As far as I know, the still-authoritative paper on this puzzle and all of its generalizations is still Joe Buhler's "Hat Tricks", which I ran in the Mathematical Intelligencer in 2002. (MI 24 (2002) #4, pp44-49) --Michael On Fri, Jul 15, 2011 at 10:21 AM, Richard Hess <rihess@cox.net> wrote:
Dear funsters, The Hat Game problem below came to light over 10 years ago and the best strategy is not yet known for arbitrary N. It is known when N is one less than a power of 2. Can anyone tell me the best strategy for N=5 and for N=6? Happy puzzling, Dick
THE HAT GAME N PLAYERS ENTER A ROOM AND A BLACK OR WHITE HAT IS PLACED ON EACH PERSON'S HEAD AS DETERMINED BY A FAIR COIN TOSS. EACH SEES THE HATS ON THE OTHERS BUT NOT HIS OWN. AT A SIGNAL EACH PLAYER MUST SIMULTANEOUSLY EITHER ANNOUNCE THE COLOR OF HIS HAT OR PASS. NO COMMUNICATION IS ALLOWED EXCEPT FOR AN INITIAL STRATEGY SESSION. THE GROUP SHARES A LARGE PRIZE IF AT LEAST ONE GUESSES CORRECTLY AND NO PLAYER GUESSES INCORRECTLY. CAN THEY DO ANY BETTER THAN A 50% CHANCE? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.