Question

At a party, everyone shook hands with everybody else. There were 435 handshakes. How many people were there at the party?

Answer 1

we can think this problem as a complete graph problem.

In a 4 vertices complete graph, no. of edges are n(n-1)/2, i.e. 6

Similarly here n(n-1)/2=66

so n(n-1)=132,

hence n=12.