Brain Teasers
The Color of My Hat
Three men are buried in the sand all facing forwards with their heads above ground. Each man has a hat placed on his head selected from a bag containing 3 red hats, and 2 black hats. The men cannot turn around to see the men behind them. The man at the back is asked what hat he is wearing. He replies 'I do not know'. The middle man is asked what hat he is wearing. He also replies 'I do not know'. The man at the front is then asked what hat he is wearing. He replies 'I am wearing a red hat'. How did he know?
Answer
Since the man at the back could not determine his own hat, this means that the front two men could not have been wearing black hats and that, therefore, there must be at least one red hat on the two front men. Therefore the middle man must not be able to see a black hat otherwise he would know he had a red one on. Therefore the front man must be wearing a red hat - which finally he deduces. Interestingly, the other two can never determine their own hats.Hide Answer Show Answer
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Comments
nice
Who would burry men in the sand and ask the color of their hats?
I don't agree that the other two could never know the color of their own hats. If the front two were both wearing black hats, the man in the back would know he was wearing a red hat, and hence the other two would know they were wearing black
jdnorway, that is true that the man in back would know if the other 2 were black. BUT the puzzle clearly states that the man said he did not know what color he was. You can therefore deduce that the other 2 have either 1 black and 1 red, or 2 reds. Follow the logic from there.
very common riddle just different story line
I agree with Mogmatt!
The solution does work. If the r = red, b = black and x = red or black, then:
the guy at the back said "I dont know, which leaves us with 3 situations:
i) x, r, r
ii) x, b, r
iii) x, r, b
(The case of x, b, b is discounted because then the guy at the back would know that he has a red hat on)
now in case i) and ii) the middle guy sees a red hat in front of him, but he himself could be wearing either a red or a black hat, and will answer "I dont know".
in case iii) he sees a black hat, and as these cases are exhaustive of all the possibilities, he must be wearing a red hat.
To summarise:
1) if middle guy says "I am wearing a red hat", then front guy must have a black hat, and
2) if middle guy says "I dont know", then front guy must be wearing a red hat.
the guy at the back said "I dont know, which leaves us with 3 situations:
i) x, r, r
ii) x, b, r
iii) x, r, b
(The case of x, b, b is discounted because then the guy at the back would know that he has a red hat on)
now in case i) and ii) the middle guy sees a red hat in front of him, but he himself could be wearing either a red or a black hat, and will answer "I dont know".
in case iii) he sees a black hat, and as these cases are exhaustive of all the possibilities, he must be wearing a red hat.
To summarise:
1) if middle guy says "I am wearing a red hat", then front guy must have a black hat, and
2) if middle guy says "I dont know", then front guy must be wearing a red hat.
I still don't get it
The front guy is relying on the two other guys to use good, solid logic.
And can you really expect good solid logic out of someone who agrees to be buried in the sand to play a guessing game ;)
And can you really expect good solid logic out of someone who agrees to be buried in the sand to play a guessing game ;)
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