Can You Solve the Prisoner Hat Riddle? Brain Exercise # 2

This is the second episode of our series "Impossible Puzzles"
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Puzzle:
Four prisoners are arrested for a crime, but the jail is full and the jailor has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are executed.
The jailor puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats. The jailor explains that there are two black hats, and two white hats; that each prisoner is wearing one of the hats; and that each of the prisoners only see the hats in front of him but not on himself or behind him. The fourth man behind the screen can't see or be seen by any other prisoner. No communication among the prisoners is allowed.

If any prisoner can figure out and say to the jailor what color hat he has on his head with 100% certainty (without guessing) all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.
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Clarification regarding the 5 Hat Variant:
Let's consider the following two cases:
1) B has a Red and A has a BLACK hat.
2) When A&B both wear BLACK.
In both, the cases B would remain silent as he won't be able to decide his hat color.
So A would understand that B is not able to answer.
Now think from A's perspective. If A would have worn a Red Hat, B would have answered. Why? Because B would know that C has seen different colored hats and hence was silent.
If both A and B were wearing Red Hats, C would have answered quickly.
So finally A can conclude that given any situation Either B or C would have answered. Only in one situation, they remain silent and that's when A wears a Black hat.
So whenever A gets to answer (i.e. when B remains silent) he just has to say, Black. Hope I cleared your doubt. :)
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Note:
We recommend you to pause the video after watching the question and try to solve it yourself.
Write down whatever comes to your mind regarding the solution to this puzzle and then watch the solution.
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[rxin]

Take off the hat and look at it...the only rule is that you couldn't communicate.

[ddebenedictis]

Excellent puzzle and I like the extended version at the end, which is a bit more challenging.

[jakenbaked]

answer: decriminalize marijuana-- statistics show that 3 out of 4 of those men were probably arrested on a drug related charge

[helena]

Why would I want 4 criminals out free? 😂😂 How about they don't find the solution and stay wherever they are ?😂😂

[Kyrelel]

The guy in the middle can see a black hat. He waits. The guy behind him says nothing, so he knows that the guy behind must not be seeing two black hats, so he knows that he is wearing a red hat.

Now, let's watch the video and find out . :)

[andrewsauer]

If the first two hats are the same color, then the third prisoner back knows what his hat's color is and would say it. Therefore, if a few minutes go by and the third prisoner doesn't speak up, then the second prisoner knows that his hat color is different from the first prisoner's hat and he would say the answer.

[TheScienceVerse]

I remember a Ted Ed vid just like this

[javierortiz]

How could A know that his colour is red or black ? I would have thought that since C didn't answer, B and A must have different coloured hats, because if they had same colour, then C would have said he's wearing the missing colour.

As said in the video, B would know B and A have different colours. By seeing A's colour, he can deduce that he's wearing the other colour.

Nice content ! I was just confused on that. Keep up the good work 👌

[mrscottcheek]

Sucks to be prisoner number 4, who can see no hats and has no idea that the rest of his buddies got out 5 years ago.

[rickromney]

Answer: The third in line can guess his hat color if he sees both red or both green in front. If it's a red and a green, he cannot tell so he falls silent. The second in line should then realize that since the third cannot tell his color, he is wearing a color different from the first in line. So, he should answer the color different from the one in front of him. This is assuming the third in line isn't dumb.

[legato]

Nice puzzle! The 5 hat twist was neat! I had to write all the combinations out...to make sure I didn't miss anything...haha!

[pak]

What if prisoners A, B, C all have black hats? Easy execution.

[lysandersage]

Well of course they're gonna die he'd lose his job if he didn't ._.

[evanmasterpierround]

If the second guy in line is intelligent, he'll realize that the guy in the back of the line will only stay silent if the first two have on different hats. If the first two had the same hat, then the third guy would know that both himself and the man in the room had the opposite hats. If the third guy says nothing, the second guy will know that he and the person in front of him have different color hats on, so he knows he's wearing the color that the person in front of him is not wearing.

[samkitkundalia]

So anyway D, was not worthy of escaping?

[ProfessorSyndicateFranklai]

Solution, the prisoners call it a cruel and unusual punishment and the judge sends the jailor to jail. Wait, now there are 5 prisoners.

[karanowalekar]

If the prisoners would be so intelligent to think in such a way ... then they would never b caught ... !!!

[jusjustjustin]

In the second 4 hat scenario, only 2 prisoners will escape...

[PopeSalty]

I got it! I think...

The 2nd guy can see the 1st guy's hat. He knows that the guy behind him can see his hat as well. Now if he has the same colour hat on as the guy in front of him, the guy behind him would be able to accurately determine that his hat is the other colour. That's the easy part. But, if the 3rd guy says nothing, that's the 2nd guy's cue. The 3rd guy's silence confirms that his hat is the opposite colour from that of the 1st guy. Either way, someone could determine their own hat colour.

Am I right?

[marcrusch]

the guy in the middle knows that the guy in behind of him can see the hats of the two front people. If the guy in the back can see both, he would know the color of his hat if both in front of him are the same color. So if the guy at the back doesnt say a solution, the color of the guy in the middle must be different than the one in front of him. So the one in the middle can always tell the answer.