Three Men and Five Hats

Because most of you are enduring a social isolation never once imagined, perhaps you have time for a brain teaser requiring logical thinking to come up with the correct solution. Spend as much time as you wish but do not despair if you cannot figure it out insofar as you will be no different than the majority of humanity (that, in this case, includes me). My major professor in graduate school, most determined, took two months to solve it. But this may not be the case for you. A small minority of souls have solved it in a matter of minutes but, again keep in mind, that we are talking about a small minority.

Here it is:

There are three men, sitting next to each other in a room, all wearing blindfolds. With their blindfolds on, all three men are told that they are to choose from five hats in a container, three of which are black and two of which are white. Upon selecting their hats, both of the first two men are told to remove their blindfolds but not to look at their own hat. Therefore, both of these men can see the color of the hats that the other two men are wearing but not their own hat. Meanwhile, the third man is told that he must leave his blindfold on resulting in his not seeing his own or anyone else’s hat in the room.

The first man is then asked what color hat he has on. He replies: “I don’t know.” The second man is then asked the same question and he also says: “I don’t know.” Finally, the third man is asked the same question and he replies by saying: “I know.”

What color is the third man’s hat and, how do he and you know?

By docallegro

Consulting Psychologist
Specialties in: Cognitve-Behavioral Interventions, Conflict Resolution, Mediation, Stress Management, Relationship Expertise, Post Traumatic Stress Disorder and Fluent in Spanish

2 replies on “Three Men and Five Hats”

Fun riddle! Reminds me of a LSAT logic game. The hat is black. My approach was to lay out all the possible combinations of hats (there aren’t that many) and rule out combinations that it couldn’t be.

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