100 people are sitting in a circle, where every person can see the 99 other people. All of them are wearing hats but they can only see the hats of other people, meaning they can't see their own hat. There are 99 white hats and 100 black hats. People start saying what they know about the color of their own hats. The game ends when a person says the color of their hat with clear knowledge of it.
- The 1st person says: "I don't know the color of my hat."
- The 2nd person says: "I don't know the color of my hat."
- The 3rd person says: "I don't know the color of my hat."
Everyone gives the same answer until it is your turn. You are the 100th person. All you see is black hats. What is the color of your hat?
(I have developed an answer to this question, but it doesn't feel right. I would like you to explain where exactly I have made a mistake in my answer - if I have. I would also encourage you to try the question on your own first.)