4

Part of 1972 Poland - Second Round

Problems(1)

n^3 unit cubes partiton a cube

Source: Polish MO Second Round 1972 p4

A cube with edge length

n

is divided into

n^3

unit cubes by planes parallel to its faces. How many pairs of such unit cubes exist that have no more than two vertices in common?

combinatoricscombinatorial geometry3D geometrygeometry