The Puzzle of Black and White Hats

The puzzle of white and black hats – Emma the pastry chef, a well-known fan of mathematical puzzles and logic problems after a long study decided to select the most beautiful logical-mathematical games of each time by proposing separately also the relative solutions. These questions require both logical and creative skills to be solved. The perfect mathematical puzzle must propose a simple situation to explain and a solution just as easy to understand but very complicated to find, often at the limit of the impossible for an average mind.

In this page we present The puzzle of white and black hats, a logic game where you need to identify yourself in the situation and find the logical path to the desired solution.

Have fun!

il rompicapo dei cappelli bianchi e neri
il rompicapo dei cappelli bianchi e neri


Giovanni and Emma are relaxed at a bar enjoying themselves

a good coffee. Emma falls for the eye on a front-page news of a newspaper leaning on a table next to it that dealt with a capital execution in a State of the USA. This reminds him of an old puzzle that he immediately proposes to Giovanni.

“In a South American country, four men are sentenced to death.” said Emma as she turned the teaspoon to melt the ton of sugar she had poured into the cup.

“But they are given a chance to save their lives. Each of them wears a hat.” he continued sipping his coffee.

“They are told that two wear a white hat, and two black, but neither of them knows what color their hat is. To complicate things, they get stuck on the ground, one behind the other in single file so that it is impossible for them to turn around.”

“Interesting!” Giovanni said while tinkering with his smartphone.

“Between A and B…

… is erected a wall beyond which it is not possible to see. The executioner explains to them that to be pardoned it is enough that in 5 minutes one of them guesses the color of his hat. But if he makes a mistake, all four will be executed immediately.” Emma declared serious.

“That’s it?” asked John thoughtfully.

“It’s forbidden to talk to each other and exchange any kind of information.”

Giovanni put his cell phone away and finally began to think seriously about the problem.

“After one minute, one of the four convicts responds by saving everyone’s life.

Could you tell which of the four answers exactly and why is he so certain of his deduction?” concluded Emma.

“Do you have any specific indications?” said the friend.

“Well… only there are no pitfalls – there is, for example, no mirror on the wall or other strange things. There is no external element that can help them to respond or any means to communicate. Ultimately, A and B can see nothing but the facade of the wall that is in front of them, C can see the hat of B, and D can see those of B and C.

Il rompicapo dei cappelli bianchi e neri

(The Solution is at the bottom of the page)

Musical interlude

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Come and discover the magical musical world of Lorenzo Pescini!

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