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Unformatted text preview: Answer 1) In general, if there are (k>1) children with mud on their forehead, the first k-1 times she asks the question, they will all say No, but then the kth time the children with muddy foreheads will all answer Yes. Suppose that there is only one child with mud on his forehead. He can see that nobody else has mud on his forehead. Also his mom announced that there is at least one child with mud on his forehead. He can combine his observation and facts to immediately recognize that he alone is dirty. As soon as the mom asks the question (first time), he will say yes. Now, if there are two children with mud on their forehead. The two muddy children can only see one child with mud on his forehead as they can’t see their own. So, the first time Mom asks the question, both will remain quite. After they see each other being quite, they will both realize that there is one more child with mud on his forehead. Both can see each other but not their own forehead will immediately realize that they are the one....
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This note was uploaded on 07/04/2011 for the course CIS 3360 taught by Professor Guha during the Fall '06 term at University of Central Florida.
- Fall '06