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: 2006

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: : 11 : :

:

1- : = 100 - 99 2- : (+) = 3- :/ / = 4- = + 99 5- 6-

: 11 11

: 11 :

11 , 11 11 , 11 11 . : , .

(1) 11 253: = 53 = 0253 + 02 = 55 55 11 253 11.

(2) 11 1298: = 98 = 1298 + 12 = 110 110 11 ( 11 10 ) 1298 11.

(3) 11 1318: = 18 = 1318 + 13 = 31 31 11 1318 11

(4) 11 15730: = 30 = 57 = 0130 + 57 + 1 = 88 88 11 15730 11.

(5) 11 16060: = 60 = 60 = 0160 + 60 + 1 = 121 121 11 ( 11 11 ) 16060 11.

(6) 11 178959: = 59 = 89 = 1759 + 89 + 17 = 165 165 11 .65 + 1 = 66 165 11 178959 11.

(7) 11 247567: = 67 = 75 = 2467 + 75 + 24 = 166 166 11 247567 11.

(8) 11 1932612: = 12 = 26 = 93 = 0112 + 26 + 93 + 1 = 132 132 11 ( 11 12 ) 1932612 11.

: 11 : : " 11 " . 11 , .

(1) : 132 11 = 12 3 .

(2): 308 11 = 28 , 3 , 8+3 = 11 3 2 28.

(3): 11 429: 2 4 + 9 = 13 , 13 > 11 4 3 429 11 = 39.

(4): 11 671: 7 1+6 = 7 , 7 < 11 6 671 11 = 61.

: " 11 " : . . 11 . 11 .

(1): 11 7381 : 8 .1 + 3 =4 , 4 < 11 8 + 7 = 15 , 15 > 11 73 7 + 1 = 67 7381 11 = 671

(2): 11 1243: 4 .3 + 2 = 5 , 5 < 11 4 + 1 = 5 , 5 < 11 12 1 = 11 1243 11 = 113.

(3): 11 7546: 4 .6 + 5 = 11 4 + 7 = 11 75 7 1 + 1 = 68 7546 11 = 686

: ( 7-97)

: :

: . : = 100 99 . : 7 = 105 99 = 6 19 = 114 99 = 15 23 = 115 99 = 16

( 7-97) :

() ()17621353173419155231662917731258371294124104330114742

() ()12537135919146123156735167143177347187959198367208979219795

: : : 321 = 21 = 3 4321 = 21 = 43

54321 = 21 = 543 654321 = 21 = 6543 = 3 = 43 = 543

: + ( + ) =

: : . 7 :1051001100031000021000006

321 = 21 = 3 4321 = 21 = 43 54321 = 321 = 54 654321 = 321 = 654 : = = + 1

: () / / / = / = 321 105 = 21 = 3 / = 5 / = 1

/ / = 4321 1017 = 21 = 43 / = 17 / = 10 / / = 10 21 17 43 = : : + 99 =

: () 7 () 6 6 + 99 = 105 105 7 () 19 () 15 15+ 99 = 114 114 19

: . 10 . .

: 7 ( ) 6 + 99 = 105 5 10 = 50 50 7 = 7 1 1001

1 10 = 10 10 7 = 1 3 10003 3 10 = 30 30 7 = 4 2 100002

:- 875 7 : - :- : :- = 875 = 7 = 6 = 75 =8+ = 75 + 8 = 83 = 6 7 = 48 ( + ) = 48 83 = 35 35 = 7 5 875 7

: :- = 875 = 105 = 75 = 8/ = 5 / =1 :- / / =1 75 5 8 =75 40 = 35 35 = 75 875 7

:- 3682 7 :- : :- = 3682 = 7 = 6 = 82 = 36 + = 82 + 36 = 118 = 636 = 216 ( + ) =216 118 = 98 98 = 7 14 3682 7

: :- = 3682 = 1001 = 82 = 36 / = 1 / = 10 :- / / = 10 82 136 = 820 36 = 784

: :- = 784 = 105 = 84 = 7/ = 5 / =1 :- / / = 1 84 57 = 84 35 = 49 49 = 7 7 3682 7

