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I remember when I was a small child, I read about the Problem of 6174 that if we follow the algorithm of abstract any number and its reverse several times, then we must reach a invariant number 6174 at some step. I also read that this problem was unsolved. But time has flew by. So is there any solution to this problem now?

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6174 tells me Kaprekar's constant but I don't see unsolved connections?? Perhaps, I am wrong too. – user21436 Feb 26 '12 at 1:04
According to Wikipedia, this only pertains to four-digit numbers, so of course it's been solved (and WP even has a couple graphics illustrating the solutions). Am I not aware of something here? – anon Feb 26 '12 at 1:30
up vote 4 down vote accepted

Here is the relevant Wikipedia article, referenced in the comments.

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.

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