 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...
