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2021年6月26日 · Kaprekar's constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174. 6174 is known as Kaprekar's constant after the Indian mathematician ...
四位数数学黑洞. 四位数数字黑洞就是著名的卡不列克常数6174，因为画图的时候6174、7164、4617...等都是等价的，所以直接使用1467替代。. 在四位数的王国中，1467一枝独秀，是当之无愧的王。. 这是一个大一统的国家，他们实行三权分立制度，2358枝繁叶茂，2466次 ...
2015年6月14日 · $\begingroup$ @Mythomorphic If you are still a fan of $6174$ you may take a look at a fresh answer to a Kaprekar question which is quite parallel to yours. $\endgroup$ – Hanno Commented Nov 2, 2020 at 6:27
How to prove that by performing Kaprekar's routine on any 4-digit number repeatedly, and eventually we will get the 4-digit constant $6174$ rather than get stuck in a loop, without really calculating
2012年8月12日 · Kaprekar discovered the Kaprekar constant or 6174 6174 in 1949 1949. He showed that 6174 6174 is reached in the limit as one repeatedly subtracts the highest and lowest numbers that can be constructed from a set of four digits that are not all identical. e.g. starting with 1234 1234, we have 4321 − 1234 4321 − 1234 = 3087 3087, then 8730 ...
观察发现， 6174 是 f 的一个不动点（即： f 作用于其上，相当于没有作用）。通过枚举法可得：它是该函数唯一的不动点。所以，所谓“黑洞数”无非是说： \forall x \in S: f \circ f \circ \cdots \circ f(x) = 6174 即 f 迭代7次以内，函数值收敛至 f 的不动点。
2014年7月26日 · Clearly the only value for which this process is constant is 6174 but that doesn't explain why there should be convergence. One attempt at proof is to determine all the possible numbers that converge to 6174 after a single iteration, and then attempt to reason that each too can be reached by the convergence of even more numbers in such a way ...
2003年7月24日 · 数学黑洞6174 (求证) 已知一个任意的四位正整数，将数字组合成一个最大的数和最小的数相减，重复这个过程，最多七步必得6174，即7641-1467=6174将永远出不来。. 求证：所有四位数字（相同的除外）均能得到6174输出掉进黑洞的步数。.
2013年6月22日 · 关于C语言“6174问题”，请教各位前辈. 假设你有一个各位数字互不相同的四位数，把所有的数字从大到小排序后得到a,从小到大后得到b,然后用a-b替换原来这个数，并且继续操作。. 例如，从1234出发，依次可以得到4321-1234=3087、8730-378=8352、8532-2358=6174，又回到了它 ...
2012年2月26日 · The problem is "solved" in the sense that it is easy to check (using a computer) that all 4-digit numbers except repdigits do end up at 6174. On the other hand, it doesn't seem that there is any more satisfying and principled explanation of why this process should end up at the same fixpoint, when this is not the case for 5-digit numbers.
