What Is The 4 Prisoners In A Hat Riddle? Puzzle Explained With Answer
4 male prisoners stood in a ine looking at camera all in orange uniforms
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What Is The 4 Prisoners In A Hat Riddle? Puzzle Explained With Answer Solved

Jasmyne Jeffery February 18, 2023

We all love puzzles and quizzes, but not when it’s keeping us up because we can’t figure out the answer. That’s what’s happened with the 4 hat riddle and people just want it solved. Thankfully, you don’t need to look any further as we can explain it all.

Riddles are great for testing our minds and bragging to our friends when we figure it out. Unfortunately, they’re not quite as fun when they completely stump you and you can’t help but constantly think about it. Luckily, the internet is here for those who’ve simply had enough and just want to know the answer.

What is The Riddle With Prisoners And Hats?

There are 4 prisoners, all wearing hats. All of them can be freed if one of them can tell the guard the color they are wearing.

Prisoner 1 can see the color hat of prisoners 2 and 3. However, prisoner 2 can only see the hat of prisoner 3. Prisoner 3 is facing a wall and cannot see anyone’s hat. On the other side of the wall is prisoner 4, who cannot see anybody’s hat.

If the prisoners don’t know the answer, they keep quiet. All they know is that there are 4 people and 2 black hats and 2 white hats.

One of them tells the guard “I know what color hat I am wearing.” Which one is it?

Here is a visual aid to help you picture the scenario, letting you know who is wearing what hat.

The 4 Hat Riddle Explanation

If you haven’t been able to solve the 4 hat riddle, then don’t beat yourself up as you’re definitely not the only one. We can explain how to figure out the answer and then you can act as if you knew it all along anyway.

Firstly, you have to rule out the ones it can’t be, which are prisoners 3 and 4. They can’t see any hats whatsoever, so they won’t be able to figure out their own.

Then we’re left with prisoners 1 and 2. Now, prisoner 1 can see both prisoners 2 and 3’s hats, but that doesn’t necessarily mean he knows what hat he is wearing. Prisoner 2, on the other hand, will be able to know regardless of whether prisoner 1 has figured it out or not.

Let’s explain.

All 4 prisoners know that there are 2 white hats and 2 black hats. So, if prisoner 1 sees that both 2 and 3 and wearing the same color hat, then he can work out that his hat must be different.

The Riddle Solved

If prisoner 1 stays quiet, that means that prisoners 2 and 3 are wearing different colored hats, meaning he can’t figure out which one he has. With that knowledge, prisoner 2 will know his hat is different from prisoner 3, and therefore know the color of his hat!

So, regardless of which scenario has happened, prisoner 2 can always figure it out!

It makes a lot of sense what it’s broken down, that you might be kicking yourself now that you couldn’t get the 4 hat riddle solved before. Now you do know it, you can brag to your friends that you figured it out by yourself.

Don’t worry, we won’t tell anyone.

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Jasmyne Jeffery is a full-time Entertainment and News Writer on university-themed website Freshered and HITC, and joined the company having previously worked in a freelance role. She attended the University of South Wales where she was also a student blogger and graduated in 2022 with a first-class honours degree in English and Creative Writing. Now, she puts her creativity to use reviewing university bars, Love Island episodes and the latest apps any 18-25-year-old is using.