Colored Hats and Party Games

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Colored Hats and Party Games

Post  John on Tue Feb 07, 2012 8:59 am

Puzzle wizard and all around interesting mathematician Martin Gardner, claimed that Colored Hat Logic problems have existed at least since the 1960s. Prior to the recent resurgence in the popularity of these puzzles due to developing applications in algebraic coding theory, Raymond Smullyan in, The Lady or the Tiger, presented a simplified version of the problem:

"Three subjects -A, B, and C-were all perfect logicians. Each could instantly deduce all the consequences of any set of premises. Also, each was aware that the others was a perfect logician. The three were shown seven stamps: two red stamps, two yellow stamps, and three green stamps. They were then blindfolded, and a stamp was pasted on each of their foreheads; the remaining four stamps were placed in a drawer. When the blondfolds were removed, A was asked, "Do you know one color that you definitely do not have?" A replied, "No." Then B was asked the same question and replied, "No." Is it possible, from this information, to deduce the color of A's stamp, or of B's, or of C's?"

For extra credit: If A's stamp was Green, B's was Blue, and C's was Green, and there were thirty five other people in the room wearing Green stamps on their respective foreheads, twenty seven with yellow, and five with red, what is the probability that two individuals with Green stamps have the same birthday?

For extra² credit: What was A's hat size?
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