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Classic hat problem with a twist 
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#19
Jan1213, 08:07 AM

P: 218

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. 


#20
Jan1313, 06:44 AM

Mentor
P: 11,601

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. 


#21
Jan1313, 07:08 AM

P: 218

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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