A professor and their spouse are at a party. At the party there are four more couples (overall five couples).

During the party couples shake hands with the following rules:
a. One does not shake hands with oneself.
b. One does not shake his/her spouse’s hand.

At the end of the party the professor asked all the other guests at the party (including their spouse) how many different people they shook hands with. Each person tells him a different answer (meaning, if one person said “five,” no one else said “five”).

With how many people did the professor shake hands?

Communicated by Michael Geike (who heard it in college in 1999).