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IMO 1989 Problem 1

  • Day 1

Prove that in the set {1,2,…,1989}\{1,2, \ldots, 1989\} can be expressed as the disjoint union of subsets Ai,{i=1,2,…,117}A_i, \{i = 1,2, \ldots, 117\} such that

i.) each AiA_i contains 17 elements

ii.) the sum of all the elements in each AiA_i is the same.

Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.

Official text: IMO 1989 official English paper, page 1.

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