The Beans Game

[From the notes of Emily Moore with modifications by Samuel A. Rebelsky.]

We start with 17 beans in a pile. Two players alternate, each removing 1, 2, 3, or 4 beans in a turn. The player who removes the last bean wins. What strategy should the first player use to guarantee that (s)he will win? Will this strategy work for other size piles? Are there any size piles for which the second player has a winning strategy?

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