Tuesday, July 24, 2012

Dinner Party

Fun little graph theory problem from my applied combinatorics homework today:

"Carolyn and Richard attended a party with three other married couples. At this party, a good deal of handshaking took place, but (1) no one shook hands with his or her spouse; (2) no one shook hands with himself or herself; and (3) no one shook hands with anyone more than once. Before leaving the party, Carolyn asked the other seven people how many hands she or he had shaken. She received a different answer from each of the seven. How many times did Carolyn shake hands at this party? How many times did Richard?"


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