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PAMO 2004 Problem 5

  • Day 2

Each of the digits 11 , 33 , 77 and 99 occurs at least once in the decimal representation of some positive integers. Prove that one can permute the digits of this integer such that the resulting integer is divisible by 77 .

Dataset text AI-MO AoPS. Quoted with source.

Official text: Pan-African Mathematics Olympiad 2004 official paper, page 1.

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