Take one, three or four
A pile holds 20 stones. On a turn a player removes 1, 3 or 4 stones (never 2). The player who takes the last stone wins.
Who wins from 20 with best play, and what is the winning first move? Find the pattern of losing positions and explain why it repeats.
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Work upwards from 0, marking each pile size as losing or winning. Look for a repeating block.
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