High Quality Content by WIKIPEDIA articles! Sylver Coinage is a mathematical game for two players, invented by John H. Conway. It is discussed in Winning Ways for your Mathematical Plays.The two players take it in turn to name a positive integer that is not the sum of multiples of previously named integers. After 1 is named, all positive integers can be expressed in this way: 1 = 1, 2 = 1 + 1, 3 = 1 + 1 + 1, etc., ending the game. The player who named 1 loses. This makes Sylver Coinage a misere game, since by the usual convention in combinatorial game theory the last player able to move is the winner. Sylver Coinage is named after James Joseph Sylvester, who proved that if a and b are relatively prime positive integers, then (a ? 1)(b ? 1) ? 1 is the largest number that is not a sum of nonnegative multiples of a and b.

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