Let n be a natural number. Let's take the following 2 player game. We have .n matches. Player 1 takes one or two matches from the pile, then as long as there are still matches, player 2 takes one or two matches, and so on, alternating until there are no more matches left. The player who takes the last match loses. The losing player gets a benefit of -1 and the other player gets a benefit of 1. Represent this game for n=2 ,n=3 and n=4 and say how many strategies each player has.

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