Modified Kaprekar Process on 4-Digit Number terminates in 2538

Theorem

Let $n$ be a $4$-digit number.

Let $n$ be operated on by the modified Kaprekar process.

The eventual result is always $2538$.

Proof

This theorem requires a proof. In particular: I find these processes dull. Does anyone else want to go into a detailed analysis of this and other similar? You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Historical Note

This result is reported by David Wells in his $1997$ work Curious and Interesting Numbers, 2nd ed. to appear in volume $22$ Journal of Recreational Mathematics on page $34$ in an article authored by Charles Wilderman Trigg, but this has not been corroborated.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2538$