iSixSigma

Christmas Quiz

There are five hats, two Black and three White. In a room sit three people, two can see and one is blind. The room is darkened and a hat is placed at random on each person’s head. People can only see the other hats not their own.

The first person on seeing the other two hat colors declares that they do not know what color hat they are wearing.

The second person on seeing the other two hat colors declares that they do not know what color hat they are wearing.

The blind person knows what color hat they are wearing.

What color is it (and why)?

Wishing you all a peaceful & merry Christmas!

Comments 8

  1. SQLRockstar

    it’s white. if it were black, then that would imply the first two hats would have to be either one of each (explaining the first two answers of "i don’t know") or both white (because if either of the first two saw two white hats they still could not know what they have).

  2. Robin Barnwell

    Hello SQLRockstar

    Remember there will be two hats left over from the original five. So the reasons you have given, I’m afraid, are incorrect. For example one of each color does not define black.

    Merry Xmas
    Robin

  3. PM

    BP (Blind Person) is wearing White hat

    For 1 to know, 2 & BP would have Black hats. Since 1 doesn’t know, that eliminates 1/4 combinations. (See chart below of each person & hat combo)
    1 2 BP
    W B B – eliminated since 1 doesn’t know
    ? B W
    ? W B
    ? W W

    For 2 to know, 1 & BP would have Black hats. And, 2 knows that 1 eliminated the first combo.
    1 2 BP
    W B B – eliminated by 1
    B W B – eliminated since 2 doesn’t know
    W ? W
    B ? W

    If BP was listening, he/she knows that the only 2 combos left have them wearing a White hat.

  4. SQLRockstar

    sorry i was not clear. let me try again.

    the blind person must be white. if the blind person was wearing a black hat, then these are the only possible combinations (given as 1st, 2nd, blind):

    W-B-B
    B-W-B
    W-W-B

    as i tried (poorly) to state before, either the first two people have mixed colors or are both white. if the 1st person sees W-B then they say "unknown", otherwise they see two blacks and declare themselves to be white. so, the first scenario above is not possible.

    the second person goes and also sees a mix of colors, meaning the second scenario is not possible.

    that means the only possible choice left would be the third one. now, here comes the logic:

    since player one said "unknown", player two upon seeing the black hat on the blind person would therefore declare "white", because the only way for the first player to say "unknown" would be if there was a mix of hats and not two black hats. since player two also says "unknown", the blind person knows that they must be wearing a white hat.

  5. Remi

    Nice one Robin,
    I can only determine what color hat the blind one is wearing.
    When will you post the solution?
    Remi

  6. Remi

    Robin,
    I have the solution if P1 and P2 do not know that P3 is blind.
    Note: with "they" you mean "the other two" I assumed and not "they themself".
    Hmmm, maybe i’m not using the info "the room is darkened’ in the right way…

    Remi

  7. Robin Barnwell

    To clarify, neither person one or person two know what color hat they are wearing. They can however see the color hats on the other two people to base their decision on what color hat they are wearing.

    The solution asks why the blind person knew what color hat they were wearing based on the answers they hear.

  8. Robin Barnwell

    Yes, well done to PM, SQLRockstar & Remi you all got the answer.

    Please take an extra days holiday and if your employer raises any issue just say I approved it.

    Here is my wording of the solution:-

    • When either person one or two knows the colour of their own hat then the blind person’s hat is Black
    • When neither person one or two knows the colour of their own hat then the blind person’s hat is White

    .
    Here is the table of combinations

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