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CIS 3360 Homework 4
Due Date: November 6, 2006
Worth: 4%
1. (5+5+10+5 = 25)
Several children are playing together outside. After playing they
come inside and their mother says to them,
at least one of you has mud on your head
.
Each child can see the mud on others but cannot see his or her own forehead. She then
asks the following question over and over:
can you tell for sure whether or not you have mud on your head
?
Assuming that all of the children are intelligent, honest, and answer simultaneously, what
will happen in the following three scenarios?
i.
Suppose that there is exactly one child with mud on their forehead. Explain why, after
the mother asks the question once, the muddy child is able to answer yes and the other
children cannot answer yes.
ii.
Suppose that there are exactly two children with mud on their forehead. Explain why,
after the mother asks the question once, no child is able to answer yes. Also explain why,
after the mother asks the question the second time, the children with mud on their
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 Fall '06
 Guha

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