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        riddles >> medium >> Three men and some hats.
        
(Message started by: Johno-G on Jan 10^th, 2003, 1:58am)

Title: Three men and some hats.
Post by Johno-G on Jan 10^th, 2003, 1:58am

Three men, A B and C, are all held captive, sat on chairs, blindfolded and have hats placed on each of their heads - A's hat is black, B's hat is white, and C's is black. They are strategicaly positioned, and the blindfolds are removed.
They are positioned such that C can see the colour of the hats A and B are wearing, B can see the colour of the hat A is wearing, and A can see nothing. None of the men can see the colour of the hats that they are wearing themselves, and none of them is alowed to move.
All the men know that, of the three hats they are all wearing, one is white, one is black, and the other is either white or black. They also know how everyone is positioned.
The men are not allowed to converse, they are only allowed to announce out loud what colour hat they have on.
The men are told they will be shot in ten minutes unless one of the men works out what colour hat he is wearing. They will also be shot if one of the men guesses incorectly what hat he is wearing.
Which of A, B or C works out the colour of their own hat and saves them all? (and, of course, why?)

Title: Re: Three men and some hats.
Post by wowbagger on Jan 10^th, 2003, 2:53am

Here's my answer (hidden by colour):

If C sees two hats of the same colour on the heads of A and B, he'll announce his own hat to be of the other colour.
If C doesn't announce anything (after a reasonable period of time, say 8 or 9 minutes), B will claim his hat to be of different colour than A's.

BTW: This riddle is closely related to 3 hats (http://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml#3hats) (which also has a forum thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1027807475)), but beware: The statement of that riddle could turn out to be a strong hint.