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Borek said:Are the hats placed as drawn, or is it just an example?
micromass said:As drawn. But you can of course try to find the solution of every permutation of hats!
OrangeDog said: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
JorisL said: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 n^{th} 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?
The "Another hats and prisoners puzzle" is a logic puzzle that involves a group of prisoners who are given the opportunity to save themselves by correctly guessing the color of their own hat.
There are an infinite number of prisoners in the puzzle, but only a finite number are given hats.
The objective of the puzzle is for the prisoners to correctly guess the color of their own hats. If at least one prisoner guesses correctly, all prisoners will be set free. However, if no one guesses correctly, all prisoners will be executed.
The rules of the puzzle are as follows:
The prisoners can solve the puzzle by using a strategic guess, based on the color of the hats they can see in front of them. By observing the colors of the hats in front of them and the number of hats of each color, they can make an educated guess about the color of their own hat. However, there is no guaranteed solution to the puzzle, as it relies on chance and probability.