Block counting questions hide some of the cubes behind the ones in front, so counting what you can see is always wrong. The fix is a method rather than sharper eyes: find the base, give every column a height, and add the heights.
Quick answer: block counting asks how many identical cubes are in a 3D pile, including the ones hidden behind and underneath. Papers assume the pile is solid and supported, so every cube you can see on an upper level has a cube beneath it holding it up. The reliable method is to work out the shape of the base, write down the height of each column, and add the heights rather than counting cubes.
A block counting question shows a pile of identical cubes drawn in three dimensions and asks how many cubes are in the pile altogether. The catch is that the drawing hides some of them: cubes at the back and underneath are covered by the ones in front, so a child who counts only the cubes they can see always gets it wrong.
Papers set these up in a few ways. Sometimes the pile is a rough Z shape or T shape and the question is a plain total. Sometimes you are asked how many cubes are hidden, or how many more cubes you would need to finish off a full box shape. In non-verbal reasoning papers you may also be shown four or five drawings labelled A to D and asked which ones show the same object.
Every version rests on one assumption that exam papers make and rarely spell out: the pile is solid and supported. Nothing floats in mid air, so if you can see a cube sitting up on a second level, there is a cube underneath holding it up even though you cannot see it.
Counting cubes one by one is slow and unreliable. Counting columns is fast and self-checking.
Work out the shape of the ground floor first, usually a small rectangle such as 3 by 2 or 3 by 3. That tells you how many columns there are before you count a single cube.
Go along the front row, then the next row back, writing down how tall each column is: 3, 2, 1 and so on. A hidden column still has a height, and the cubes resting on it tell you what it is.
The total is just the sum of the column heights. Adding six or nine small numbers is far more accurate than trying to count twenty cubes in a picture.
Cover the answer, count with your child, then check the reasoning.
Start with the ground floor. The base is a neat rectangle three cubes wide and two cubes deep, so the bottom level has 3 × 2 = 6 cubes, even though the two at the back are almost completely hidden.
Then the level above. Two cubes sit on top, at the left-hand end. Nothing else is up there.
6 + 2 = 8, so the answer is C. The commonest wrong answer is 6 or 7, from counting only the faces you can actually see.
Nine columns, because the base is 3 by 3. That is the whole trick: the moment you know the base, you know you are adding nine numbers, and you know none of them can be zero.
Now read the heights. The tallest corner is 3 cubes high. Next to it, two columns are 2 high. Every remaining column is a single cube: there are six of them, including the ones hidden behind the tall corner.
3 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 = 13, so the answer is C. Notice that six of the 13 cubes are wholly or partly hidden by the ones in front.
Work out the finished box first. 3 × 2 × 2 = 12 cubes when it is complete.
Now count what is there. The base is a full 3 by 2 rectangle, so that is 6 cubes. On the second level there are 3 more. Total so far: 9.
12 − 9 = 3, so the answer is B. Doing it the other way round, by trying to count the empty spaces directly in the picture, is where most mistakes come from.
Once counting is reliable, move to cube rotation questions, which use the same counting skill as a first line of elimination, and to spatial reasoning cube nets for the other half of the 3D syllabus.
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A full Non-Verbal Reasoning paper at real exam difficulty, including spatial-style puzzles, with a printable answer sheet and a worked answer key for every question.
Download the paperAll eight spatial reasoning question types in one place, with diagrams, the solving rule for each and which exams test them.
Read the spatial reasoning guideFree English, Maths, Verbal Reasoning and Non-Verbal Reasoning papers, each with worked answers, plus vocabulary flashcards and interactive tools.
Browse the printablesWork out the shape of the base first, usually a small rectangle such as 3 by 2 or 3 by 3, then give every column in that base a height, including the columns you cannot see. Any cube drawn on an upper level must be supported by a cube underneath, so its column is at least that tall. Add the column heights to get the total.
Exam papers assume the pile is solid and fully supported, so nothing floats in mid air. If a cube appears to be sitting up on a second or third level, there is a hidden cube directly beneath it. That single assumption is what lets you count cubes you cannot actually see.
They are the same question type with a memorable outline: the pile is arranged so that from above it looks like a letter Z or a letter T. The letter shape only tells you the shape of the base, which is exactly the information the column method needs, so treat them like any other pile.
Count the cubes in the stem and in every option first, because a rotation never changes the number of cubes, so any option with a different total is wrong immediately. Then compare arm lengths and proportions, and only then try to rotate the shape in your head. Cube rotation questions are covered in more detail on our cube rotation page.
It sits inside non-verbal reasoning, in the spatial part of GL-style papers. Our spatial reasoning guide lists it as one of the eight spatial question types used in 11+ style exams, and it is the type most guides leave out.
Use real interlocking cubes or Lego. Build a pile, ask your child for the total, then take it apart and count. Building the pile themselves is the fastest way to understand that hidden cubes exist, because they put them there. After that, move to drawn questions such as those in our free Non-Verbal Reasoning practice paper.
Keep going: the full spatial reasoning guide lists all eight question types, cube rotation reuses the counting check, nets and cubes covers folding, and the free Non-Verbal Reasoning practice paper is a printable PDF with worked answers.