Unsuspecting, I picked this classic baby toy up at a local charity sale. As it turned out, it harbours a little combinatorial challenge that I never suspected! The toy is a set of five stacking cubes with a different face on each face. Save for size, the cubes are all the identical; flower, hexagon, square, triangle, circle, and the open face.
As I was playing with it I thought, “Can I stack the cubes such that no two shapes coincide?”. Fun!
This is the same as asking if you can orient 5 6-sided (axis-aligned) dice so that no two dice show the same number on the same side.
Is there more than one way to do it? Can it be done with 6 stacking cubes?