Cube & Dice Questions with Solutions

Cube and dice questions test visualisation. Dice questions show one or more positions of a die and ask which number or symbol is opposite a given face. Cube questions describe a large painted cube cut into smaller identical cubes and ask how many small cubes have paint on three, two, one or no faces. For dice, if two positions share a common face, the faces in the same position relative to it are opposite each other. Faces that appear together in any single view can never be opposite. For a painted cube cut into n x n x n small cubes, 8 have three painted faces, 12(n - 2) have two, 6(n - 2)^2 have one, and (n - 2)^3 have none. These formulas solve most cube questions instantly. Practise the cube and dice questions below, each with a step-by-step solution.