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Non-verbal Reasoning · Spatial

Count cubes in a structure

Infer the total cubes in a pictured structure, including supported hidden cubes.

Practise it now

Some cubes are buried where you cannot see them. Spin the model and work out how many are hidden.

It covers most of this skill rather than all of it.

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A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Finding the buried cubes

This stack is built from 34 cubes standing on 16 squares. A hidden cube is one that is completely boxed in, so you could not see it from any side. Work along the stack and find them.

3 cubes in this stack are walled in on all four sides with a cube on top, so they are hidden.

Cube stack viewed from the default viewpoint. Cubes are at (0, 0, 0); (1, 0, 0); (2, 0, 0); (3, 0, 0); (3, 1, 0); (3, 2, 0); (0, 0, 1); (0, 1, 1); (1, 0, 1); (1, 1, 1); (1, 2, 1); (2, 0, 1); (2, 1, 1); (2, 2, 1); (3, 0, 1); (3, 1, 1); (0, 0, 2); (1, 0, 2); (1, 1, 2); (1, 2, 2); (2, 0, 2); (3, 0, 2); (3, 1, 2); (0, 0, 3); (0, 1, 3); (1, 0, 3); (1, 1, 3); (1, 2, 3); (2, 0, 3); (2, 1, 3); (2, 2, 3); (3, 0, 3); (3, 1, 3); (3, 2, 3). The count options are option 1 count 6. option 2 count 3. option 3 count 4. option 4 count 5.

  1. 6
  2. 3
  3. 4
  4. 5

Answer: 3

How you get there

The stack holds 34 cubes. Check only columns away from the edges, then test each level for a roof and four walls. The boxed-in positions are column 2 from the left and 2 from the back, level 1; column 3 from the left and 2 from the back, level 1; column 2 from the left and 3 from the back, level 1. At each listed position there is a cube above and one to the left, right, front and back, while the table covers the base. That gives 3 cubes, so the answer is 3.

Why the other answers tempt

A cube at the back of the stack is not hidden. You could walk round and see it, so it does not count.

If they are stuck, say this

Take one column at a time. A cube in that column is hidden when there is a cube above it and a cube in each of the four columns beside it at the same level.

Now do it live in Block Builder

What this exercise is doing

Block Builder

Some cubes are buried where you cannot see them. Spin the model and work out how many are hidden.

Counting a solid means counting what you cannot see. This model has 15 cubes in total and 1 of them are completely buried - a buried cube has cubes on all four sides of it and a cube on its roof, and its base is flat on the table, so no face of it is left showing however far you spin the model. Work stack by stack from the plan, never from the picture alone.

What to say if they get stuck

  1. Drag to spin the whole model right around. If you can spot a cube from ANY side, it is not hidden.
  2. A cube is hidden when it is walled in on all four sides with another cube on top of it. Only the plan grid can prove it.
  3. Count every cube first, then count the ones you can actually see. The gap between them is the hidden pile.

Open Block Builder on its own page to share it

What usually goes wrong here

  • Counts only visible cubes where support implies hidden cubes.

This is the wrong answer 11+ papers are built to offer, so it is worth watching for directly: a child who does this will look confident and still lose the mark. If it keeps happening on count cubes in a structure, the fix is the misunderstanding rather than more questions.

Related non-verbal reasoning skills

All non-verbal reasoning 11+ skills

Questions parents ask about count cubes in a structure

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

Infer the total cubes in a pictured structure, including supported hidden cubes. It is one of 22 named non-verbal reasoning skills in the 11+, in the spatial strand, and this page carries 1 interactive exercise that practises it.

One wrong answer is a slip, the same wrong answer every time is a habit

A free diagnostic looks at which mistakes repeat across all four subjects, not just whether count cubes in a structure was right on the day.

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