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.