Kaprekar's Process on 5 Digit Number/Mistake

Source Work

 * The Dictionary
 * $99,954$
 * $99,954$


 * The Dictionary
 * $99,954$
 * $99,954$

Mistake

 * Kaprekar's process for all $5$-digit numbers whose digits are not all equal leads to one of $3$ separate cycles. The smallest cycle is $99,954 - 95,553$. The other two cycles are $98,532 - 97,443 - 96,642 - 97,731$ and $98,622 - 97,533 - 96,543 - 97,641$.

Correction
Those are not the numbers in the cycles themselves, but those after arranging them in descending order of their digits.

The cycles themselves are:


 * $53 \, 955 \to 59 \, 994 \to 53 \, 955$


 * $61 \, 974 \to 82 \, 962 \to 75 \, 933 \to 63 \, 954 \to 61 \, 974$


 * $62 \, 964 \to 71 \, 973 \to 83 \, 952 \to 74 \, 943 \to 62 \, 964$