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Answer to The Professor's Balls

This is the answer to the puzzle The Professor's Balls.  If you haven't read it yet, here's the link.

The Professor's Balls

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There exists in the professor's mind a remarkable billiards game. It consists of any number of balls, but only three colours: red, green and blue. 






There's one player. 
Each round the player chooses a ball and takes a shot.  If two balls collide and they're different colours, they both turn to the third colour.   That is:


However, if two balls collide and they’re the same colour, nothing changes.
Occasionally the player may also find that they can play a trick shot by allowing three balls to collide simultaneously.  When that happens, and they're of different colours, all three change to one colour at the player’s choice.  If two of the balls are one colour and the third is a different colour, nothing happens and the player takes the next shot. 
However if three balls collide and the balls consists of only two colours, then the two balls that are the same colour change to third colour.