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A row of ten counters

gamessymmetrystrategy

Ten counters lie in a straight row. Two players take turns removing either one counter or two adjacent counters (adjacent meaning side by side with no gap). Removed counters leave gaps; the remaining counters do not slide together. Whoever removes the last counter wins.

Which player wins with best play? Give the winning first move and the rule for every later move. What changes with eleven counters?

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Try to make the position symmetric, so that you can always copy your opponent.

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Ants on a Pole and Collision ArgumentsBurnside's Lemma and Polya CountingChoosing Coordinates That Kill the ProblemSymmetry Shortcuts for Draws Without ReplacementGame Theory Basics

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