# 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.

- Think of a 3-digit number where not all the digits are the same.
- 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.
- Subtract the smaller number from the larger number.
- Go back to step 2.

If you repeat this process over and over again, you will end up with 495!

You don’t believe it? Let’s have 3 examples:

**Example 1**

- Our number is 592.
- Arranging it in descending and ascending number, we have 952 and 259.
- Subtracting 259 from 592 we get
**693**. - Repeating steps 2-3, we have 963 -369 =
**594** - Repeating steps 2-3 again, we have 954 – 459 =
**495** - Repeating steps 2-3 again, we have 954 – 459 =
**495**

Notice: If the difference contains the digits 9, 5, and 4, you will end up with 495 in each repitition.

**Example 2**

- Our number is 466
- Arranging in ascending and descending we have 664 and 466.
- Subtracting 466 from 664 we have
**198**. - Repeating steps 2-3, we have 981 – 189 =
**792**. - Repeating steps 2-3, we have 972 – 279 =
**693**. And this is the same as the number 3 in Example 1 above, which will end up in 495.

**Example 3**

- Let’s have 990.
- Arranging the digits in ascending and descending, we have 990 and 099 or simply 99.
- Subtracting, we have 990 – 99 =
**891**. - Repeating steps 2-3, we have 981 – 189 =
**792**. And this is the same as difference in Example 2 step 4. This means that it will also end up in 495!

The number 495 is the Kaprekar constant for three digit numbers. Yes, if you choose any 3-digit number, you will end up in 495 (try other numbers). The more famous Kaprekar constant is 6174 for 4-digit numbers.

In the next post, we are going to investigate the mystery behind 495.