THE’riddle of the four hats it is also known as the riddle of the four condemned men to death and is a logic test simple but intricate.
The situation is this: a four sentenced to death is given one last chance to save himself. They are given four hats – two white and two black – and are placed in a row in front of a wall in the following way: condemned A sees B and C in front of him, condemned B sees C, while C and D only see the wall in front of him, each from a different side.
The hats are arranged above the condemned as in the figure: A white, B black, C white and D black. However, none of the four condemned men know the color of their hat.
In order to save themselves, at least one of them must guess the color of their hat, considering that if they are wrong, they will all be condemned.
Which of the four condemned men can, again without talking to each other, guess their color and thus save everyone’s lives?
The solution to the riddle of the four hats
Let’s start with theexclude C and Dbecause both they see in front of them only the wall and for this reason they have no indication either of their own hat color or that of others.
With regard to Bthe condemned you see in front of him a white hatbut knowing that there are two whites and two blacks, he is unable to establish his own color.
In the end, See in front of him both B and CMeaning what a white hat and a black one. Unfortunately this does not help him to answer, because not knowing the color of D’s hat, for all he knows A could have either a black or a white hat. If instead he had had two black hats in front of him or two hats white, he could have answered his color with certainty, knowing that there are, in fact, two hats of each colour.
And this is precisely where the solution lies! Initially none of the four condemned men respond, because as we said no one can say their color with certainty. For this reason the convicted Bfeeling that A doesn’t answerunderstands that A he can’t tell what color hat he wears. This uncertainty on A’s part makes B understand that A does not see two hats of the same color in front of him, but rather two different colours.
From this intuition, B realizes that his hat is the opposite color to Cand therefore correctly answers that he is wearing a black hat, thus saving all the condemned.
In conclusion: if B and C have hats of the same color A can deduce the color of his hat and free everyone; otherwise, A’s silence allows B to deduce that his hat is different from C’s. In both cases it is possible for the four condemned men to receive pardon!
