谁有本事~？！
A father tells his two children, a boy and a girl, to play in their backyard without getting dirty. However, while playing, both children get mud on theri foreheads. When the children stop playing, the father says "At least one of you has a muddy forehead", and then asks the children to answer "Yes" or "No" to the question. What will the children answer each time this question is asked, assuming that a child can see whether his or her sibling has a muddy forehead, but cannot see his or her own forehead? Assume that both children are honese and theat the children answer each question simultaneously.
Solution: Let s be the statement that the son has a muddy forehead and let d be the statement that the daughter has amuddy forehead. When the father says that at least one of ther two children has a muddy forehead he is stating that the disjunction "s or d" is true. Both children will answer "NO" the first time the question is asked because each sees mud on the other child's forehead. That is, the son knows that d is true, but does not know whether s is true, and the daughter knows that s is true, but does not know whether d is true.
After the son has answered "NO" to the first question, the daughter can determine that d must be true. This follows because when the first question is asked, the son knows that "s or d" is true, but cannot determine whether s is true. Using this information, the daughter can conclude that d must be true, for if d were false, the son could have reasoned that because "s or d" is true, then s must be true, and he would have answered "Yes" to the first question. The son can reason in a similar way to determine that s must be true. It follows that both children answer "Yes" the second time the question is asked.
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1 楼suntiger（windows2000超级补丁）回复于 2003-06-03 14:42:12 得分 0
好多单词不认得！Top
