In the mysterious 495, (1) we chose any 3-digit number, (2) arranged the digits in decreasing order forming the largest integer, (3) arranged the digit in increasing order forming the smallest integer, and (4) subtracted the smaller from the larger. Each time a difference is obtained, we repeated steps 2-4 several times and we ended up having 495. We explained the mystery behind this ‘phenomenon’ and we were quite fascinated.
In this post, we examine the 4-digit Kaprekar constant. That is, if the digits of a 4-digit number are not all equal, there is a certain number that we will end up with if we repeat the enumerated process above. Let’s have an example. Continue reading
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): Continue reading
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! Continue reading