The “Four Hat” Riddle: Try to Solve the Viral Riddle

The numbers are small, but the stakes are high in the "four hat" riddle. We tip our hat to whomever can logic their way out of this one.

Something many famous riddles have in common is that they’re capable of confounding even the mightiest of minds. In fact, some of the hardest riddles are designed to be incredibly challenging to solve. Some, like the “How many numbers are on a clock?” riddle, use verbal trickery. Others, like the “Man steals $100 from a shop” riddle and the “Who killed Mrs. Smith?” riddle, plant red-herring-type clues that are intended to mislead. And others, such as math riddles, require you to slog through all the necessary calculations. But not all riddles take that sort of approach. And that brings us to the “four hat” riddle.

Arguably one of the more satisfying viral riddles, the “four hat” riddle features life-or-death stakes and requires the power of logic to solve. Try it below.

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The “four hat” riddle

Also called the “prisoner hat” riddle, the “four hat” riddle begins with four prisoners who have all been lined up, one behind the other and all facing in the same direction. The first (prisoner A) has been separated from the others by an impenetrable brick wall. The others (prisoners B, C and D) have all been lined up facing the brick wall. Each of the prisoners is wearing a hat. Two of the hats are white, and two are black, but no one knows the color of his own hat.

Now, here’s the sinister kicker: All the prisoners will be killed unless one calls out the correct color of his own hat within 10 minutes. The prisoners are not allowed to confer with one another, nor are they allowed to move around or change position.

Fortunately for all, just before the stopwatch strikes 10 minutes, one prisoner correctly calls out the color of his own hat. Your job, should you accept the challenge of the “four hat” riddle, is to figure out which prisoner it was.

The hints

The solution to the “four hat” riddle relies on neither trickery nor obfuscation. That doesn’t make it an easy riddle, but the solution is within your grasp, provided you suss it out logically.

And just to clarify: There is only one correct answer. In this scenario, only one of the prisoners could possibly have come up with the correct answer, and he has, in fact, done so.

The answer

Prisoner C (who calls out that he is wearing a black hat).

The explanation

As vexing as it might seem, the “four hats” riddle can be solved using the process of elimination. And two of the prisoners (prisoners A and B) can be eliminated right off the bat. That’s because neither can see any of the other prisoners, so neither possesses any information with which to make an educated guess.

That leaves just prisoners C and D.

Prisoner D might seem the obvious choice because he can see the hats of both prisoners C and B in front of him, whereas prisoner C can see only the hat of prisoner B. Indeed, if prisoners B and C were wearing the same color hat, then prisoner D would have known immediately that he was wearing the other color. However, in this scenario, prisoners B and C are wearing different colored hats. Seeing this, prisoner D, in effect, has no more information than prisoners A and B. Accordingly, he too is left in the position of being unable to make an educated guess.

As for prisoner C, prisoner D’s silence is all the information he needs. Had prisoner C and prisoner B been wearing the same color hat, prisoner C surmises, then surely prisoner D would have piped up with the answer already. Accordingly, at the end of the 10 minutes, prisoner C deduces that he and prisoner B must be wearing different color hats. And since prisoner C can see that Prisoner B is wearing a white hat, then prisoner C knows that he must be wearing a black hat.

Ah, the power of logic. Care to flex yours some more? Try these fun and challenging logic puzzles.

Lauren Cahn
Lauren Cahn is a New York–based writer whose work has appeared regularly on Reader's Digest and in a variety of other publications since 2008. She covers life and style, popular culture, law, religion, health, fitness, yoga, entertaining and entertainment. Lauren is also an author of crime fiction, and her first full-length manuscript, "The Trust Game," was short-listed for the 2017 CLUE Award for emerging talent in the genre of suspense fiction.