Question 21
Consider $2009$ cards, each having one gold side and one black side, lying in parallel on a long table. Initially all cards show their gold sides. Two players, standing by the same long side of the table, play a game with alternating moves. Each move consists of choosing a block of $50$ consecutive cards, the leftmost of which is showing gold, and turning them all over, so those which showed gold now show black and vice versa. The last player who can make a legal move wins.
a. Does the game necessarily end?
b. Does there exist a winning strategy for the starting player?
a. Does the game necessarily end?
b. Does there exist a winning strategy for the starting player?