Consider 2016 coins, all of which initially showing heads, lying in a straight line on a long table. Two players, Alex and Ben, standing by the same side of the table, play the following game with alternating moves: each "good move" consists of choosing a block of 15 consecutive coins, the leftmost of which showing head, and turning them all over. Alex starts first, and the last player who can make a "good move" wins the game.
a) Will this game always end?
b) Does Alex have a winning strategy, and why?