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Four heaps of matches two-player games

Source: Baltic Way 1996 Q19

March 19, 2011
combinatorics proposedcombinatorics

Problem Statement

Four heaps contain 38,45,6138,45,61 and 7070 matches respectively. Two players take turn choosing any two of the heaps and take some non-zero number of matches from one heap and some non-zero number of matches from the other heap. The player who cannot make a move, loses. Which one of the players has a winning strategy ?
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