HMMT 2002 T12

Now suppose that before the game begins, the players choose the initial game state as follows:

• 1. The first player chooses $s_{1}$ subject to the constraint that $2 \leq s_{1} \leq 5$; then
• 2. the second player chooses $s_{2}$ subject to the constraint that $2 \leq s_{2} \leq 5$ and then specifies the board configuration.

Prove that the second player can always make her decisions so that she will win the game with probability strictly greater than $\frac{1}{2}$.