Starting with any four digit number (that has at least two different digits) just follow the following steps:
- Arrange the digits of the four digit number in descending/ascending order to make the largest and smallest numbers possible.
- Subtract the smaller number from the larger one.
- 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
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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