MathDB

A bee travels in a series of steps of length

1

: north, west, north, west, up, south, east, south, east, down. (The bee can move in three dimensions, so north is distinct from up.) There exists a plane

P

that passes through the midpoints of each step. Suppose we orthogonally project the bee’s path onto the plane

P

, and let

A

be the area of the resulting figure. What is

A^2

Problem Statement