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n couples arrived at a party and were greeted by the host and the hostess at the door. After several rounds of handshaking the host

n couples arrived at a party and were greeted by the host and the hostess at the door. After several rounds of handshaking the host asked the guests as well as the hostess (his wife) to indicate the number of hands each one of them had shaken. He got 2n+1 different answers. Given that no one shook hands with his or her own spouse, how many hands had the hostess shaken? Explain your answer.

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