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A,B subsets of 1-n |A|+|b|> n-

Source: 1953 Hungary - Kürschák Competition p1

October 10, 2022
combinatoricsSubsets

Problem Statement

AA and BB are any two subsets of {1,2,...,n−1}\{1, 2,...,n - 1\} such that ∣A∣+∣B∣>n−1|A| +|B|> n - 1. Prove that one can find aa in AA and bb in BB such that a+b=na + b = n.
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