MEMO 2013 Problem 8

The expression $$\pm \Box \pm \Box \pm \Box \pm \Box \pm \Box \pm \Box$$ is written on the blackboard. Two players, $A$ and $B$ , play a game, taking turns. Player $A$ takes the first turn. In each turn, the player on turn replaces a symbol $\Box$ by a positive integer. After all the symbols $\Box$ are replace, player $A$ replaces each of the signs $\pm$ by either + or -, independently of each other. Player $A$ wins if the value of the expression on the blackboard is not divisible by any of the numbers $11, 12, \cdots, 18$ . Otherwise, player $B$ wins. Determine which player has a winning strategy.