2000-01 Solution

• 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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