Problem:
At a gathering of people, there are people who all know each other and people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?
Answer Choices:
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Solution:
Each of the people who know each other shakes hands with people. Each of the people who know no one shakes hands with people. Because each handshake involves two people, the number of handshakes is .
The problems on this page are the property of the MAA's American Mathematics Competitions