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The four-digit subtraction routine that reaches 6174

Choose four decimal digits that are not all identical. Arrange them into the largest and smallest four-position numbers, subtract, and repeat, keeping leading zeros. The routine reaches 6174, where the next subtraction returns the same number.

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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