Imagine a row of 2000 squares. 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.

Source: (USAMO ’99)

The Usamo 99 gives this formulation, which is sligthly different, because if there is a S,O,S the last player wins.

Two players play a game on a line of 2000 squares. Each player in turn puts either S or O into an empty square. The game stops when three adjacent squares contain S, O, S in that order and the last player wins. If all the squares are filled without getting S, O, S, then the game is drawn. Show that the second player can always win.

Posted by armando on 2016-06-03 16:42:20