[Daily puzzle] Prisoner Hats \ stacker news ~science

656 sats \ 9 comments \ @south_korea_ln 7 Nov science

With a little bit of delay, another classic puzzle today.

Four prisoners are lined up in a row. A wall separates the last prisoner from the first three, so that the fourth prisoner cannot see the others, and the first three prisoners can only see forward. The prisoners know that each of them is wearing either a black or white hat, and that there are two hats of each color.

The prisoners can only make one guess about the color of their own hats. If they guess correctly, they will all go free. If anyone guesses wrong, they will all remain in prison.

Starting from the back, each prisoner in turn (from fourth to first) is asked if they know the color of their hat. Only one of them says, "Yes." Which prisoner speaks, and what color is their hat?

Previous iteration: #756004 (several correct answers in the thread)

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150 sats \ 0 replies \ @OneOneSeven 7 Nov

I remember this one from a while ago.

Two speaks and declares he’s wearing the opposite of what he sees in front?

128 sats \ 0 replies \ @nym 7 Nov

Prisoner 2 speaks, because he knows his hat is the opposite color of Prisoner 1's hat?

42 sats \ 0 replies \ @Aardvark 7 Nov

You're either incredibly early or incredibly late. Either way I'm too exhausted to think, or really read so my guess is yellow.

0 sats \ 2 replies \ @SimpleStacker 7 Nov

I'm a bit confused. Is my descripction below accurate?

Prisoner 4 cannot see anyone

Prisoner 3 can see prisoners 2 and 1

Prisoner 2 can see Prisoner 1

Prisoner 1 cannot see anyone

The order in which they are asked is: 4, 3, 2, 1

0 sats \ 1 reply \ @south_korea_ln OP 7 Nov

Yes, this description is accurate.

105 sats \ 0 replies \ @SimpleStacker 7 Nov

If the configuration is BBWW or WWBB, then prisoner 3 answers, B or W, respectively.
If the configuration is WBWB or BWWB, then prisoner 2 answers W
If the configuration is WBBW or BWBW, then prisoner 2 answers B

Logic:

4 will not answer because he has no info
If 3 sees two of the same color, he must have the opposite color
If the process gets to 2, then he knows that he and 1 have opposite colors.

0 sats \ 2 replies \ @Rothbardian_fanatic 7 Nov

Nice puzzle, let me think on it. Of course, they can’t take there hats off and look, right? :)

20 sats \ 1 reply \ @south_korea_ln OP 7 Nov

Nope, they can't.

Well, you are a sovereign individual, who am I to say if the prisoners are allowed to take off their hats in your imagination?~~

0 sats \ 0 replies \ @Rothbardian_fanatic 7 Nov

Lovin’ it!! My imagination rules!!