David Gale's Mathematical Entertainments columns in the Mathematical Intelligencer, a prime source of entertainment for everyone with an interest in mathematics, are here collected in book form for the first time. Gale has ranged widely over the entire field of mathematics yet returns often to favorite concerns: triangles, tilings, the mysterious properties of sequences given by simple recursions, and the peculiar automaton that gives this collection its title. This book requires some familiarity with mathematical concepts but not great sophistication.

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