Medal to the best answer.

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

Question

Medal to the best answer.

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

anonymous · Answer

I've heard of this problem before, I think you'll need quadratics. :/ Sorry, can' help here as I haven't learnt it yet. Good luck!

mathmate · Answer

You're probably doing graph theory.
If you are, think of degree of complete graphs.

anonymous · Answer

$$\left(\begin{matrix}n \ 2\end{matrix}\right)-2=66$$
then 
$$\left(\begin{matrix}n \ 2\end{matrix}\right)=64$$
implies that n=12

lichking · Answer

12 is correct

lichking · Answer

but i need an explpicit method

anonymous · Answer

I regret sir, i only know this method

mathmate · Answer

Let there be n people at the party.
Each person shook hands with (n-1) others.
Total of n(n-1) handshakes, but we double counted because it takes two people to make a handshake.
So we end up with
n(n-1)/2=66
Solve for n.