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缺8数

来自维基学院

缺8数(12345679)

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为什么会少了个8

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  • 假如123456789 x 9 = 1111111111并不是非常有趣的。
  • 事实上十进制中123456789 x 9 = 1111111101 , 偏偏有一位是0 。
  • 奇怪在于去除了8 , 又得了12345679 x 9 = 111111111 。
  • 123456789 x 9 + 9 = 1111111110
  • 123456790 x 9 = 1111111110
  • 12345679 x 9 = 111111111

缺8数的奇妙乘法性质

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数字轮流休息(一)

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12345679 x 1 = 12345679 (缺8)

12345679 x 2 = 24691358 (缺7)

12345679 x 4 = 49382716 (缺5)

12345679 x 5 = 61728395 (缺4)

12345679 x 7 = 86419753 (缺2)

12345679 x 8 = 98765432 (缺1)

数字轮流休息(二)

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12345679 x 1 = 12345679

12345679 x 10 = 123456790

12345679 x 19 = 234567901

12345679 x 28 = 345679012

12345679 x 37 = 456790123

12345679 x 46 = 567901234

12345679 x 55 = 679012345

12345679 x 64 = 790123456

12345679 x 73 = 901234567

12345679 x 2 = 24691358

12345679 x 11 = 135802469

12345679 x 20 = 246913580

12345679 x 29 = 358024691

12345679 x 38 = 469135802

12345679 x 47 = 580246913

12345679 x 56 = 691358024

12345679 x 65 = 802469135

12345679 x 74 = 913580246

12345679 x 4 = 49382716

12345679 x 13 = 160493827

12345679 x 22 = 271604938

12345679 x 31 = 382716049

12345679 x 40 = 493827160

12345679 x 49 = 604938271

12345679 x 58 = 716049382

12345679 x 67 = 827160493

12345679 x 76 = 938271604

12345679 x 5 = 61728395

12345679 x 14 = 172839506

12345679 x 23 = 283950617

12345679 x 32 = 395061728

12345679 x 41 = 506172839

12345679 x 50 = 617283950

12345679 x 59 = 728395061

12345679 x 68 = 839506172

12345679 x 77 = 950617283

12345679 x 7 = 86419753

12345679 x 16 = 197530864

12345679 x 25 = 308641975

12345679 x 34 = 419753086

12345679 x 43 = 530864197

12345679 x 52 = 641975308

12345679 x 61 = 753086419

12345679 x 70 = 864197530

12345679 x 79 = 975308641

12345679 x 8 = 98765432

12345679 x 17 = 209876543

12345679 x 26 = 320987654

12345679 x 35 = 432098765

12345679 x 44 = 543209876

12345679 x 53 = 654320987

12345679 x 62 = 765432098

12345679 x 71 = 876543209

12345679 x 80 = 987654320

三位数重复三次

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12345679 x 3 = 37037037

12345679 x 6 = 74074074

12345679 x 9 = 111111111

12345679 x 12 = 148148148

12345679 x 15 = 185185185

12345679 x 18 = 222222222

12345679 x 21 = 259259259

12345679 x 24 = 296296296

12345679 x 27 = 333333333

12345679 x 30 = 370370370

12345679 x 33 = 407407407

12345679 x 36 = 444444444

12345679 x 39 = 481481481

12345679 x 42 = 518518518

12345679 x 45 = 555555555

12345679 x 48 = 592592592

12345679 x 51 = 629629629

12345679 x 54 = 666666666

12345679 x 57 = 703703703

12345679 x 60 = 740740740

12345679 x 63 = 777777777

12345679 x 66 = 814814814

12345679 x 69 = 851851851

12345679 x 72 = 888888888

12345679 x 75 = 925925925

12345679 x 78 = 962962962

12345679 x 81 = 999999999

纯位数

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12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

阶梯上升的金字塔

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12345679 x 9 = 111111111

12345679 x 99 = 1222222221

12345679 x 999 = 12333333321

12345679 x 9999 = 123444444321

12345679 x 99999 = 1234555554321

12345679 x 999999 = 12345666654321

12345679 x 9999999 = 123456777654321

12345679 x 99999999 = 1234567887654321

12345679 x 999999999 = 12345678987654321

  • 右边是回文数 , 左右两边对称部分形成上升的金字塔 ; 中间重复的数字下降 。

缺8数与循环小数1/81有关

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1/81 = 0.(012345679)

  • 1/81循环节九位数字012345679。

n/81的循环小数表示

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1/81 = 0.(012345679)

3/81 = 0.(037)

9/81 = 0.(1)

27/81 = 0.(3)