I have been looking into the proof behind why 6174 is the unique 4 digit number that has the property that the difference between the digits arranged in ascending and descending order is the same number, however I cannot get my head around proofs that show that the rest of 4 digit numbers may converge to that value - why can we not get stuck in a recurring cycle for example? A lot of the literature I came across online seems very much to be proof by exhaustion as there is only a finite number of cases, but does anyone have a more elegant proof?
2026-05-14 13:20:17.1778764817
Convergence of Kaprekar's constant
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