Classic hat problem with a twist

mfb

Quote by oli4

What is this set of rules ?

See first post:

Quote by sorax123

Three logical individuals, Amy, Bob and Carol, sit in a circle wearing Christmas hats. Each hat has a number on it so all three can see the others� numbers but not their own. They are told that the numbers are three different positive digits. They are each to make a statement in turn and are told to raise their hands when they know their own number.

What are they allowed to say, or not allowed to say ?

Everything, when it is their turn.

Is the game won only if everyone finds his number

Exactly.

Do those who win get more points if some others don't find their number ? (you get 2 points for finding your own number, plus 1 point for every player that didn't find his number, those who don't find their number get 0 and those who think they find it but are wrong get -1 point (something like that :))

There are no points, they can just win together or lose together.

oli4

As we said before, Amy, Bob and Carol could just tell the others' numbers and that wouldn't make for a very fun game.
Since they do play it and take immense risks by not playing the obvious way to win the game, it is because there must be one more rule to the game and I think I guessed what it is.
It is compatible with what happened, it was just not stated.
So add the rule that whoever raises his hand can't talk any more (and of course cheating (as in not raising the hand although the number is known/knowable) is not allowed).
In this case, Amy can't say something like B+C=15 because then both B and C would raise their hands and A couldn't get any hint for herself and the game is lost.

mfb

That is a nice idea, and probably compatible with the statements they made.
But, as I posted, it is not relevant for the problem I solved.

oli4

Indeed, that wasn't my claim either, but because of your post I got myself puzzled into how this game could even happen to be played (and in this particular way anyway) without enough rules to make it a game worth playing.
Otherwise, Amy Bob and Carol could just as well play the 'we won game'.
Everybody says 'we won' and there it is everybody wins and congratulates each other while commenting how much close Amy was to say 'We lost' etc. :)

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mfb Recognitions: Homework Help Science Advisor	That is a nice idea, and probably compatible with the statements they made. But, as I posted, it is not relevant for the problem I solved.