Posers and Puzzles

Posers and Puzzles

  1. Joined
    14 Dec '12
    Moves
    1
    14 Dec '12 05:53
    Three men sit in chairs (#1, #2, and #3), in a straight line, all facing north, one behind another. Each man will have a hat placed on his head. No one can see his own hat at any time. The man in Chair #1 is in the front, he cannot see anyone else. The man in Chair #2 is behind Chair #1 and he can only see the man in Chair #1. The man in Chair #3 is behind Chair #2 and he can see both men in Chairs #1 and #2.

    On the table, there are three blue hats and two white hats. Each of the three men will be randomly given one of those five hats and two will be discarded. No one will know the color of the discarded hats or the color of his own hat. The first person to use logic to determine what color hat is on his own head wins.

    After five minutes, the man in Chair #1 stands up and says, "I win. I know the color of my hat."

    The riddle is: What color was it, and how did he figure it out?

    - Jeffrey Rosenspan
  2. Joined
    12 Mar '03
    Moves
    37893
    14 Dec '12 12:002 edits
    Blue.

    If #1 and #2 were both wearing white, then #3 would have known immediately that he had blue himself. So, at least one blue hat is worn by either #1 or #2.

    #2 deduces the same and still doesn't know his own colour, that means he is not seeing white in front of him that would give him the clue that his own hat is blue.

    From the silence of #2, then #1 knows he is wearing no white hat.
  3. Joined
    04 Nov '08
    Moves
    15384
    29 Dec '12 23:56
    Sorry for being slow but where do the black caps come in?
  4. Standard memberAgerg
    The 'edit'or
    converging to it
    Joined
    21 Aug '06
    Moves
    11458
    08 Jan '13 12:13
    Originally posted by Habeascorp
    Sorry for being slow but where do the black caps come in?
    The blue ones are probably black on the inside.
  5. Joined
    26 Apr '03
    Moves
    26583
    08 Jan '13 23:44
    If I was 3 and could see two whites I might wait for 10 minutes or so for one of the others to make a fool of themselves, is this strategy flawed?
  6. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
    Moves
    46219
    09 Jan '13 05:56
    It reveals the hidden premises for sure. ^_^

    Gamemaster: #1, you've had a minute to ponder. Any idea what you wear?
    Contestant #1: no clue, I see nothing and no one has spoken.

    Gamemaster: #2, you've had two minutes. What color?
    Contestant #2: dunno

    Gamemaster: #3, three minutes in, what do you wear?
    Contestant #3: I don't have enough information.

    Gamemaster: #2, four minutes in, what do you wear?
    Contestant #2: it's either blue or white..

    Gamemaster: #1, we are five minutes in. Do you know the color of your hat?
    Contestant #1: yes.. logically I know, but since #3 is just waiting for me to make a total idiot of myself.. dunno.

    Contestant #3: *snickers* gotcha
  7. Joined
    26 Apr '03
    Moves
    26583
    09 Jan '13 23:25
    Originally posted by talzamir
    It reveals the hidden premises for sure. ^_^

    Gamemaster: #1, you've had a minute to ponder. Any idea what you wear?
    Contestant #1: no clue, I see nothing and no one has spoken.

    Gamemaster: #2, you've had two minutes. What color?
    Contestant #2: dunno

    Gamemaster: #3, three minutes in, what do you wear?
    Contestant #3: I don't have enough informatio ...[text shortened]... waiting for me to make a total idiot of myself.. dunno.

    Contestant #3: *snickers* gotcha
    I think it is flawed:

    3 refuses to say anything even though he can see two whites.

    2 Can see a white, since 3 says nothing, 2 says "my hat must be blue"

    It is announced that 2 is wrong.

    1 thinks, "For 2 to announce that he must have been sure, therefore he must think 3 is not answering because he can't see two whites, however if I was wearing blue then 2 would not have know what to say, therefore I must be wearing white.

    1 quickly says white and 3 loses the game.
  8. Joined
    26 Apr '03
    Moves
    26583
    10 Jan '13 22:23
    Originally posted by iamatiger
    I think it is flawed:

    3 refuses to say anything even though he can see two whites.

    2 Can see a white, since 3 says nothing, 2 says "my hat must be blue"

    It is announced that 2 is wrong.

    1 thinks, "For 2 to announce that he must have been sure, therefore he must think 3 is not answering because he can't see two whites, however if I was wearing ...[text shortened]... hat to say, therefore I must be wearing white.

    1 quickly says white and 3 loses the game.
    Of course as soon as 2 makes a statement I suppose 3 can say his hat colour, before 1 gets to hear whether 2 is right or not. That means 3 doesn't lose, so maybe the strategy is fine.

    For perhaps an even more annoying strategy, 3 could pick his "delay" until saying the right answer from a random variable with something like the cauchy distibution, so his opponents have no idea how quickly he should answer and that may stump them completely, even if they have a clear 2 whites because they have no logical method to work out their hat colour.
  9. Joined
    15 Jun '06
    Moves
    16334
    16 Jan '13 05:32
    Originally posted by iamatiger
    Of course as soon as 2 makes a statement I suppose 3 can say his hat colour, before 1 gets to hear whether 2 is right or not. That means 3 doesn't lose, so maybe the strategy is fine.

    For perhaps an even more annoying strategy, 3 could pick his "delay" until saying the right answer from a random variable with something like the cauchy distibution, so h ...[text shortened]... they have a clear 2 whites because they have no logical method to work out their hat colour.
    Its flawed because it is dependant on both #1 and #2 having white hats and the fact that the white doesn't know #1 or #2 will answer incorrectly as either one could be correct from a completely random guess.
Back to Top