[math-fun] Hat Game
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?
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.
On Fri, Jul 15, 2011 at 10:54 AM, Michael Kleber <michael.kleber@gmail.com>wrote:
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)
http://www.springerlink.com/content/v0mh81r244053315/
--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.
-- Forewarned is worth an octopus in the bush.
participants (2)
-
Michael Kleber -
Richard Hess