Problem

Mr. and Mrs. Lewis hosted a party for n married couples. As the guests arrived, some peo...

Mr. and Mrs. Lewis hosted a party for n married couples. As the guests arrived, some people shook hands, Later Mr. Lewis asked everyone else (including his wife) how many hands each had shaken. To his surprise, he found that no two people gave him the same answer. If no one shook his or her own hand, no spouses shook hands, and no two persons shook hands more than once, how many hands did Mrs. Lewis shake? Prove your answer by mathematical induction.

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