The expression ±◻±◻±◻±◻±◻±◻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 ◻ by a positive integer. After all the symbols ◻ are replace, player A replaces each of the signs ± 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,⋯,18. Otherwise, player B wins. Determine which player has a winning strategy.
Problem
Source: Middle European Mathematical Olympiad 2013 T-8
Tags: number theory proposed, number theory