Jan and his wife invite three couples to dinner. Some shake hands to greet each other, others do not. At the end of the evening, Jan asks each person how many hands they shook and gets different answers from all of them (Jan excluded). No person shakes their own hand, the hand of their spouse, or the hand of the same person multiple times.
How many guests did Jan's wife shake hands with?
Jan asked seven people and got seven different answers. Since no one shook hands with his or her spouse, only one person shook hands with all six people and one person did not shake hands with anyone. These two people must be a married couple, since everyone else’s hand was shaken at least once.
So, the person who answered "five" shook hands with everyone except the person who shook "zero" hands. Thus, five people have already shaken two hands. So for the answer "one," only the spouse of the person who answered "five" remains. According to the same principle, the person who answered "four" must be married to the person who shook hands with two people. This leaves the answer "three" for Jan's wife.