: 81529 7 : :-:- = 81529 = 7 = 6 = 29 = 815 + = 29 + 815 = 844 = 6 815 = 4890 ( + ) = 4890- 844 = 4046

:- = 4046 = 7 = 6 = 46 = 40+ = 46 + 40 = 86 = 6 40= 240 ( + ) = 240- 86 = 154

:- = 154 = 7 = 6 =54 =1+ =54 +1 = 55 = 6 1 =6 ( + ) = 6- 55 = 49 49 = 7 7 81529 7

: :- =81529 = 10003 = 529 = 81 / = 3 / =10 :- / / = 10 529 381 = 5290 243 = 5047

: :- = 5047 = 1001 = 47 = 50/ = 1 / =10 :- / / = 10 47 150= 470 50 = 420

: :- = 420 = 105 = 20 = 4/ = 5 / =1 :- / / = 1 20 54= 20 20 = 0 81529 7

:- 489216 7 : :-:- = 489216 = 7 = 6 = 16 =4892 + =16 + 4892 = 4908 = 6 4892 = 29352 ( + ) = 29352- 4908 = 24444

:- = 24444 = 7 = 6 = 44 = 244+ = 44 + 244 = 288 = 6 244= 1464 ( + ) = 1464- 288 = 1176

:- = 1176 = 7 = 6 =76 =11+ =76 +11 = 87 = 6 11 =66 ( + ) = 66- 87 = 21 21 = 7 3 489216 7

: :- =489216 = 100002 = 216 = 489 / = 2 / =100 :- / / = 100 216 2489 = 21600 987 = 20622

: :- = 20622 = 10003 = 622 = 20/ = 3 / =10 :- / / = 10 622 320= 6220 60 = 6160

: :- = 6160 = 1001 = 60 = 61/ = 1 / =10 :- / / = 10 60 161= 600 61 = 539

: :- = 539 = 105 = 39 = 5/ = 5 / =1 :- / / = 1 39 55= 39 25= 14 14 =72 489216 7

11 :- 583 11: - :- : :- = 583 = 11 = 0 = 83 =5+ = 83 + 5 = 88 = 0 5 = 00 88 = 88 88 = 11 8 583 11

: :- = 583 = 110 = 83 = 5/ = 10 / = 1 :- / / =1 83 10 5 =83 50 = 33 33 = 113 583 11

13 :- 819 13 : - :- : :- = 819 = 13 = 5= 19 =8+ = 19 + 8 = 27 = 5 8 = 40 ( + ) = 40 27 =13 13 = 13 1 819 13

: :- = 819 = 104 = 19 = 8/ = 4 / = 1 :- / / =1 19 4 8 =19 40 = 13 13 = 131 819 13

17 :- 935 17 : - :- : :- = 935 = 17 = 3= 35 =9+ = 35 + 9 = 44 = 3 9 = 27 ( + ) = 27 44 = 17 17 = 17 1 935 17

: :- = 935 = 102 = 35 = 9/ = 2 / = 1 :- / / =1 35 2 9 =35 18 = 17 17 = 171 935 17

19 :- 741 19 : - :- : :- = 741 = 19 = 15 = 41 =7+ = 41 + 7 = 48 = 15 7 = 105 ( + ) = 105 48 = 57 57 = 19 3 741 19

: :- = 741 = 114 = 41 = 7/ = 14 / = 1 :- / / =1 41 14 7 =41 98 = 57 57 = 193 741 19

23 :- 529 23 : - :- : :- = 529 = 23 = 16 = 29 =5+ = 29 + 5 = 34 = 16 5 = 80 ( + ) = 80 34 = 46 46 = 23 2 529 23

: :- = 529 = 115 = 29 = 5/ = 15 / = 1 :- / / =1 29 15 5 =29 75 = 46 46 = 232 529 23

29 :- 348 29 : - :- : :- = 348 = 29 = 17= 48 =3+ = 48 + 3 = 51 = 17 3 = 51 ( + ) = 51 51 = 0 348 29

: :- = 348 = 116 = 48 = 3/ = 16 / = 1 :- / / =1 48 16 3 =48 48 = 0 348 29

31 :- 713 31 : - :- : :- = 713 = 31 = 25 = 13 =7+ = 13 + 7 = 20 = 25 7 = 175175 20 = 155

