But I'm terrible at these things...
10 people, so there's a 10x10 truth table. Conditions 1 and 2 imply that each person could shake hands with at most 8 people. That leaves 9 unique combinations (8 to 0). So there would have to be a duplicate to cover all 10 people, wouldn't there?
Then there's the problem of figuring out which one is the wife of the LAN administrator. Unless we accept that it's impossible for a LAN administrator to be married. ;-)