Poison is played on a board with n ≥ 1 non-overlapping circles. The two players take turns marking one or two unmarked circles. The player who marks the last circle loses. Determine for each value of...

Poison is played on a board with n ≥ 1 non-overlapping circles. The two players take turns marking one or two unmarked circles. The player who marks the last circle loses. Determine for each value of n which player has a winning strategy and describe the winning strategy. Hint: Start by examining small values of n and then generalize.