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Part of 2023 Girls in Math at Yale

Problems(1)

Girls in Math at Yale 2023 Tiebreaker 2 - bee travels in 3D

Source:

10/7/2023
A bee travels in a series of steps of length 11: 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 PP that passes through the midpoints of each step. Suppose we orthogonally project the bee’s path onto the plane PP, and let AA be the area of the resulting figure. What is A2A^2?
combinatoricsgeometry