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有趣的数学现象

 xwlr 2007-08-21

1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
123456 × 8 + 6 = 987654
1234567 × 8 + 7 = 9876543
12345678 × 8 + 8 = 98765432
123456789 × 8 + 9 = 987654321

1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = 111111
123456 × 9 + 7 = 1111111
1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111
123456789 × 9 + 10 = 1111111111

1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321
11111 × 11111 = 123454321
111111 × 111111 = 12345654321
1111111 × 1111111 = 1234567654321
11111111 × 11111111 = 123456787654321
111111111 × 111111111 = 12345678987654321

9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 × 9 + 4 = 88888
98765 × 9 + 3 = 888888
987654 × 9 + 2 = 8888888
9876543 × 9 + 1 = 88888888
98765432 × 9 + 0 = 888888888

12345679 × 9  (9×1) = 111111111
12345679 × 18 (9×2) = 222222222
12345679 × 27 (9×3) = 333333333
12345679 × 36 (9×4) = 444444444
12345679 × 45 (9×5) = 555555555
12345679 × 54 (9×6) = 666666666
12345679 × 63 (9×7) = 777777777
12345679 × 72 (9×8) = 888888888
12345679 × 81 (9×9) = 999999999

9 × 1  = 9   | 9 + 0 = 0
9 × 2  = 18  | 1 + 8 = 9
9 × 3  = 27  | 2 + 7 = 9
9 × 4  = 36  | 3 + 6 = 9
9 × 5  = 45  | 4 + 5 = 9
9 × 6  = 54  | 5 + 4 = 9
9 × 7  = 63  | 6 + 3 = 9
9 × 8  = 72  | 7 + 2 = 9
9 × 9  = 81  | 8 + 1 = 9
9 × 10 = 90  | 9 + 0 = 9

1 = 1^2
1 + 3 = 4 = 2^2
1 + 3 + 5 = 9 = 3^2
1 + 3 + 5 + 7 = 16 = 4^2
1 + 3 + 5 + 7 + 9 = 25 = 5^2
1 + 3 + 5 + 7 + 9 + 11 = 36 = 6^2
1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7^2

142857·1 = 142857
142857·2 = 285714
142857·3 = 428571
142857·4 = 571428
142857·5 = 714285
142857·6 = 857142

142 + 857 = 999
285 + 714 = 999
428 + 571 = 999
571 + 428 = 999
714 + 285 = 999
857 + 142 = 999

14 + 28 + 57 = 99
28 + 57 + 14 = 99
42 + 85 + 71 = 99 + 99
57 + 14 + 28 = 99
71 + 42 + 85 = 99 + 99
85 + 71 + 42 = 99 + 99

1·7 + 3 = 10
14·7 + 2 = 100
142·7 + 6 = 1000
1428·7 + 4 = 10000
14285·7 + 5 = 100000
142857·7 + 1 = 1000000
1428571·7 + 3 = 10000000
14285714·7 + 2 = 100000000
142857142·7 + 6 = 1000000000
1428571428·7 + 4 = 10000000000
14285714285·7 + 5 = 100000000000
142857142857·7 + 1 = 1000000000000
1428571428571·7 + 3 = 10000000000000
14285714285714·7 + 2 = 100000000000000
142857142857142·7 + 6 = 1000000000000000
1428571428571428·7 + 4 = 10000000000000000
14285714285714285·7 + 5 = 100000000000000000
142857142857142857·7 + 1 = 1000000000000000000

3 2 6 + 4 5 1 = 7 7 7
2 6 4 + 5 1 3 = 7 7 7
6 4 5 + 1 3 2 = 7 7 7
+ + + + + +
4 5 1 + 3 2 6 = 7 7 7
5 1 3 + 2 6 4 = 7 7 7
1 3 2 + 6 4 5 = 7 7 7

3 2 6 + 4 5 1 = 7 7 7
2 6 4 + 5 1 3 = 7 7 7
6 4 5 + 1 3 2 = 7 7 7
+ + + + + +
4 5 1 + 3 2 6 = 7 7 7
5 1 3 + 2 6 4 = 7 7 7
1 3 2 + 6 4 5 = 7 7 7
= = = =
7 7 7 7 7 7
7 7 7 7 7 7
7 7 7 7 7 7

12345679×12=148148148
12345679×15=185185185
12345679×57=703703703

12345679×10=123456790 lose 8
12345679×11=135802469 lose 7
12345679×13=160493827 lose 5
12345679×14=172839506 lose 4
12345679×16=197530864 lose 2
12345679×17=209876543 lose 1

12345679×243=2999999997 2+7=9

12345679×28=345679012
12345679×37=456790123

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