CMO 2001 Problem 2

There is a board numbered $-10$ to $10$ . Each square is coloured either red or white, and the sum of the numbers on the red squares is $n$ . Maureen starts with a token on the square labeled $0$ . 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 $\frac a b$ . Given that $a + b = 2001$ , determine the largest possible value for $n$ .