Problem of the Week 924

Singular Tic-Tac-Toe

Alice and Bob play the game of alternately replacing blanks by numbers in the system:

_ x + _ y + _ z = 0
_ x + _ y + _ z = 0
_ x + _ y + _ z = 0

with Alice moving first. Alice will win if the final system has a nonzero solution. Find a winning strategy for whoever has one.

Source: From a Lithuanian Mathematical Olympiad 1996 (in Crux Mathematicorum Sept. 2000).

© Copyright 2000 Stan Wagon. Reproduced with permission.