A rather amazing puzzle that a friend posed to me last year:

Four couples attend a party. Some of them shake hands when they meet. Afterwards I ask everyone else how many hands they shook. I get a different number from each person. How many hands did my wife shake?

It's amazing because there seems to be far too little information to solve it, yet there's a unique answer. And there's no "trick" either: no one shakes their own hand or their spouse's hand; the seven people I ask each answer my question with a different integer (0-6).

Hint: draw a diagram. Challenge: consider a different number of couples.

(this puzzle turns out to have been in a Martin Gardner "Mathematical Games" column decades ago; cf. OnSomethingness (2000-01-17), No Concepts At All (2001-02-22), GatewaysToMathematics (2004-05-20), ...) - ^z - 2010-05-06