Frechette, Chloe

Title:
Sylver Coinage Digraph Analysis

Abstract:
Conway’s Sylver Coinage is a 2-player game on the set N of natural numbers.The players alternate choosing integers that are not the sum of nonnegative integer multiples of previously chosen integers; the player who chooses 1 loses. Despite its simplicity, Sylver Coinage is not fully solved; some winning positions are known, but strategies to maintain winning positions are in general unknown. When the gameboard is finite, game states can be represented by digraphs. We analyze families of digraphs and present new results in determining winning and losing positions, and the resulting strategies applied to Sylver Coinage.