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Sylver Coinage is a game invented by J. H. Conway in which players take turns choosing positive integers—but a player may only choose an integer that cannot be expressed as a sum of positive multiples of integers already chosen. The player who is forced to choose “1” loses the game. The name of the game is a nod to J. J. Sylvester, who proved that ... is the largest sum that cannot be paid exactly using coins of value ... and ... , if ... and ... are relatively prime. Gameplay is simple: just click the value you want to "coin", and illegal moves will be removed from the board automatically. Finding a winning strategy may not be so simple, however. This implementation enforces some restrictions on the opening moves in order to keep gameplay within a finite (and reasonably small) range of values.
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