Question 886544
Do this yourself through inductive thinking.  Start with just three people.   How many handshakes?  To do this, draw the vertices of a triangle (three points, regular polygon).  Next, draw the four vertices of a square, and assuming each point represents a person, draw and count all the handshakes.  How many handshakes?  Keep going; now, the vertices of a pentagon.  How many handshakes?  Pentagon shape vertices?   How many handshakes?  Keep doing this.  Look for a rule inductively for vertices and "handshakes".


Also, look at the <b>Mesh</b> part of the article, <a href="http://en.wikipedia.org/wiki/Fully_connected_network#Mesh">http://en.wikipedia.org/wiki/Fully_connected_network#Mesh</a>