Three very clever students, Huey, Dewey, and Louie, are shown a box containing three red hats and two
white hats. The students are then blindfolded and their teacher randomly chooses a hat and puts one on
each student's head. The two remaining hats are placed back in the box and the lid is closed.
The teacher removes the blindfold from Huey. Huey looks at the hats of the two other students and says
that he cannot say with certainty the color of his own hat. After hearing Huey, Dewey removes his
blindfold and looks at the hats of the other two students and says that he cannot say with certainty the
color of his own hat either.
After thinking, and without having his blindfold removed, Louie states that he knows with certainty the
color of his hat. Which one or more of the following statements are false? Note that any combination of
A, B, C, and/or D may be the correct answer.
A) Louie has enough information to determine the color of his hat without removing his blindfold.
B) Louie's hat can be white.
C) The three students can be wearing hats of the same color.
D) Both remaining hats in the bag can be red.
ANSWER:
B.
EXPLANATION: The key to solving the puzzle is figuring out what is known by the fact
that neither Huey nor Dewey can figure out the color of their hat. There are three scenarios where
Louie could have a white hat:
1) if Huey has a red hat and Dewey has a white hat
2) if Huey has a white hat and Dewey has a red hat
3) if both Huey and Dewey have red hats
We can rule out the first scenario because Huey would have known his hat was red (since there were only
2 white hats in the box). We can rule out the second scenario because Louie would have used the same
logic. And we can rule out the third scenario because Dewey would have known he was wearing a red hat
if Louie was wearing a white hat, because otherwise Huey would have seen that both Louie and Dewey were
both wearing white hats. Because Dewey did not know that he was wearing a red hat, Louie could not have
been wearing a white hat.
As for the other three statements, we know A is true because Louie cannot be wearing a white hat. C is
true as well as there is no information that would invalidate each student wearing a red hat. And
D is also true as there is no information that would invalidate Huey and Louie having white hats
(remember, Dewey doesn't remove his blindfold).
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
