# How the number of binary collisions increases with centrality faster than the number of participant in heavy ion collisions?

How the number of binary collisions increases with centrality faster than the number of participant in heavy ion collisions at different particle colliders?

It's combinatorics, a variant of the "handshake problem." Suppose you are at a party with $N$ other people and you want to shake everyone's hand: you're going to give $N$ handshakes. But so is everyone else, so the total number of binary interactions handshakes will be $\frac12N(N+1)\approx N^2/2$. You can do this by hand for small parties: