3 ms·
Kaprekar's Magic 6174
- ur-whale 2y agoNo attempts at generalization to larger numbers of digits?
- dmichulke 2y agoFrom https://en.wikipedia.org/wiki/D._R._Kaprekar https://en.wikipedia.org/wiki/D._R._Kaprekar A similar constant for 3 digits is 495.[7] However, in base 10 a single such constant only exists for numbers of 3 or 4 digits; for other digit lengths or bases other than 10, the Kaprekar's routine algorithm described above may in general terminate in multiple different constants or repeated cycles, depending on the starting value
- hiperlink 2y agoPrevious discussion: https://news.ycombinator.com/item?id=39018769 https://news.ycombinator.com/item?id=39018769
- dash2 2y agoSort the digits to 'wxyz', where each letter is a 0-9 digit. 'wxyz' - 'zyxw' = 999(w - z) + 90(x - y) w - z is between 1 and 9, since w > z (we have ruled out numbers like 1111). x - y is between 0 and 9. So there are at most 90 such numbers. In fact there are fewer because x-y <= w-z. This is why there are many collisions in the first step.
- dimastopel 2y agoNumberphile video on the topic: https://youtu.be/d8TRcZklX_Q?si=t9x2HLWYOpPiTbn4 https://youtu.be/d8TRcZklX_Q?si=t9x2HLWYOpPiTbn4
- pierrebai 2y agoInterestingly, there is a common pattern for fixed-points and cycles for different number lengths: numbers made of 4, 5 and 9. For example length 3: fixed-point 495 length 5: 2-cycle containing 59994 length 6: fixed-point 59994 Similarly for digits 6, 1, 4, 7: length 4: 6174 length 5: 4-cycle containing 61974 length 6: fixed-point 631764