Math in the Middle Institute Partnership


Date of this Version



In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Jim Lewis, Advisor July 2008


Wythoff’s Game, named after Willem Abraham Wythoff, is a well known game amongst number theorists. Dr. Wythoff, who received a Ph. D. in mathematics from the University of Amsterdam in 1898, described this game in these words: “The game is played by two persons. Two piles of counters are placed on a table, the number of each pile being arbitrary. The players play alternately and either take from one of the piles an arbitrary number of counters or from both piles an equal number. The player who takes up the last counter or counters, wins.” This game was previously known in China as tsyan-shidzi (“choosing stones”), but was reinvented by Wythoff. Wythoff published a full analysis of this game in 1907.