# The Professor

by Philip Newman

The most hands any single person can shake is 8, and the least is 0. Since the range 0-8 has 9 values, all must be accounted for since the Professor got 9 answers.
The person that shook 8 hands shook every person's hand except for his/her own and his/her spouse. Thus, each person outside this couple shook at least one hand. Therefore, since we know someone shook 0 hands, the spouse must be the anti-social one.
Similarly, the 7 and 1 must be paired, the 6 and 2 must be paired, and the 5 and 3 must be paired. This leaves the wife as the person shaking 4 hands (and "unpaired" among the people asked, as the Professor did not ask himself).
As a side puzzle, can you figure out how many hands the Professor shook?