Worlds In Collision

[From the Fourth Annual Iowa Collegiate Mathematics Competition. Written by Paul Zeitz. Slight modifications by Sam Rebelsky.]

A bubble chamber contains three types of of sub-atomic particles.

Whenever an X particle and Y particle collide, they both become Z particles. Similarly, when a Y particle and a Z particle collide, they both become X particles and when a X particle and Z particle collide, they both become Y particles.

Can the particles in the bubble chamber evolve so that only one type is present?


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