3. In the SOS game,

(a) Suppose that N = 4 and the first player places an S in the first square. Was this a good move for the first player? Justify your answer.

(b) Who wins the game if N = 7? (The possibilities are the first player, the second player, or a draw. You must assume the players are playing to win!) Justify your answer with either a (possibly pruned) game tree or with a thorough argument.

sos game Consider the following game played on a 1x N board: Two players take turns writing on the board. Each player can place an S or an 0 in any square, and the first player who completes a sequence of three consecutive boxes that spells SOS wins the game. For example, if N = 3 a possible game is as follows: The first player writes an S in the first square, so the game is at position S-- The second player places an S in the last square, so the game is at position S-S (this is not a very smart move, by the way) The first player places an 0 in the second square, so the game is at position SOS (so the first player wins). The game can be generalized to any possible N > 3