
22 ‫ح‬
110 ‫ح‬
210 ‫ح‬
11500 ‫ح‬
21500 ‫ح‬
1‫ح‬ ‫ح‬
2‫ح‬ ‫ح‬
10
||| |||| ||||| ||||||
4 ‫ح‬3 ‫ح‬2 ‫ح‬1 ‫ح‬
WW WWWW WWWWWW WWWWWWWW
4 ‫ح‬3 ‫ح‬2 ‫ح‬1 ‫ح‬
♣ ♣♣♣ ♣♣♣♣♣ ♣♣♣♣♣♣♣
4 ‫ح‬3 ‫ح‬2 ‫ح‬1 ‫ح‬
   
4 ‫ح‬3 ‫ح‬2 ‫ح‬1 ‫ح‬

11. 11 ‫ح‬
241 ‫ح‬
142 ‫ح‬
282 ‫ح‬
12010 ‫ح‬
24010 ‫ح‬
130001500 ‫ح‬
260001500 ‫ح‬
12 2n n× =‫ح‬ ‫ح‬
24 4n n× =‫ح‬ ‫ح‬
)43
1-1 ‫ح‬
2-2 ‫ح‬
3-3 ‫ح‬
4-4 ‫ح‬
5-10 ‫ح‬
6-253 ‫ح‬
‫ح‬ ‫ح‬
11
1 ‫ح‬ 2 ‫ح‬ 3 ‫ح‬

12. )5
1-1 ‫ح‬2-2 ‫ح‬3-4 ‫ح‬4-5 ‫ح‬5-10 ‫ح‬6-‫ح‬ ‫ح‬
5:(
12345×××
113579×××
2246810×××
16
26
110
210
235
150
2‫ح‬
1‫ح‬
12
* ** *** ****
** *** ****1 ‫ح‬
*** ****2 ‫ح‬
****3 ‫ح‬
4 ‫ح‬

13. 1
162 6 1 11× − =
262 6 12× =
1102 10 1 19× − =
2102 10 20× =
2352 35 70× =
1502 50 1 99× − =
2‫ن‬2 2n n× =
1‫ن‬2 1 2 1n n× − = −
6:(
12345×××
11471013×××
22581114×××
33691215×××
36
26
16
320
350
2‫ن‬
220
120
230
145
3‫ن‬
1‫ن‬
13

14. 3
3
32
363 6 18× =
263 6 1 17× − =
163 6 2 16× − =
3203 20 60× =
3503 50 150× =
2‫ن‬3 1 3 1n n× − = −
2203 20 1 59× − =
1203 20 2 58× − =
2303 30 1 89× − =
1453 45 2 133× − =
3‫ن‬3 3n n× =
1‫ن‬3 2 3 2n n× − = −
)6
12345...
1246810...
2357911...
16
26
17
27
220
14

15. 124
1500
1‫ن‬
2500
2‫ن‬
)7
12345×××
11591317×××
226101418×××
337111519×××
448121620×××
46
36
26
16
1‫ن‬
3‫ن‬
27
112
320
4100
2‫ن‬
4‫ن‬
)8
12345×××
11020303050×××
21222324252×××
324446484104×××
15

16. 16
26
36
19
1‫ن‬
3‫ن‬
29
39
230
367
2‫ن‬
16

17. 1 2 3‫ن‬ ‫ن‬ ‫×ن‬××
75656 7 8÷ =567562 4 8 14 7 28‫ن‬ ‫ن‬ ‫ن‬ ‫ن‬ ‫ن‬
756756567
3321 654 987 890 567 1234‫ن‬ ‫ن‬ ‫ن‬ ‫ن‬ ‫ن‬
12345678909876543213(
33
5684501034567810
17
.

18. 35510510
0550
39:
3576
3576 3 1000 5 100 7 10 6= × + × + × +
( ) ( ) ( )3 999 1 5 99 1 7 9 1 6= + + + + + +
( )3 999 5 99 7 9 3 5 7 6× + × + × + + + +
9 99 999‫ن‬ ‫ن‬3
3 999 5 99 7 9× + × + ×33576
3
3 5 7 6+ + +3(*)
3 5 7 6 21 3 7+ + + = = ×35763
9 99 999‫ن‬ ‫ن‬939
357693 5 7 6 21+ + + =9.
18

19. 2359
1.7308
2.32220
3.34206
4.6349
5.13587
6.9765
7.623
6.
8.24686.
48:
237532432432324
32 237500 237532+ =
23750010042375324324.
8
532 237000 237532+ =
19

20. 1000823700085328237532853282375328
11:
136818
3 8 8 19+ + =
1 6 1 8+ + =
19 8 11− =13681811
1 100000 3 10000 6 1000 8 100 1 10 8 136818× + × + × + × + × + =
( ) ( ) ( ) ( ) ( )1 100000 1 3 1 9999 6 1001 1 8 1 99 1 11 1 8= + − + × + + × − + × + + × − +
( ) ( )1 10001 3 9999 6 1001 8 99 1 11 3 8 8 1 6 1= × + × + × + × + × + + + − + +
( ) ( ) ( )11 1 9091 3 909 6 91 8 9 1 3 8 8 1 6 1= × + × + × + × + + + + − + +
13681811( ) ( )1 6 1 3 8 8+ + − + +11
20

21. 4811
9.7448
10.18722
11.84216
12.36342
13.323488
14.82364
15.347192311.
7:
21177
777.
71
210534877
21053487 7 21053480− =
2105348
2178 21×
2105348 8 21 2105348 168− × = −
2105180=
21

22. 210518:
210518 8 21 210350− × =
21035 35 21000− =
210007210534877
7( )7 143 1001 1001× =10011
21053477
3 1001 3003× =73 1001 73073× =473 1001 473473× =3
2105347 473473 20580000− =
2058
2058 2002 1057− =
5656721053477.
549012577
54901257 7 54901250− =
5490125
5490125 125125 536500− =
22

23. 5365
5365 5005 360− =
36
367549012577
7
16.1198008
17.6404028
18.48359721
19.30945827452018692
20222 3 4 5 6 7 8 9 1011
20.35 29 748 214 827 751
21.472 03358116459824
22.82451120045793265
23.3468231234
24.47120562311
23