Geometric Reasoning: Painted Cubes

Methods in this video

Tap a time to jump to where the video teaches that method.

1. 1

   Corners, edges, faces, inside: sort by place

   ▶ 0:40

   When to use it: A big cube or cuboid made of small cubes, asking about only some of them: the ones you can't see, the ones painted or not painted, the ones on the edges, the ones left after tunnels are cut, or how many a new outer layer needs.

   • The hidden cubes are inside. Peel all six faces: take 2 off each direction.
   • On the edges, set the 8 corners aside first. Each edge keeps n − 2.
   • Choose which places you need, count each one, then add. At least one painted face = all − inside.