Three Hats

Dross · 2007-02-28 21:54:04

Three prisoners are given the following task, with a time-limit of two minutes:

They are given a hat to wear, though when it is put on they are blindfolded so that they cannot see what colour hat they are wearing. They are then (still blindfolded) stood in line, one behind the other, all facing the same way and told to keep facing forward. Their blindfolds are then removed. (Que Dross' most excellent drawing skills at this point) As you can see from attached diagram, person A can see what colour hat persons B and C are wearing, person B can only see the colour of person C's hat, and person C cannot see what anybody is wearing. Nobody can see the colour of their own hat.

The prisoners are then told that each hat is either black or white, and all the hats are not the same colour. Then, without speaking to each other, if one of them can announce the colour of their own hat within two minutes, they will all be allowed to go free. If one of them announces the colour of their hat incorrectly, or if nobody announces the colour of their hat, they will be sent to prison for life.

My question is: Who announces the colour of their hat (correctly, without guessing) after one minute and fifty-five seconds, and how do they know what colout hat they're wearing?

Last edited by Dross (2007-03-01 02:36:56)

mathsyperson · 2007-03-01 02:34:22

I don't see a brilliantly drawn diagram anywhere, Dross.
I've seen this puzzle before though, so I'll let other people work out the answer. It's a good one though.

JaneFairfax · 2007-03-01 03:07:46

In the diagram, youve drawn A and C as wearing white hats and B as wearing a black hat. Are we to assume this this true for the problem as well?

EDIT: Maybe not, because Ive got the solution without having to assume this.

Last edited by JaneFairfax (2007-03-01 03:17:05)

Dross · 2007-03-01 03:20:39

Sorry - the image didn't upload when I first posted it, perhaps the upload slots clear when you preview a post?

And I should have been clearer about that, Jane - yes, the colours of the hats in the Brilliantly Drawn Diagram(tm) represent the colours of the hats the prisoners are actually wearing in the problem.

Edit: ...although it obviously doesn't pose too much of a problem for you if that's not the case

Last edited by Dross (2007-03-01 03:22:21)

mathsyperson · 2007-03-01 04:30:12

That's the answer I had as well. An interesting extension is when there are 4 prisoners all lined up, and with all the other conditions unchanged.

Can someone still determine their hat's colour?

Maelwys · 2007-03-01 04:50:36

mathsyperson wrote:

That's the answer I had as well. An interesting extension is when there are 4 prisoners all lined up, and with all the other conditions unchanged.
Can someone still determine their hat's colour?

Yes, using much the same strategy.

Toast · 2007-03-01 22:26:00

Nice puzzle, genius answers.

Oh and by the way, if they have to wait 1 minute and 55 seconds, then it must be B who answers ^_^

pointblank · 2007-05-28 13:43:47

good puzzle. I could get answer to three prisoners but failed to get four prisoner one.

Cheers

PB

Math Is Fun Forum

#1 2007-02-28 21:54:04

Three Hats

#2 2007-03-01 02:34:22

Re: Three Hats

#3 2007-03-01 03:07:46

Re: Three Hats

#4 2007-03-01 03:20:39

Re: Three Hats

#5 2007-03-01 04:30:12

Re: Three Hats

#6 2007-03-01 04:50:36

Re: Three Hats

#7 2007-03-01 22:26:00

Re: Three Hats

#8 2007-05-28 13:43:47

Re: Three Hats

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