Solve this Puzzle: Four Men in Hats

Can solve this puzzle on your on own without looking at the answer first?

Shown above are four men buried up to their necks in the ground. They cannot move, so they can only look forward. Between A and B is a brick wall which cannot be seen through.

They all know that between them they are wearing four hats–two black and two white–but they do not know what color they are wearing. Each of them know where the other three men are buried.

In order to avoid being shot, one of them must call out to the executioner the color of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.
After one minute, one of them calls out.

Question: Which one of them calls out? Why is he 100% certain of the color of his hat?

[mycoted | Via]

25 Responses to Solve this Puzzle: Four Men in Hats

  1. C says blue, because he knows that there is a white hat on B, and that D has insufficient information to work out what he is wearing due to the pause. If he had been wearing a white hat, D would have shouted that he was wearing blue, but since D can't know, C must be wearing blue.

  2. There's one problem with that answer — it assumes that the four men trust each other to be able to find the answer. It's entirely possible D would think that C is a moron and would take the 50/50 chance of being right and saving their lives Or that B is a complete dumbass and would yell out a color in panic.

  3. C shouts black, because he can see that B and D are wearing white, so therefore, he must be wearing black. That's it.

      • Because if C had been wearing the same hat as B, then D would have called out, but there was a minute-long pause, so C knew that D could not have known, therefore, he was wearing the color that B was not wearing.

  4. C. C knows that if he were wearing the same hat as B, then D would call out the opposite color. Therefore, C has a different color hat than B.

  5. C, because he sees that B is white, and if he(C) were white, then D would see two white hats and know that he(D) was black, and therefore yell out his own color. But because D didn't respond and B is white, C has concluded he must be black.

  6. If D had seen 2 black or 2 white, he would have known his own color and called that out. Since he doesn't do that, C realizes he and B must have different colored hats. Since C sees B has white, he knows he has black, and calls it out.

  7. It must be D. Since we are looking at the men in a profile view, You cannot assume that the men are equidistant from our prospective. So D could be closer to us and his view may not be blocked by the wall to see man A and therefore knows what color everyone’s hat is. It is only stated that A and B are blocked in view by the wall , not A and D.

  8. C is the right answer : if he was wearing the same hat as B, D would be able to give the answer. Since D didn't say anything after a minute, it means that B and C are wearing hats of different colors.

  9. In this setup nobody can know 100%. If D doesn't calls out, maybe he want's to die, or maybe he likes suspense and is waiting almost till the end. So C can't be 100% certain.

  10. I don't think the answer is 100% accurate because what if B wore black and C wore white, D would still stay quiet, and would C still call out black with 100% certainty?

    The answer is flawed.

    • If B wore black and C wore white, D would still stay quiet. C would be able to call out white, because he can see that B is wearing black, so C knows C's hat must be white and different from B's since D was unable to answer.

  11. The problem with the wording of the question and the diagram is that it doesn't make clear that D can see both B and C. From the diagram it looks as if C's hat would be exactly in line that it would block D from seeing B's hat. Of course, if you explictly state that D can see both B and C, you're tipping off the answer a little.

  12. The logic of the riddle is flawed. It states that the four men know where each other are buried and that they are facing forward. However in this scenario C does not know the direction D is facing, only where he buried and that he is looking "forward" and cannot look in a different direction. This means that C has to go by faith that the executioners designed the puzzle to be solved and therefore have faced D toward C and B. But here is the other flaw, if he uses faith in the fairness of the executioners as a basis for his decision, then he cannot be 100% certain of his hat color. In terms of practical application it wouldn't matter, but given the parameters of the Puzzle this would make his response invalid.

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