## 2000-01 Solution

(courtesy of Jacob Corbin <jacob@neurometrics.com>)

- At most the partygoers could shake eight other people's hands.
- The number of handshakes reported by each person must have been zero to
eight, and the mathematician must have shook the same number of hands as
someone else.
- The person who shook eight hands must have a spouse who shoke no-one's
hand, since this is the only way someone could shake eight hands and have
everyone's answer be different.
- Similarly, the person who shakes hands with seven people must have the
spouse who shook hands with one person.
- The sum of each couple's handshakes must equal eight, and since everyone
answered a different number, the mathemetician and his/her spouse (how
un-sexist of me!) must both have shook
**four** hands (since the mathematician
didn't ask his/her self).

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