Problem:
At a gathering of people, there are people who all know each other and 10 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 20 people who know each other shakes hands with 10 people. Each of the 10 people who know no one shakes hands with 29 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