## 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

## The mysterious number 495

There are certain numbers that have certain characteristics.   Until now, many of these numbers become source of fascinations of mathematicians and non-mathematicians alike. Many mathematicians have spent their entire lives solving the mysteries of some numbers.  In this post, we are going to talk about the mysterious number 495.
Let’s have  a game.
1. Think of a 3-digit number where not all the digits are the same.
2. Arrange the digits in descending order and ascending order from left to right. This will give you two 3-digit numbers — one the smallest number that you an form from the digits, and the other the largest.
3. Subtract the smaller number from the larger number.
4. Go back to step 2.
If you repeat this process over and over again, you will end up with 495! » Read more