Suppose you begin with a stack of n $>=2$ sheets of paper

You split this pile until you have n piles of $1$ sheet paper

Each time a split is made, you will multiple the number of sheets in each

of the smaller piles. Ex: if your split resulted in k sheets and l sheets, you

will compute kl

Prove that no matter how you split the piles, the sum of products computed

at each step is:

n$($n$1)$

$2$