The mystery of 495 explained

In yesterday’s post, we chose a three digit positive integer and we arranged the digits in ascending and descending order forming the largest and the smallest integer that can be formed using the three digits. We subtracted the smaller integer from the larger, and repeated the process several times. We  ended up with 495. We tried other integers and repeated the process, and they all ended up with 495.  In this post, we are going to discuss the reason behind our observation.

Let’s take the first example in yesterday’s post. We chose 592. Arranging the numbers in descending and ascending order, we got 259 and 952. Subtracting the numbers, we got 693.

Let us examine closely what happens when we subtract the numbers with rearranged digits (examine the figure above): » Read more