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2013 ToT Fall Junior A p7 game with 11 piles of ten stones each

Source:

March 22, 2020
game strategygameHi

Problem Statement

On a table, there are 1111 piles of ten stones each. Pete and Basil play the following game. In turns they take 1,21, 2 or 33 stones at a time: Pete takes stones from any single pile while Basil takes stones from different piles but no more than one from each. Pete moves fi rst. The player who cannot move, loses. Which of the players, Pete or Basil, has a winning strategy?