AMC 12 Cube Colouring Question

Explore a challenging mathematical puzzle involving cube coloring in this 31-minute video from Tom Rocks Maths. Dive into the problem of painting 27 unit cubes with three colors to form a larger 3x3 cube in three different monochromatic configurations. Learn step-by-step problem-solving techniques, including counting faces, identifying different cube roles, and analyzing possible partitions. Follow along as Dr. Tom Crawford from the University of Oxford guides you through the solution process, uncovering multiple valid answers to this intriguing combinatorial problem.

Introduction
The Problem
The Solution
Brilliant
Counting faces
Different roles
Invisible cube
Partitions
Possible Configurations
Solution
Second valid solution