10 students will stand equidistant from the center of the classroom. They are all holding hands to begin with. They must go and shake hands with all other students whose hands they are not holding. No handshake will occur more than once. how many handshakes will take place?

If we number the students 1 to 10 then number 1 student will not shake hands with number 2 or number 10, so he'll shake hands with the other 7 students.

Number 2 wont shake hands with number 1 or number 3 so he'll shake hands with the other 7.

hmm I cant think of an easy way to do this - counting will be a bit tedious

There is ten people holding hands. each is holding the hand of two people. that leaves eight people to shake hands with. so. 10 x 8 = 80.

80 hand shakes will take place.