More Hat Logicians

Logic Level 1

Alice, Bob, and Carol—who always tell the truth and are perfectly logical—have a box with two black hats and two white hats.

Each person is randomly assigned a hat such that they can see the other two people's hats but not their own.

Alice says, "I do not know the color of my hat."

Can Bob and Carol now figure out their own hat colors?

Note The three logicians are close friends, so each of them knows that they are all perfectly logical and always tell the truth.

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