Imagine three friends, let's call them Alice, Bob, and Carol. They are all wearing special hats, but they can't see their own hats. They can only see the hats that their friends are wearing.
Now, these hats come in two colors: red and blue. But there's a rule: at least one person has to be wearing a red hat, and at least one person has to be wearing a blue hat.
So, let's see what happens:
Alice is the first person, and she looks at Bob and Carol's hats. She thinks for a moment but says, "I don't know." That means she can't tell for sure what color her own hat is just by looking at their hats.
Then, Bob is the second person, and he also looks at Alice and Carol's hats. He thinks and says, "I don't know" too. Just like Alice, he can't figure out his hat's color by looking at the others.
Now, it's Carol's turn, the third person. But here's the clever part: she doesn't even need to look at the others' hats. She just confidently says the color of her own hat, let's say "red."
So, the third person, Carol, is wearing a red hat, and here's why she knew it:
Since Alice and Bob both said, "I don't know," that means they saw different hat colors on their friends. If Alice and Bob saw the same color hat on both of their friends, they would have known the color of their own hat.
So, Carol listened to Alice and Bob. If they both said, "I don't know," it means they saw different colors on their friends. Since there has to be at least one red hat and one blue hat, Carol knows that if Alice and Bob saw different colors, she must be wearing the color that's left. In this case, it's a red hat.
That's how Carol was so clever and figured out her hat's color without even looking at it! She knew it had to be red because of what her friends said.
Great job, Carol! You're really good at solving hat puzzles!