Kaprekar Number 6174 Theory

The number 6174 is the only unchanged mysterious number discovered by Kaprekar's operation. Discover the mystery behind the 6174 loop by using any four digit number.

Rules

   Step 1  

Select any four digit number, but do not select the ones in which all the four

  digits are the same like 1111, 2222, ...  

   Step 2  

Arrange the digits in decreasing order. 

   Step 3  

Arrange the digits in increasing order. 

   Step 4  

Subtract the smaller number from the larger number. 

   Step 5  

Repeat the steps 2, 3 and 4 until you get 6174 in repetition. 

Example

  Step : 1 ==> 4 digit number is 5620. 

  Step : 2 ==> Arrange decreasing order : 6520 

  Step : 3 ==> Arrange increasing order : 0256 

  Step : 4 ==> Subtract the smaller number from the larger number : 

       6520 - 0256 = 6264 

  Step : 5 ==> Take the final result and repeat the steps 2, 3, and 4 until

you get the repetition of 6174. 

  Like,

6264 = 6642 - 2466 = 4176 

  4176 = 7641 - 1467 = 6174 

6174 = 7641 - 1467 = 6174 

Have fun with this math trick and discover why all the 4 digit numbers on subtracting using the kaprekar operation reach to the mysterious number 6174.