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Stat 155: solutions to midterm examMichael LugoOctober 21, 20101. We have a board consisting of infinitely many squares labeled 0,1,2,3, . . .from leftto right. Finitely many counters are placed on these squares. A game is played, in which amove consists of one player moving a counter to the left, subject to the following rules:•no counter can jump over another counter;•it is not allowed to have two or more counters on the same square.The last player who is able to move wins.Say we have counters at positions 5, 8, 11, 15, and 22, as illustrated below.Find allwinning moves.••••1