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interesting combinatorics EGMO P5

Source: EGMO 2015, Problem 5

April 17, 2015
combinatoricsEGMOgameEGMO 2015Hi

Problem Statement

Let m,nm, n be positive integers with m>1m > 1. Anastasia partitions the integers 1,2,…,2m1, 2, \dots , 2m into mm pairs. Boris then chooses one integer from each pair and finds the sum of these chosen integers. Prove that Anastasia can select the pairs so that Boris cannot make his sum equal to nn.
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