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DE-BUNDESWETTBEWERB 2000 Problem 1

  • Round 1

Two natural numbers have the same decimal digits in different order and have the sum 999⋯999999\cdots 999 . Is this possible when each of the numbers consists of 20002000 digits?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Bundeswettbewerb Mathematik 2000 official paper, page 1.

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