Kaprekar's Process on 5 Digit Number/Mistake

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Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary
$99,954$


1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$99,954$


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:

$53 \, 955 \to 59 \, 994 \to 53 \, 955$
$61 \, 974 \to 82 \, 962 \to 75 \, 933 \to 63 \, 954 \to 61 \, 974$
$62 \, 964 \to 71 \, 973 \to 83 \, 952 \to 74 \, 943 \to 62 \, 964$


Sources