Problem #PRU-64583

Problems Set theory and logic Algorithm Theory Game Theory Game Theory Methods Pigeonhole principle Pigeonhole principle (other)

Problem

A chequered strip of \(1 \times N\) is given. Two players play the game. The first player puts a cross into one of the free cells on his turn, and subsequently the second player puts a nought in another one of the cells. It is not allowed for there to be two crosses or two noughts in two neighbouring cells. The player who is unable to make a move loses.

Which of the players can always win (no matter how their opponent played)?