:- = 155 = 31 = 25= 55 = 1+ = 55 + 1 = 56 = 25 1= 25 ( + ) = 25- 56 =31 31= 31 1 713 29

: :- = 713 = 124 = 13 = 7/ = 24 / = 1 :- / / =1 13 24 7=13 167 = 155

: :- = 155 = 124 = 55 = 1/ = 24 / =1 :- / / = 1 55 241= 55 24 = 31 31 = 311 713 31

37 :- 814 37: - :- : :- = 814 = 37 = 12= 14 =8+ = 14 + 8 = 22 = 12 8 = 96 ( + ) = 96 22 = 74 74 = 37 2 814 37

: :- = 814 = 111 = 14 = 8/ = 11 / = 1 :- / / = 14 11 8 = 14 88 = 74 74 = 37 2 814 37

41 :- 943 41 : - :- : :- = 943 = 41 = 24= 43 =9+ = 43+ 9 = 52 = 24 9 = 216 ( + ) = 216 52 = 164 164 = 41 4 943 41

: :- = 943 = 123 = 43 = 9/ = 23 / = 1 :- / / =1 43 24 9 =43 207 = 164 164=414 943 41

43 :- 817 43: - :- : :- = 817 = 43 = 30=17 =8+ = 17 + 8 = 25 =30 8 = 240 ( + ) = 240 25= 215 215 = 43 5 817 43

: :- = 817 = 129 = 17 = 8/ = 29 / = 1 :- / / =1 17 29 8 =17 232 = 215 215 = 43 5 817 43 47

:- 423 47 : - :- : :- = 423 = 47 = 42= 23 =4+ = 23 + 4 = 27 = 42 4 = 168 ( + ) = 168 27= 141 141 = 473 423 47

: :- = 423 = 141 = 23 =4/ = 41 / = 1 :- / / =1 23 41 4 =23 164 = 141 141 = 47 3 423 47

53 :- 742 53 : - :- : :- = 742 =53 = 7= 42 =7+ = 42 + 7 = 49 = 7 7 = 49 ( + ) = 49 49= 0 742 53

: :- = 742 = 106 = 42 = 7/ = 06 / = 1 :- / / =1 42 6 7 =42 42 = 0 742 53

59 :- 413 59 : - :- : :- = 413 = 59 = 19= 13 =4+ = 13 + 4 = 17 = 19 4 = 76 ( + ) = 76 17 = 59 413 59

: :- = 413 = 118 = 13 = 4/ = 18 / = 1 :- / / =1 13 18 4 =13 72 = 59 59 = 59 1 413 59

61 :- 427 61 : - :- : :- = 427 = 61 = 23= 27 =4+ = 27 + 4 = 31 =23 4 = 92 ( + ) = 92 31 =61 427 61

: :- = 427 = 122 = 27 = 4/ =22 / = 1 :- / / =1 27 22 4 =27 88 = 61 61 = 61 1 427 61

67 :- 536 67 : - :- : :- = 536 = 67 = 35= 36 =5+ = 36 + 5 = 41 =35 5 = 175 ( + ) = 175 41 =134 536 = 672 536 67

: :- = 536 = 134 = 36 = 5/ =34 / = 1 :- / / =1 36 34 5 =36 170 = 134 134 = 34 2 536 67

71 :- 497 71 : - :- : :- = 497 = 71 = 43= 97 =4+ = 97 + 4 = 101 =43 4 = 172 ( + ) = 172 101 =71 71 =71 1 497 71

: :- = 497 = 142 = 97 = 4/ =42 / = 1 :- / / =1 97 42 4 =97 168 = 71 71 = 71 1 497 71

73 :- 292 73 : - :- : :- = 292 = 73 = 47= 92 =2+ = 92 + 2 = 94 =47 2 = 94 ( + ) = 94 94 =0 292 73

: :- = 292 = 146 = 92 = 2/ =46 / = 1 :- / / =1 92 46 2 =92 92 = 0 292 73

79 :- 237 79 : - :- : :- = 237 = 79 = 59= 37 =2+ = 37 + 2 = 39 =59 2 = 118 ( + ) = 118 39 =79 237 79

