hmm can they react like moving away?
Lets say I saw 3-4 persons close together with red hat, and I try to come close, they see me coming and they move away. I guess it means I have a blue hat, so I go to another small group with the same color as my hat and they welcome me without moving away.
Not a bad idea, but I'd call that non-verbal communication. Also, how would the people know that they aren't wearing the same coloured hat as you without communicating with each other?
Is this really possible to work out? I've been puzzling over it for a bit and from what I can tell, you would eventually have to figure out the colour of your own hat to join the right group, which would involve some sort of communication with other people and hence be impossible. I'd love to be proven wrong though.
I'm perplexed. Unless of course there are an equal number of blues and reds and you can just count to determine which you are, but that seems too easy...