1) If man 1 does not yell, then man 2 knows his hat is opposite of man 3
2) Given the picture, man 2 will yell first
3) This will indicate that man 1 and 3 have the same color hat, prompting man 1 to yell
4) Man 3 will then yell
5) Man 4 is sh*t out of luck because even if he did yell he is still stuck behind that wall
There's a minor mistake in there.
In step 3 you say man 1 should yell, but how would he know if he has the same color as 2 or 3?
In fact the only one that can yell (with certainty) is number 3 knowing he has the opposite color of 2.
Let me introduce some shorthand notation for the setup, the nth letter in the string "BWB | W" indicates the color of person n.
Case 1: "BWB | W" or "WBW | B"
The answer has been given above, number 1 and 4 have to gamble if they want to go free (I think?)
Case 2: "WWB | B" or "BBW | W"
See case 1 :P
Case 3: "WBB | W" or "BWW | B"
- Person 1 can yell out its color immediately since he sees both hats of the color opposite to his in front of him.
- Person 2 and 3 know their hat has the opposite color
- Person 4 knows he has the same color as person 2
That's about it. Although I recall a different puzzle, those that call out their color correctly go free, those that are wrong or silent get sentenced to death.
How many of you clicked to see the 3 cases?