How to get better at cube counting on the DAT
Updated October 29, 2026
Cube Counting shows a figure made of identical cubes glued together and painted on every exposed side except the bottom. Each question asks how many cubes have exactly a given number of painted sides.
Cube counting rewards a careful, systematic method more than any spatial talent. Several questions usually use the same figure, so one careful tally answers them all.
- Questions
- 15, the fifth subtest of the PAT
- Answer choices
- 5 counts
- Time to aim for
- About 30 seconds each, with the tally done once per figure
- What it tests
- Systematic counting in 3D
The method, step by step
- 1
Know the rules
All cubes are the same size. After being glued together, the figure is painted on every exposed side except the bottom it rests on. The only hidden cubes are the ones needed to support cubes you can see.
- 2
Make a tally table
On your noteboard, write rows for 0, 1, 2, 3, 4 and 5 painted sides. A cube can never have 6, because the bottom of every cube touches either the surface or another cube.
- 3
Go in a fixed order
Count column by column, from the back left to the front right, and from the top of each column down. A fixed order keeps you from skipping or double counting cubes.
- 4
Count each cube's painted sides
For each cube, check its top and its four sides. A side is painted only if it touches nothing. The bottom is never painted.
- 5
Check your total
Add up the tally and compare it with the number of cubes in the figure, including hidden support cubes. If they don't match, you skipped or double counted a cube.
Try one
A real medium-difficulty question from PAT Grind. Use the method above, then check the worked explanation.
Cube Counting tips and tricks
Top cubes have their top painted
The top cube of every column always has a painted top, plus one painted side for each side that sticks out. A lone tower cube with nothing beside it has 5 painted sides.
Wall cubes in the middle are usually 2
A cube in the middle of a one-cube-thick wall, with neighbours on both sides and above, has only its front and back painted.
Don't forget support cubes
If you see a cube resting on the third level, the two cubes below it exist even if you can't see them. They count, and they often have fewer painted sides than you'd guess.
Tally once, answer many
Do the full tally the first time you see a figure, even if the question only asks about one number. Every other question on that figure then takes seconds.
Common mistakes and how to fix them
A two-week plan to improve
Days 1 to 3: build the tally habit
Do 15 cube counting practice questions a day with a full tally every time, even when it feels slow. PAT Grind's explanations show the tally level by level so you can see exactly where you slipped.
Days 4 to 7: bigger figures
Keep going in adaptive mode as figures get taller and wider. Always check your tally total against the cube count.
Days 8 to 14: speed
Do sprint sessions. With a reliable tally, accuracy should stay near 100% as you speed up.
Measure it
Take a check-up before and after to see your cube counting score change.
Pacing on test day
Budget about 8 minutes. Most of the time goes into the first tally for each figure. The follow-up questions take seconds.
Questions
Is the bottom of the cube painted in DAT cube counting?
No. The figure is painted on every exposed side except the bottom it rests on, so bottom faces are never painted.
Do hidden cubes count?
Yes. The only hidden cubes are the ones needed to support cubes you can see, and they count like any other cube.
What's the fastest way to do cube counting?
A tally table with rows for 0 to 5 painted sides, filled in once per figure in a fixed order. It's slower on the first question and much faster on the rest.
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PAT Grind is an independent study tool. It is not affiliated with or endorsed by the American Dental Association, which administers the Dental Admission Test (DAT).