Thanks to PB, an "A" grade quiz taker who has a nearly perfect score answering all the quizzes over the years, for recently sending the subject quiz below. Naturally I held my breath waiting for PB to let me know whether or not I was able to figure the riddle out.
I was quite relieved when I received the message "
Doug, Congratulations, you got it."Please let me know how you work the problem. I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.
Three Men – Five Hats Quiz
Three men are captured by cannibals in the jungle. The cannibals decide to give the men one chance to escape with their lives. They bind the men to stakes in such a way that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man cannot see anybody. The cannibals show the men five hats. Three of them are black; the other two are white. Then they blindfold the men and place one of the hats on each man's head, hiding the two remaining hats. After removing the blindfolds, the cannibals tell the men that if one of them can guess what color hat he's wearing, they can all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was the hat? How did he know?
OK Doug, it has to be a black hat.
ReplyDeleteThe first guy could only see two white, 2 black or one of each. If he saw 2 whites, he would know his hat had to be black. But he didn't.
The second guy could see only one hat on the 3rd guy. If he saw a white hat, he would know that he (the #2 guy) would have to have a black hat, or else the 1st guy would have known. If he saw a black hat on #3, he could not make a determination.
Therefore the 3rd guy had to have a black hat.
My scientific formula may not be up to snuff, but the answer is correct!
Your scientific formula may not be up to snuff but your logic is excellent.
DeleteNot sure i have this but here goes....The man in front was wearing a black hat. Assuming the men could not verbally communicate the third man back would ONLY know his hat color if BOTH men in front of him had on white hats. If that were the case he would know his hat was black as both white hats were accounted for. Since the third man remained silent the first two men KNEW they BOTH weren't wearing white hats. So the second man knew they both weren't wearing white hats but that's all he knew , if the first man had on a white hat the second man would then KNOW his hat was black, but since he remained quiet the first man then knew he must be wearing a black hat.
ReplyDeleteToo long an explanation , I know, but its the best I can do. Let me know.I hope you followed all that
Don't know how you could have explained it shorter. Excellent reasoning.
DeleteThis was your most difficult quiz to date...I feel good to have gotten it correct.
DeleteDoug - I see that others already posted the solution before me, but I'll submit this anyway just to let you know that I enjoyed doing this quiz.
ReplyDelete===========================================================
If the back guy saw white hats on both the front and middle guys,
he would know that his hat was black (since there are only 2 white hats).
The back guy didn't announce that his hat was black, though.
Therefore the middle and front guys know that both of their hats are not white.
With this information, the middle guy now knows that if he sees a white hat on
the guy in front of him, that his own hat would have to be black.
But the middle guy is quiet, meaning that he sees a black hat on the front guy.
The front guy, knowing that both the back and middle guys were silent,
therefore knows that his hat is BLACK.
The cannibals go hungry!
Very nice write up. Now lets hope they are honorable cannibals.
DeleteI guessed black. 2 white, 3 black, so if 2 white were used in back of him he would have black. if one of each color in back of him check the odds. Black would be a good guess. Weird reasoning, but the best I can do!!!
ReplyDeleteI usually go with the odds, 2-1 is acceptable for me.
Here is the solution I presented to PB to solve the problem:
ReplyDeleteThe first thing I did was read the riddle three times to make sure I understood the premises, summarized as follows:
1. Any one of the three men can save the day by figuring out what color hat he is wearing;
2. I focused on man #3 who could not see anything, but he was the one who saved the day. Man #3 must rely on clues from the other two men who had some vision.
If man #1 sees two white hats he knows he is wearing a black hat & will say so & they will all go free. This obviously does not happen since man #3 is given as the hero.
If man #1 sees a white & black hat on the other two men or sees two black hats on the other two men he still can say nothing because there are still both black & white hats unaccounted for from his point of vision.
Man #2 sees the color of the hat man #1 is wearing – it is black - but is just as unsure of his own hat color because there are two options man #1 gave as described above (if man #2 sees a black hat he will not know if he is wearing one of the other black hats or one of the white hats so he cannot say with certainty what color hat he is wearing – if he sees a white hat he can say he is wearing a black hat).
Man #3 knows he is wearing a black hat because he knew man #1 did not see two white hats & he knew man #2 did not see a white hat either because if he did man #2 would have said he was wearing a black hat.
Conclusion – we do not know what color hats men #1 & #2 are wearing but we do know that man #3 is wearing a black hat. The two men with vision were unable to determine what color hats they were wearing.