Counting Cubes Puzzles
How many cubes are in the stack? The ones you can't see still count.
Practice
How many cubes are in this solid? Every cube rests on the floor or on another cube.
Pick A, B, C or D.
Count stack by stack
The mistake almost everyone makes is counting the cubes they can see. In a stack, most of the cubes are hidden under others. The fix is to count columns, not cubes:
- Look at the floor and find each square that has cubes on it.
- For each one, find the top cube and count down to the floor: that is the stack's height.
- Add up the heights.
Why every answer is certain
Each puzzle is checked by computer so that the top of every stack is visible. Since cubes can't float, a visible top cube tells you exactly how tall its stack is, and the total can only be one number.
Counting cubes questions
Do hidden cubes count?
Yes. Every cube sits on the floor or on another cube, so a cube you can see at the top of a stack means every cube below it is there too, even if you cannot see them.
What is the quickest way to count?
Count stack by stack. For each square of the floor, find the top cube and read how tall the stack is, then add the heights. Counting faces or visible cubes misses the hidden ones.
Can a cube be completely hidden?
In these puzzles, every stack's top is visible, so every cube can be worked out. That is what makes each answer certain.
Are counting cubes questions used in tests?
Yes. Block counting appears in spatial ability tests, school maths (volume with unit cubes) and some job aptitude tests.
More 3D practice: cube nets, mental rotation and the 3D puzzle game.