Handshake problem

Greet & Shake hands with some of your colleagues at your table.

If everyone at your table shakes hands with each other, how many handshakes would you have ? Show us how you would prove it to your friend. Try the handshake applet at GMU’s COMPLETE MATH


At a birthday party, every child shakes hands with every other child. If 190 handshakes take place, how many people were at the party?


After organizing the data in a table it was possible to find the rule. The rule written in the form of a formula is used to find a given number to determine the handshakes. The rule consists of Symbolic representation n(n-1)/2=h where n is the number of people shaking hands and h the total number of handshakes. The 1 is subtracted from the number since there will be no handshake by one person. When the class consists of 20 students the rule makes it easier to calculate the number of handshakes rather than drawing pictures or filling in the numbers in a chart. Over all, the formula shortens the continuous computation of numbers. For example,


20(20-1) =h

20 (19)  =h

380/2 =h

When there are 20 students

there are 190 handshakes.

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