Cube counting looks intimidating, but it's one of the most learnable and consistent sections on the PAT. With a simple system you can turn it into easy points. Here's the method.
The setup
A figure is built from glued cubes and painted on every exposed surface except the bottom that rests on the table. Each question asks how many cubes have exactly N painted faces — including cubes you can't directly see.
The tally method
Make a quick mental (or scratch-paper) table:
| Painted faces | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Cubes |
Then scan the figure once, assigning each cube exactly one number. No double counting, no skipping.
Count the total number of cubes first — including hidden ones. Your tally has to add up to that total. It's a built-in error check that catches almost every mistake.
Two rules that trip everyone up
- The bottom isn't painted. Cubes in the bottom layer have one fewer painted face than they look like they should.
- Hidden cubes exist. Cubes tucked behind or beneath the stack are usually your zero-painted-face answers. Hunt for them deliberately instead of counting only what's visible.
Practice that builds the skill
The fastest way to get good is to drill figures you can rotate, so hidden cubes stop hiding. In the explanation, check each cube's painted-face count against your tally — you'll quickly stop making the same error.
For a sample question and the full strategy, visit the DAT Cube Counting guide.