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.

• 1998 particles of type X
• 2002 particles of type Y
• 2003 particles of type Z.

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?