Who is asking: Student
Level: Secondary

Question:
Here is the question:

There are 40 people at a party. 1 host couple, a mom and her daughter. There are 19 other guest couples, composed of moms and their daughters. The Host couple shakes hands with everyone except each other. Each guest mom shakes hands with everyone but their own daughter. Each guest daughter shakes hands with everyone except their own mom. A hand shake between two people is considered to be one handshake. HOW MANY HANDSHAKES ARE THERE? If you can figure out the answer and can provide a equation and/or proof (ie diagram...) then you would be brilliant. Anyone of this stature please feel free to email the solution to me: glamnickcage@yahoo.com

-THANKS A WHOLE LOT!

Hi Nick

Each of the 40 people at the party shakes hands with 38 people, everyone except herself and her mother or daughter. Thus there seem to be 40x38=1520 handshakes. But with this procedure you have counted each handshake twice, once for each of the two people shaking hands. Thus there are actually half that many handshakes, that is 40x38/2=760.
  There is a somewhat related question that we were asked a while ago that you might find interesting. It is called Diagonals in a polygon

Cheers
Penny