# Kaprekar's Process on 3 Digit Number ends in 495/Mistake

## Source Work

The Dictionary
$495$

## Mistake

Take any $3$-digit number whose digits are not all the same and is not a palindrome. Arrange its digits into ascending and descending order and subtract. Repeat. This is called Kaprekar's process. All $3$-digit numbers eventually end up with $495$.

The $3$-digit number in question needs only to have its digits not all the same. A palindrome ends up at $495$ in the same way as any other number, for example:

 $\ds 191$ $\to$ $\ds 911 - 119$ $\ds$ $\to$ $\ds 792$ $\ds$ $\to$ $\ds 972 - 279$ $\ds$ $\to$ $\ds 693$ $\ds$ $\to$ $\ds 963 - 369$ $\ds$ $\to$ $\ds 594$ $\ds$ $\to$ $\ds 954 - 459$ $\ds$ $\to$ $\ds 495$