I'm tutoring someone 1st year arts math and they have been given this difficult question that I cannot mind boggel. It goes as follows: There are 6 couples at a party. Each can shake another persons hand once, but they can never shake their spouses hand. At the end of the night when a husband asks his wife and all the other people how many hands they shook he gets eleven different answers. Then the question asks how many hands did the husband's wife shake? I'm very confused by it. If anyone could help that would be great.

Answer 1

With 6 couples, there are 12 people. Considering that you don't want to shake hands with yourself or your spouse, you — or your spouse — could shake hands with 10 other people. The word, "could," implies potential, not actual activity. It could be that many of the others did not shake hands with all the potential persons.

Thus someone shakes 0 hands, someone 1, someone 2,...to someone 10, giving 11 different answers. However, I don't know how to determine which one is the wife.

I hope this helps. Thanks for asking.