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Can the blind woman determine the color of the hat on her head? Question
Three perfectly logical women, one of them blind, walk into a completely dark room full of hats. They all know that two of the hats are red and the rest are black. Each woman randomly selects a hat and puts it on. Then they all walk out of the room.
The 1st sighted woman looks only at the hats worn by the other two and says, “I don’t know the color of the hat on my head.” After hearing this, the 2nd sighted woman looks only at the hats worn by the other two, thinks a bit, and says, “I don’t know the color of the hat on my head, either.”
After hearing both sighted women speak, can the blind woman determine the color of the hat on her head?
Explain your answer.
Clarification:
You can assume that all 3 women know everything that is mentioned in the above puzzle.
1 answer
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Apr 10, 2026 at 04:19 |
spoiler
There are many black hats and only two red ones. If you see two red hats you know yours is black; if you see anything else, you cannot know for sure what you're wearing.
If the blind woman had a red hat:
- Woman 1 would see the red hat on the blind woman. To not know her own hat color, she would have to see a black hat on woman 2.
- Woman 2 would see the red hat on the blind woman. She is perfectly logical, so she would know from the first response that her hat can't also be red and thus it is black.
- But woman 2 doesn't know what color her own hat is.
- Therefore the blind woman couldn't have a red hat.
- The blind woman is perfectly logical, so she now knows that she has a black hat.
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