[Guest]

I made this one myself (based upon similar puzzles), so I hope this one doesn't already exist.

Four guys are standing in a line, facing the same way, so that the last person can see all three in front of him, the third can see only the two in front of him, etc. Seven hats, 3 black and 4 white, are distributed amongst them, without them seeing the color of their own hat or the remaining hats.

Once they have their hats on, they must seem to figure out a way to get to know the color of their own hat. If one knows it, he must say it.

Now you are the first person in the line (so you won't be able to see any of the hats). For a while, everyone is silent, until suddenly you scream: "I got it!!".

What color is your hat?

Edited October 31, 2008 by lunkkun

[Prime]

Nice variation on the hats problem.

The last man's silence communicates: he sees NOT 3 black hats (or he would have guessed, his hat as white).

The 3rd man sees NOT 2 black hats.

The 2nd man sees NOT a black hat.

So the first man's hat is white.

[Prof. Templeton]

Nice variation on the hats problem.

The last man's silence communicates: he sees NOT 3 black hats (or he would have guessed, his hat as white).

The 3rd man sees NOT 2 black hats.

The 2nd man sees NOT a black hat.

So the first man's hat is white.

But what happens

No.1 has a black hat

No.2 has a white hat

No.3 has a white hat

No.'s 4,3,2 still can not answer what color hat they have.

[Guest]

There are four white hats and three black hats. Simple logic dictates that there can be AT MOST three black hats in play, and AT LEAST one white hat.

Man #4 sees the three men in front of him. If they were all wearing black hats, then he would know his is white and shout it out. But he doesn't, thus we conclude that he sees either two black hats and one white, or one black and two whites, or three whites and no blacks.

Man #3, knowing that #4 does not know his color, looks at the men in front of him. If he sees two black hats, he knows his is white because of #4's silence. If he sees two white hats or a black and white pairing, he knows that his is black or white (and thus doesn't know). So he doesn't shout out an answer.

Man #2 hears nothing from the two men behind him, and can now only see #1. He knows that there has to be at least one white hat between the two of them because of #2's silence. If #1's hat is black, then he knows he has the white hat. If #1's is white, then he doesn't know if his is black or white.

Therefore, his silence tells #1 that he has a white hat!

[Prime]

But what happens ...

No.1 has a black hat

No.2 has a white hat

No.3 has a white hat

No.'s 4,3,2 still can not answer what color hat they have.

In this scenario No.2 would have guessed his hat color.