My wife and I attend a party with four other couples. When we arrive there’s a certain amount of hand-shaking, but no one shakes his own hand and no husband shakes his wife’s hand. I ask the nine other guests how many hands each shook, and I get nine different answers. How many hands did my wife shake?
Solution: There must be exactly one person who shook 0, 1, 2, ..., 8 hands. The person who shook 8 hands shook everyone's except his/her spouses'. So everyone shook atleast one hand except for the spouse, who therefore must have shaken 0 hands. So 8 is paired with 0. Similarly, 7 is paired with 1, 6 with 2, 5 with 3, and 4 is left alone. The only person who didn't have a spouse in the people you asked is your wife, so your wife shook 4 hands.