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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $99,954$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $99,954$