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<b>Prophecy</b>, I will try to be a clearer.
The guy in the back can see the hats of the two people in front of him.
- If he were to see two white hats in front then he would know he was wearing a red hat and he would. Since he did not say anything we know that he does not see two white hats in front of him.
- If he were to see two red hats he could be wearing a red or a white hat.
- If he were to see a red and a white hat then he could be wearing a red or a white hat.
The important thing to note so far is that the guy in the back did not say anything so this means that he does not see two white hats in front of him.
The guy in the middle can only see your hat but he also knows that the guy behind him can't tell what hat he (the guy behind) is wearing. The guy in the middle, therefore, knows that him and you are not both wearing white hats.
- If the middle guy sees you were wearing a white hat then the middle guy knows that he is not wearing a white hat (he would know that he is wearing a red hat) and he would say something. He knows this because had the guy in back see two white hats he would have said something.
You are also smart so you know that the guy in the back would have said something had he see two white hats. That leaves you with three options to consider:
1. Middle = Red, You = White
2. Middle = White, You = Red
3. Middle = Red, You = Red
You also know that if your hat was white (option 1) then the middle guy would know that his had is red and he would have said something. But he did not say something. This leaves you with the other two options. In both of these options your hat is red.
Answer: You know your hat is red.
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Sticky The Stickman
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