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How Many Hands Did She Shake?

David Cowan of Bessemer Venture Partners got 15 minutes of my time today, as I worked my way through this puzzle:

My wife and I went to a dinner party with four other couples. At the beginning of the party, some people shook hands. (Obviously, no one shook his or her own hand or spouse’s hand, and no one shook hands with the same person twice.) During the party I surveyed all the other people as to how many hands each one shook. I got different answers from everyone. What did my wife say?

Very entertaining if you like logic puzzles.  The solution is available, but try it on your own first.