At the opening of the United States Supreme Court, each justice shakes hands with all the others.

a. How many justices are there?

b. How many handshakes do they make?

A. There are 9 members of the Supreme Court, with one Chief Justice and eight associates justices.

b. With 9 justices and all of them shaking their hands once, they would have to make 36 handshakes, because they wouldn't have to handshake the same person again, and for the first justice, they would have to shake either other hands, with the second one only needing to shake seven hands, the third making only six handshakes and so on, until one of them only has to make one handshake. In an equation, this is 8+7+6+5+4+3+2+1, which gives you the sum of 36. The justices have to make 36 handshakes total.