The magic number 6174
Take 5683. Make the biggest number and the smallest.
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The rule
Make the biggest and smallest number from the digits. Keep all four digits, so the smallest may start with 0. Subtract the smallest from the biggest. Repeat with the answer.
Four digits that are not all the same end at 6174.
Doing these steps once is one round. Kaprekar constant — the number 6174, where these rounds end.
Example
Start with 2012. Each round uses the digits of the last answer.
- Round 1: 2210 − 0122 = 2088.
- Round 2: 8820 − 0288 = 8532.
- Round 3: 8532 − 2358 = 6174.
That is 3 rounds. 5683 takes 7 rounds.
Three digits work the same way. If they are not all the same, they end at 495.
Watch out!
A round can give fewer than four digits. 1000 − 0001 = 999. Write it as 0999 and continue.