Sunday, April 24, 2005



This was told to me the other night.

The four prisoners puzzle.

Four prisoners of war are buried up to their necks in the ground. They are told that two of them will be given black hats and two will be given white hats. Prisoner A is looking to the right while the others are looking to the left. The prisoners cannot look behind them. There is also a brick wall between A and the other prisoners, so A can't see anyone and the others can't see A. The prisoners are told that unless one of them can work out which colour hat is on his head and shout it out, then they will all be killed. They have 10 minutes. The prisoners aren't allowed to talk to each other either.

At the ninth minute one of the prisoners correctly shouts out the colour of his hat. Which prisoner was it and how could he be so sure?

7 comments:

goldenlad said...

I think the one that knows is C. If D could see that B & C where both wearing the same colour then D would know that he was wearing the opposite colour. C knows this, but because D has not called out therefore C knows that he must be wearing a different colour to B.

I hope that's right, otherwise I've made a complete prat of myself!!!

Ian comatose said...

wow goldenlad, I could never have worked that out

William John said...

Perhaps, seeing as the prisoner is calling out the answer at the ninth minute (out of 10 mins available), the other prisoners have already called out their guesses? As such, the last prisoner to guess will know what his hat color is. :)

William John.

William John said...

Oh, by this logic Prisoner A would most likely be the last to guess because he has no information to go on in the beginning.

William John.

William John said...

Oh... I don't know...

leave me alone!

:)

William John.

William John said...

OK... tell me, for chrisakes! You're killing me here!

;)

William John.

Lubin said...

Goldenlad has it exactly right - it's to do with inferring that the others can't know the answer because they haven't shouted out, and then deducing the colours of the hats based on that.