Cube Counting shows a figure built from identical cubes glued together. Every exposed side is painted except the bottom, and you count how many cubes have exactly a given number of painted sides.
PAT Grind has 1,200 cube counting questions at three difficulty levels. Each one is checked by an independent solver and comes with a step-by-step explanation.
How the questions work
- The figure rests on a surface, so bottom faces are never painted.
- The only hidden cubes are the ones needed to hold up other cubes.
- A side is painted only if it touches nothing: no other cube and not the surface below.
Strategy
- Make a quick tally table with rows for 0 to 5 painted sides, then go column by column so you don't double count.
- Start with the top cube of each column. It always has its top painted, plus any side that sticks out.
- Cubes buried in the middle of a wall usually have only two painted sides, front and back.
- One tally answers every question about the same figure on the real test, so it pays to be careful once.
Common traps
- Counting the bottom face.
- Forgetting the hidden support cubes underneath.
- Double counting a cube seen from two sides.