Tag: kaprekar constant 6174

The Kaprekar constant 6174

High School Mathematics, High School Number Theory

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. » Read more

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The mysterious number 495

High School Mathematics, High School Number Theory, Number Theory
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
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