Ask Dr. Math 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...