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How Many Handshakes?

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How Many Handshakes?, a selection of answers from the Dr. Math archives.

How Many Handshakes?
There are 40 people in a room. They shake each other's hands once and only once. How many handshakes are there altogether?

Handshake Problem
If you have n people in a group and each shakes everyone else's hand only once, how many handshakes take place?

Math Poster: Handshakes
If there are 15 people in the room and each person shakes hands with every other person, how many handshakes will there be?

Handshakes at a Party
At a party, everybody shakes hands with each other once. There are 45 handshakes. How many people are there at the party?

Shaking Hands - How many were at the party?
Each person shook hands with everyone else. Mr. Li shook hands with 3 times as many men as women. Mrs. Li shook hands with 4 times as many men as women.

Handshakes and Polygon Diagonals
If a polygon has 42 sides, how many diagonals does it have?

Handshake Problem Variant
Five couples go to a party and start shaking hands. One of the men shouts, "Stop! How many hands did you shake?" Every person gives a different answer...

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