Whole Lotta Hand Shakin' Goin' On

Jan 24, 2005

RAY: John and Mary are married. They agree to go out to dinner with four other married couples. So, there are five couples, or ten people, altogether.

They arrive at the restaurant and, because there are some people who don't know other people, there are some handshakes that take place, and introductions. Anyone who doesn't know somebody will shake hands with that person. People will not shake hands with someone they already know, and, of course, you don't shake hands with your own spouse.

TOM: Unless you're meeting her for the first time.

RAY: Right. At the end of the dinner, John asks all the people there, including his own wife, how many hands each of them shook.

He gets the following answers: 0,1,2,3,4,5,6,7, and 8.

There are 9 other people there, and they give him 9 different answers.

Here's the question: How many hands did John's wife Mary shake?

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