- , , . , . ( , ).
, ! , . !
1.
: 11. , .
: 32 × 11.
3 + 2 = 5, . : 352. ?
53 × 11.
5 + 3 = 8, : 583.
. , , : 81 × 11? 891? !
: , . , : 85 × 11
8 + 5 = 13, 8135! 3 8 5, 1 8 935.
. 57 × 11. 5 + 7 = 12, : 627
( ) 11? . , 314 × 11 3 4. 3 + 1 = 4 1 + 4 = 5, 3454.
2. ( )
, , , , . , 7 7 × 7, 49. , ( ) .
, 5. .
1. , , .
2. 25.
, 35, (3)
4, , 25. 3 × 4 = 12, , 1225. , 35 × 35 = 1225. : 35 × 35
3 × 4 = 12
5 × 5 = 25
: 1225
85? 8 × 9 = 72, : 85 × 85 = 7225.
, , 10. , ( , ), , . , 83 87. ( 8, 3 + 7 = 10.) 8 × 9 = 72 3 × 7 = 21, 7221.
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84 × 86 = 7224.
. 26 × 24. ? 2 × 3 = 6. ? 6 × 4 = 24. , 26 × 24 = 624. , , , 10.
3. 1 XXI
.
1
2
3
4
5
6
7 0
, , 1 2030 . , ( 30 .) 25% , . ( , . 30 15, 15 7,50. , 7 .) , 37 . , ( ) 7 (0, 7, 14, 21, 28, 35, 42, 49, ) . , 37 35 = 2, , 1 2030 , .
1 2043 ?
: 43
: + 10 = 53
7: 49
4 =
: , 1 , . , 1 2032 25% 32 8 . 1 32 + 7 = 39. 7 39 35 = 4. , 1 2032 , .
4.
, - . , , , .
1. .
2. 12.
3. 2.
4. .
: " 6? , 6, . (, 18). ( 9).
5. 1089
. , :
1) , (, 851 973);
2) ;
3) , .
1089, . : 851 158 693 + 396 = 1089
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1089 , 1089 , . (, 1089 × 256 = 278 784) , . 6.
: . . , : . , 7. , 9 , , 9. 1 + 0 + 8 + 9 = 18 9, , 1089 9. 1089 9. 29, 9, 29, 36, 7 ( 29 + 7 = 36).
6.
- , . , , . , 68, 68 × 68 × 68 = 314 432 . , 68. ?
, 1 10.
13 = 1
23= 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
, , π. . 314 432? , , , . , .
1. , 314 .
2. 314 63 = 216 73 = 343, 60 ( 603 = 216 000 703 = 343 000). , 6.
3. , 8 2 (83 = 512), 8. 314 432 68. . , 0 9 . 19 683?
1. 19 8 27 (23 33).
2. , 20 .
3. 3, 343 = 73, , 7 .
: 27.
, , .
7.
, . , - , 7569, , ( ) 87.
.
1. (, ) .
2. 75 82 (8 × 8 = 64) 92 (9 × 9 = 81), , - 80 . , 8.
, 9: 32 = 9, 72 = 49. 3 7. , 83, 87. ?
3. 85 ( 80 × 9 0 + 25 = 7225). 7569 , 7225, , 87. . 4761? 47 62 = 36 72 = 49, 60 . 1, 1 9. 4761 652 = 4225, 69. , , .
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, . ? , , , ! , , . , . , , . !