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 = 0with 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© Copyright 2000 Stan Wagon. Reproduced with permission.Crux MathematicorumSept. 2000).

30 November 2000