神奇的6174

6174 初看一点也不起眼，也许你会问它有什么神秘的呢？

我们先进行一番计算，选择一个4位数，每位上的数都不能相同（也就是不能是1111，2222，3333，4444..），

例如选择2009（今年年份），先对这个数上的每位数字重新洗一下，得到最大的数是9200，最小的数是0029，两者相减，对结果再按照上述规则继续下去

9200— 0029=9171

9711—1179= 8532

8532—2358= 6174

7641—1467= 6174

.........
现在我们再随机选一个数：比如1234，那么

4321—1234 =3087

8730—0378= 8352

后面就不用再算了。6174这个数就是印度数学家Dattaraya Ramchandra Kaprekar发现的Kaprekar常数——任何4位数，你都可以在7步内计算得到6174（如果没得到，肯定算错了；-)）。

其它位数有的也有相应的Kaprekar常数

2（位数） 无
3 495
4 6174
5 无
6 549945, 631764
7 无
8 63317664, 97508421
9 554999445, 864197532
10 6333176664, 9753086421, 9975084201

Kaprekar还发现过很多奇异的Kaprekar数（平方后，按位数相加得到原数），如下：

9^2 = 81 ... 8+1 = 9

45^2 = 2025 ... 20+25 = 45

55^2 = 3025 ... 30+25 = 55

99^2 = 9801 ... 98+01 = 99

703^2 = 494209 ... 494+209 = 703

999^2 = 998001 ... 998+001 = 999

2728^2 = 7441984 ... 744+1984 = 2728

4950^2 = 24502500 ... 2450+2500 = 4950

5050^2 = 25502500 ... 2550+2500 = 5050

7272^2 = 52881984 ... 5288+1984 = 7272

7777^2 = 60481729 ... 6048+1729 = 7777

9999^2 = 99980001 ... 9998+0001 = 9999

17344^2 = 300814336 ... 3008+14336 = 17344

22222^2 = 493817284 ... 4938+17284 = 22222

77778^2 = 6049417284 ... 60494+17284 = 77778

82656^2 = 6832014336 ... 68320+14336 = 82656

95121^2 = 9048004641 ... 90480+04641 = 95121

99999^2 = 9999800001 ... 99998+00001 = 99999

187110^2 = 35010152100 ... 35010+152100 = 187110

318682^2 = 101558217124 ... 101558+217124 = 318682

329967^2 = 108878221089 ... 108878+221089 = 329967

351352^2 = 123448227904 ... 123448+227904 = 351352

356643^2 = 127194229449 ... 127194+229449 = 356643

390313^2 = 152344237969 ... 152344+237969 = 390313

461539^2 = 213018248521 ... 213018+248521 = 461539

466830^2 = 217930248900 ... 217930+248900 = 466830

499500^2 = 249500250000 ... 249500+250000 = 499500

500500^2 = 250500250000 ... 250500+250000 = 500500

533170^2 = 284270248900 ... 284270+248900 = 533170

538461^2 = 289940248521 ... 289940+248521 = 538461

609687^2 = 371718237969 ... 371718+237969 = 609687

643357^2 = 413908229449 ... 413908+229449 = 643357

648648^2 = 420744227904 ... 420744+227904 = 648648

670033^2 = 448944221089 ... 448944+221089 = 670033

681318^2 = 464194217124 ... 464194+217124 = 681318

791505^2 = 626480165025 ... 626480+165025 = 791505

812890^2 = 660790152100 ... 660790+152100 = 812890

818181^2 = 669420148761 ... 669420+148761 = 818181

851851^2 = 725650126201 ... 725650+126201 = 851851

857143^2 = 734694122449 ... 734694+122449 = 857143

961038^2 = 923594037444 ... 923594+037444 = 961038

994708^2 = 989444005264 ... 989444+005264 = 994708

999999^2 = 999998000001 ... 999998+000001 = 999999

摘自格致