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Horizontal board and token

Source: 2001 Canadian Math Olympiad #4

September 19, 2011
probabilitycombinatorics unsolvedcombinatorics

Problem Statement

There is a board numbered −10-10 to 1010. Each square is coloured either red or white, and the sum of the numbers on the red squares is nn. Maureen starts with a token on the square labeled 00. She then tosses a fair coin ten times. Every time she flips heads, she moves the token one square to the right. Every time she flips tails, she moves the token one square to the left. At the end of the ten flips, the probability that the token finishes on a red square is a rational number of the form ab\frac a b. Given that a+b=2001a + b = 2001, determine the largest possible value for nn.
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