2001 Stanford Math Tournament Team #11
Source:
May 24, 2014
Stanfordcollegeprobability
Problem Statement
Christopher and Robin are playing a game in which they take turns tossing a circular token of diameter 1 inch onto an infinite checkerboard whose squares have sides of 2 inches. If the token lands entirely in a square, the player who tossed the token gets 1 point; otherwise, the other player gets 1 point. A player wins as soon as he gets two more points than the other player. If Christopher tosses first, what is the probability that he will win? Express your answer as a fraction.