: :- = 237 = 158 = 37 = 2/ =58 / = 1 :- / / =1 37 58 2 =37 116= 79 79 = 79 1 237 79

83 :- 249 83 : - :- : :- = 249 = 83 = 67= 49 =2+ = 49 + 2 = 51 =67 2 = 134 ( + ) = 134 51 =83 249 83

: :- = 249 = 166 = 49 = 2/ =66 / = 1 :- / / =1 49 66 2 =49 132 = 83 83 = 83 1 249 83

89 :- 623 89 : - :- : :- = 623 = 89 = 79= 23 =6+ = 23+ 6 = 29 =79 6 = 474 ( + ) = 474 29 =445 445 = 89 5 623 89

: :- = 623 = 178 = 23 = 6/ =78 / = 1 :- / / =1 23 78 6 =23 468 = 445 445 = 89 5 623 89

97 :- 679 97 : - :- : :- = 679 = 97= 95= 79 =6+ = 79 + 6 = 85 =95 6 = 570 ( + ) = 570 85 =485 485= 97 5 679 97

: :- = 679 = 194 = 79 = 6/ =94 / = 1 :- / / =1 79 94 6 =79 564 = 485 485 = 97 5 679 97

:- 100 . : 112 14 : - :- : :- = 112 / = 14 = 13= 12 =1+ = 12 + 1 = 13 =13 1= 13 ( + ) = 13 13 =0 112 14

: :- = 112 = 112 = 12 = 1/ =12 / = 1 :- / / =1 12 12 1 =12 12= 0 112 14

( ) (7 97) : :- 427 7 : ( (+) ) : = 427 = 7 = 6= 27 = 4 + = 27 + 4 = 31 = 6 4 = 24 (+) = 24 31 = 7 7 7 = 1

: 100 ( ) = 105 7 = 15 : ( ) :4 15 = 60

: : : > + . < + . = 60 = 1 ( < +) 60 (1)= 60 + 1 = 61 = 61

(1): 893 19 : = 893 = 19 = 15 = 93 = 8 + = 93 + 8 = 101 = 15 8 = 120 (+) = 120 101 = 19 19 19 = 1 893 19

: 19 100 = 114 = 114 19 = 6 = 8 6 = 48 = 1 = 48 1 = 47 893 19 = 47

(2): 946 43 : = 946 = 43 = 30 = 46 = 9 + = 46 + 9 = 55 = 30 9 = 270 (+) = 270 55 = 215 215 43 = 5 946 43

: 43 100 = 129 = 129 43 = 3 = 9 3= 27 = 5 = 27 5 = 22 946 43 = 22

(3): 8967 61 : = 8967 = 61 = 23 = 67 = 89 + = 67 + 89 = 156 = 23 89 = 2047 (+) = 2047 156 = 1891 1891 61 = 31 8967 61

: 61 100 = 122 = 122 61 = 2 = 89 2 = 178 = 31 = 178 31 = 147 8967 61 = 147

(4): 46689 79 : = 46689 = 79 = 59 = 89 = 466 + = 89 + 466 = 555 = 59 466 = 27494 (+) = 27494 555 = 26939 26939 79= 341 46689 79

: 79 100 = 158 = 158 79 = 2 = 466 2 = 932 = 341 = 932 341 = 591 46689 79=591

(5): 438572 83 : = 438572 = 83 = 67 = 72 = 4385 + = 72 + 4385 = 4457 = 67 4385 = 293795 (+) = 293795 4457 = 289338 289338 83 = 3486 438572 83

: 83 100 = 166 = 166 83 = 2 = 4385 2 = 8770 = 3486 = 8770 3486 = 5284 438572 83 = 5284

: 100 : 888 74 = 888 / = 74 = 49 = 88 = 8 + = 88 + 8 = 96 = 49 8 = 392 (+) = 392 96 = 296296 74 = 4 888 74

: 74 100 = 148 = 148 74 = 2 = 8 2 = 16 = 16 4 = 12 888 74 = 12