Tuesday, 12 May 2020

There is always 6174

Starting with any four digit number (that has at least two different digits) just follow the following steps:

  1. Arrange the digits of the four digit number in descending/ascending order to make the largest and smallest numbers possible.
  2. Subtract the smaller number from the larger one.
  3. Take the answer and repeat the process.
Eventually you'll end up at 6174
it never takes more than seven stages to get there.

example:

Picking a number at random, 
let's try 4551,
Stage 1: 5541-1455 = 4086
Stage 2: 8640 - 0468 = 8172
Stage 3: 8721 - 1278 = 7443
Stage 4: 7443 - 3447 = 3996
Stage 5: 9963 - 3699 = 6264
Stage 6: 6642 - 2466 = 4176
Stage 7: 7641 - 1467 = 6174
Here the number "6174" is known as 'Kaprekar's Constant'

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