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P4 Cono Sur 2021

Source: Cono Sur 2021 P4

November 30, 2021
combinatoricsCombinatorial games

Problem Statement

In a heap there are 20212021 stones. Two players AA and BB play removing stones of the pile, alternately starting with AA. A valid move for AA consists of remove 1,21, 2 or 77 stones. A valid move for B is to remove 1,3,41, 3, 4 or 66 stones. The player who leaves the pile empty after making a valid move wins. Determine if some of the players have a winning strategy. If such a strategy exists, explain it.