In The Spirit Of Monty Hall and Bellboy Puzzles

[bigjohnn]

Although not really falling into the realms of probability, people seemed very interested in the Monty Hall and Bellboy puzzles. This has given me an opportunity to pose the following problem, which very few people seem to have heard about, which surprises me because it is one of my favourites:

A cruel king sentences 4 men to death. They are to be buried upto their necks in sand, and left to die in the extreme heat. However, the king likes to play games, and so proposes a game to the sentenced men. He has four hats, 2 black and 2 white. He says to the men, "I will gives you a chance to escape death. When you are buried in the sand, I will place a hat on each of your heads. You will not be able to see what colour hat you are wearing. If one of you can correctly name the colour on your head AND explain your reasons for the answer, then I will let all 4 of you go. If you get it wrong, you will continue to die."

I cant include a diagram, but imagine the four men are buried in a line- A then B, then C, then D. There is a brick wall between A and B.

A is facing right, and can only see a wall in front of him. B, C, and D are facing left. B can only see the wall. C can see B, and D can see C and B. They cannot turn their heads round.

A has a white hat on.
B has a black hat on.
C has a white hat on.
D has a black hat on.

Within a minute of the hats being put on their heads, one of the men correctly calls out his hat colour. Which man calls out, and why?

[querulous]

C 'guesses' correctly he is wearing a white hat. If he had a black hat, D could see that both B and C have black hats, and would know he had a white hat. Since he hasn't said anything, C knows he's got a white hat.

This assumes they know there are two black and two white hats.

[kyro]

[ QUOTE ]
C 'guesses' correctly he is wearing a white hat. If he had a black hat, D could see that both B and C have black hats, and would know he had a white hat. Since he hasn't said anything, C knows he's got a white hat.

This assumes they know there are two black and two white hats.

[/ QUOTE ]

I'm assuming they don't because this seems too easy.

[mostsmooth]

[ QUOTE ]
[ QUOTE ]
C 'guesses' correctly he is wearing a white hat. If he had a black hat, D could see that both B and C have black hats, and would know he had a white hat. Since he hasn't said anything, C knows he's got a white hat.

This assumes they know there are two black and two white hats.

[/ QUOTE ]

I'm assuming they don't because this seems too easy.

[/ QUOTE ]
c was my answer too for the same reason given already. and if they didnt know there were 2 and 2, you can argue they may not even know what colors they have to choose from. i assume they know theres 2 black and 2 white.

[BruceZ]

[ QUOTE ]
Although not really falling into the realms of probability, people seemed very interested in the Monty Hall and Bellboy puzzles. This has given me an opportunity to pose the following problem, which very few people seem to have heard about, which surprises me because it is one of my favourites:

A cruel king sentences 4 men to death. They are to be buried upto their necks in sand, and left to die in the extreme heat. However, the king likes to play games, and so proposes a game to the sentenced men. He has four hats, 2 black and 2 white. He says to the men, "I will gives you a chance to escape death. When you are buried in the sand, I will place a hat on each of your heads. You will not be able to see what colour hat you are wearing. If one of you can correctly name the colour on your head AND explain your reasons for the answer, then I will let all 4 of you go. If you get it wrong, you will continue to die."

I cant include a diagram, but imagine the four men are buried in a line- A then B, then C, then D. There is a brick wall between A and B.

A is facing right, and can only see a wall in front of him. B, C, and D are facing left. B can only see the wall. C can see B, and D can see C and B. They cannot turn their heads round.

A has a white hat on.
B has a black hat on.
C has a white hat on.
D has a black hat on.

Within a minute of the hats being put on their heads, one of the men correctly calls out his hat colour. Which man calls out, and why?

[/ QUOTE ]

You need to specify at a minimum that he tells the men that there are 2 white hats. With those conditions, d will see 1 white hat and can't respond. Then c will realize that this means his own hat must be white, since if it were any other color, d would see 2 non-white hats and would have said that his hat is white.

Many people have heard of this type of problem on the poker forum.