MathDB

Let

n > 1

be an integer. There are

n

boxes in a row, and there are

n + 1

identical stones. A distribution is a way to distribute the stones over the boxes, in which every stone is in exactly one of the boxes. We say that two of such distributions are a stone’s throw away from each other if we can obtain one distribution from the other by moving exactly one stone from one box to another. The cosiness of a distribution

a

is defined as the number of distributions that are a stone’s throw away from

a

. Determine the average cosiness of all possible distributions.

Problem Statement