1999 USAMO 第 5 题

The Y2K Game is played on a $1 \times 2000$ grid as follows. Two players in turn write either an S or an O in an empty square. The first player who produces three consecutive boxes that spell SOS wins. If all boxes are filled without producing SOS then the game is a draw. Prove that the second player has a winning strategy.

Y2K 游戏在 1 美元×2000 美元的网格上进行，如下所示。两名玩家轮流在空方格中写下 S 或 O。第一个连续产生三个拼出 SOS 的盒子的玩家获胜。如果所有盒子都已填满而没有产生 SOS，则游戏为平局。证明第二位玩家有获胜策略。