What Color Hat?

In this puzzle, we ask you to use logic to help each boy figure out the color of his hat.

Lucy had four hats, two red and two blue. She showed them to her three friends, then made them stand one behind another and shut their eyes.

Hats

Lucy put a hat on each of their heads. Then she hid behind a wall and put on the last hat. “To keep all the hats, just one of you must tell me what color hat you are wearing. You can open your eyes, but you must not turn around and look at the boy behind you,” she said. "Only one person should call out, and no one must talk apart from the person calling out the color of his own hat."

Each boy could see only the color of the hat or hats in front of him. How could each be sure to guess the color of his own hat correctly?

Course:

Math [1]

Result/Solution(s)

Solution: What Color Hat? Math Puzzle

To solve the puzzle, the boys need logic, teamwork, and trust.

If the boy at the back (Boy 3) could see two hats the same color, he could be sure that his hat was the other color, one of these two scenarios:

Lucy	Boy 1	Boy 2	Boy 3
Red	Blue	Blue	Red
Blue	Red	Red	Blue

If the boy at the back said nothing, the boy in the middle (Boy 2) would know that his hat was a different color from the boy at the front; that is, one of these four scenarios:

Lucy	Boy 1	Boy 2	Boy 3
Red	Blue	Red	Blue
Blue	Red	Blue	Red
Blue	Blue	Red	Red
Red	Red	Blue	Blue

So, Boy 2 waits for a moment, then, if Boy 3 remains silent, calls out the opposite color of the hat on the head of Boy 1.

math [2]
Math Puzzle [3]