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Why does this digit trick keep landing on 6174?

Choose four decimal digits that are not all the same. Arrange them to make the largest and smallest four-position numbers, subtract, and repeat, keeping any leading zeros. The result keeps arriving at 6174, where the next subtraction returns the same number. A rigid digit rule produces a surprisingly dependable destination.

3–7 min

Questions you could explore

  • Why does dropping a leading zero change the procedure?
  • What happens when the starting digits are all identical?

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