Consider this variation of the game of Nim. The game
Chapter 5, Problem 11E(choose chapter or problem)
Consider this variation of the game of Nim. The game begins with n matches. Two players take turns removing matches, one, two. or three at a time. The player removing the last match loses. Use strong induction to show that if each player plays the best strategy possible, the first player wins if n = 4 j, 4j + 2, or 4j + 3 for some nonnegative integer j and the second player wins in the remaining case when n = 4j + 1 for some nonnegative integer j.
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