Math Hats Puzzle - Solution

The Puzzle:

Math Hats
A scientist gathered four math students. They were then lined up so that each one could see the one in front of them but not behind them. Each had a hat placed on their head.

So the student in the back could see the hats of the three students in front, but the student in front could not see any hats.

"There is a red hat, a white hat, a blue hat, and a hat that is a duplicate of one of those colors," the scientist said.

Starting with the one in the back, each student was asked what color hat they were wearing. They all gave the correct answer!

What was the arrangement of the hats that made this possible?

Our Solution:

The two front students are wearing the same color hats, this is the only way all of the students could know what color hat they were wearing.


Call the colors A, B and C

The students in line have these colors: ABCC

First student sees "BCC" (two colors and a duplicate) so says "A"

2nd student sees "CC", so knows he is "B"

3rd student, using logic that the two previous students must have seen duplicates surmises he has a duplicate of the last remaining color and says "C"

4th student applies similar logic and says "C"
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