### June 2006: Shaking hands

Mr. and Mrs. Dickinson invited four couples to their house for a dinner party. Some of the guests knew each other, and others did not. Those who did not know each other shook hands upon meeting. Mrs. Dickinson happened to notice something curious: each person (not including herself) shook hands with a different number of people (one person shook no hands, one person shook one hand, one person shook two hands, etc.). How many hands did Mr. Dickinson shake?

Hint: Mr. Dickinson did not shake eight hands, for if he did, then no one could have shaken zero hands.

Dickinson College students can submit their answers to Dave Richeson. The list of solvers will be posted at the end of June.

Hint: Mr. Dickinson did not shake eight hands, for if he did, then no one could have shaken zero hands.

Dickinson College students can submit their answers to Dave Richeson. The list of solvers will be posted at the end of June.

**From:**"Effective Problem Solving, 2^{nd}Edition," Marvin Levine, Prentice-Hall, 1994
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