There are three red hats and two black hats on a hatstand.

Melba, Fran, and Brent line up in a single file line, and the mad Hatter places a hat on each person’s head and tosses the rest into a box where no one can see them.

The Mad Hatter takes off Brent's blindfold. Brent, who could see Fran’s hat and Melba’s hat, says,
“I don’t know what color my hat is.”

The Mad Hatter takes of Fran's blindfold. Fran, who could only see Melba’s hat, says, “I heard what Brent said, but I don’t know what color my hat is.”

As the Mad Hatter moved to take off Melba's hat, she said, “I don't need you to take off my blindfold. I know what color my hat is.”

What color is Melba’s hat and how does she know?

Let me try this one. The only way Brent would know her hat color is if both Fran and Melba had black hats (since there were only two black hats in the pile). So, now everyone knows that Fran and Melba don't both have black hats. The options for Fran and Melba are Black/Red, Red/Black, or Red/Red. If Fran saw a Black hat on Melba, she would know that her own hat must be Red (since it can't be Black). However, Fran says that she can't tell her own hat color after seeing Melba's. Therefore, Melba's hat must be Red since Fran couldn't determine her own hat color from knowing Melba's. Thus, Melba knows her hat is Red because she believes Brent and Fran are logical about such things.

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