MathDB
Painting a Cube

Source: Tournament of Towns Spring 2016 Junior A-Level

February 23, 2017
combinatoricsgeometry3D geometry

Problem Statement

A designer took a wooden cube 5×5×55 \times 5 \times 5, divided each face into unit squares and painted each square black, white or red so that any two squares with a common side have different colours. What is the least possible number of black squares? (Squares with a common side may belong to the same face of the cube or to two different faces.) (8 points)
Mikhail Evdokimov