3 mathematicians are at a party and the host wants them to play a game: There are 5 hats, 3 of them are white and the other 2 are black. The host randomly chooses a hat for each mathematician (they obviously ignore the colour of their hats)and then, he
3 mathematicians are at a party and the host wants them to play a game: There are 5 hats, 3 of them are white and the other 2 are black. The host randomly chooses a hat for each mathematician (they obviously ignore the colour of their hats)and then, he
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kashiwazakinenj on July 29, 2009
made them form a straight line so that the last mathematician could see the second's and first's hats, the second could see the first's, and the first could see noone's.
kashiwazakinenj on July 29, 2009
Then he asked the last one if he knew the colour of his hat, he responded NO, then he asked the second one, he responded NO, then he asked the first one and he responded correctly! Was his hat black or white?
kashiwazakinenj on July 29, 2009
Answer: the only way the last one could have known if is both the second and
kashiwazakinenj on July 29, 2009
first one were wearing black hats and they were all aware of it, so thus they (2nd and 1st) could have ONLY either one black and the other white or both white.
kashiwazakinenj on July 29, 2009
So if the first would've had a black one the second would've known his was white, so given the second couldn't respond correctly the first one knew his hat was white!
Posted on July 27, 2009
by kashiwazakinenj
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