MathDB

A beetle crawls along the edges of an

n

-lateral pyramid, starting and ending at the midpoint

A

of a base edge and passing through each point at most once. How many ways are there for the beetle to do this (two ways are said to be equal if they go through the same vertices)? Show that the sum of the numbers of passed vertices (over all these ways) equals

1^2 +2^2 +\ldots +n^2.

Problem Statement