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 :
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 mathematical trick and discover why all the 4-digit numbers on subtracting using the Kaprekar operation reach the mysterious number 6174.
