A Typical Weekly HomeworkAll Shook Up
Five couples met one evening at a local restaurant for dinner. Alicia and her husband Samuel arrived first. As the others came in some shook hands and some did not. No one shook hands with his or her own spouse. At the end Alicia noted that each of the other 9 people had shaken the hands of a different number of people. That is, one shook no one's hand, one shook one, one shook two, etc., all the way to one who shook hands with 8 of the people. How many people did Samuel shake hands with?

Note: This problem is a slightly modified version of Exercise #14, page 32, in The Heart of Mathematics, by Burger and Starbird, Key Curriculum Publishing, 2005.