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Parity of the sum of randomly chosen integers

Source: Kürschák 1986, problem 3

July 27, 2014
functionmodular arithmeticalgebrabinomial theoremcombinatorics unsolvedcombinatorics

Problem Statement

A and B plays the following game: they choose randomly kk integers from {1,2,…,100}\{1,2,\dots,100\}; if their sum is even, A wins, else B wins. For what values of kk does A and B have the same chance of winning?
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