Hats Revisited

So, Ben has been quite a source of puzzles lately, but he gave me a really neat one the other day I just had to post.
There are 3 people in a room and they are each wearing a hat. The possible hat colours are red, green, and blue, and the standard hat rules will apply. The players must simultaneously write down a guess for their hat color, or write down "pass". The players win if somebody guesses right and nobody guess wrong, they lose if somebody guesses wrong or if everybody passes. Before the hats are assigned, they may strategise. Find a strategy that works more than 1/3 of the time.

Naturally 1/3 is trivial to reach by having Bob guess red and everybody else pass. Its a bit of a combination of two hat puzzles I have done before, but I never realised that the combination of these two puzzles is also interesting.

1 comment:

ed said...

I don't know who Ben is, but this is a great puzzle! I can get 15/27, which I suspect is optimal. (It is easy to show that you can't do better than 16/27.)