Three hats

[kalise25]

3 men in a room, 2 are blindfolded and the other is blind. A fourth man enters the room with 5 hats - two black and three white. He randomly places hats on the three men's heads and throws away the extra two hats. He then takes off the first blindfolded man's blindfold and asks him what colour is his hat -black or white. The man can see the other hats but not the one on his own head. After thinking for a moment, he says he does not know. The blindfold is replaced. The second man's blindfold is removed, same question, same answer - at which point the blind man says," I know which colour hat I'm wearing!" What colour is his hat, and how does he know?

[Brugel]

He is wearing a white hat. He reasons as follows: suppose I have a black hat. Then the second man would have realised that he couldn't also have a black hat otherwise the first man would have seen two black hats and concluded that his own is white (since there only are two black hats). But the second man said nothing. So I can't be wearing a black hat- it must be white.

[Elfin]

Doesn't that assume that the fourth man told the other three (who were already blindfolded/blind) how many hats he brought in and what colours they were...?

[pinus]

Unless he tells them what he's doing, there's no point to his question to them

[Sylday]

The solution also depends on the second man knowing who the first man was - ie knowing that it was the other blindfolded man, not the blind man. That explains the significance of the first man's blindfold being replaced after his turn.

[Dazzler]

It's white for the reason Brugel said, but this assumes that the 2 blindfolded people have adequate powers of reasoning. If guy 1 sees two black hats, and lacks the wit to realise that his must be white, he screws the game up for everyone.

[deetyork]

A Similar puzzle exists, see diagram! W || B W B The scenario is that 4 prisoners are buried up to their necks! in sand. One of the men is seperated from the others by a wall (represented by ||)they are each wearing either a Black or White (B,W)hat. The Guard says to them "I will kill you all unless one of you tells me the colour of his hat, two are black, two are white" No questions are asked among the men, yet one man could definately say which colour he was wearing. Answer...The middle man of the three! If the man behind him saw two hats the same, he would have shouted the opposite colour. Because he didn't, the middle man knows he is wearing the opposite colour to the man in front of him!!

[Natty]

The blind mans' hat could have been black if the two blindfolded men were wearing white hats. So long as both blind folded men saw either a black and a white hat; or two white hats, they couldn't know which hat they were personally wearing.