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๐Ÿ“„ Spatial reasoning, question type 6

Fold and punch: paper folding questions explained

A square is folded, a hole punch goes through every layer, and your child has to picture the opened sheet. Two rules cover every version of the question: holes double with each fold, and each new hole is a mirror image across the fold line.

Folded punched paper opening out
One fold, one punch, two holes: mirrored across the fold.

Quick answer: in a fold and punch question a square of paper is folded, holes are punched through all the layers, and you pick the drawing of the opened sheet. Every fold doubles the number of holes, so one fold gives two layers, two folds give four and three folds give eight. Each hole gains a partner mirrored across the fold line, and you unfold the folds in reverse order. Counting alone eliminates most wrong options.

๐Ÿ•ณ 1 fold = 2 holes๐Ÿชž Mirror across each fold๐Ÿ” Unfold in reverse order๐Ÿ“š GL and CAT4 figure analysisโœ‚ Easy to practise at home

What fold and punch questions look like

Fold and punch, also called hole punch or paper folding, is one of the most reliably scored spatial question types once a child has seen it twice. A square of paper is folded once, twice or occasionally three times. A hole punch goes through all the layers. The paper is then opened out, and your child picks the drawing that shows where the holes ended up.

The same skill appears under a different label in the CAT4, where the figure analysis questions ask you to visualise a punched and folded sheet, and in some GL non-verbal reasoning papers as part of the spatial section. A related question type folds a flat shape into a solid instead: that one is covered on the nets and cubes page.

Folded paper with one punched hole
Folded in half, one hole punched
Arrow meaning unfold
Open it out
The unfolded paper with two holes
Two holes, mirrored across the fold line

The two rules that solve every one

Rule one: holes double with every fold. One fold means two layers, so one punch makes two holes. Two folds mean four layers, so one punch makes four holes. Three folds mean eight layers and eight holes. Two punches through a twice-folded sheet give 2 × 4 = 8 holes. Counting alone usually kills two or three of the five options before you look at any positions.

Rule two: the new holes are mirror images across each fold line. Undo the folds in reverse order, one at a time. Each time you undo a fold, every hole you already have gains a partner on the other side of that fold line, the same distance away from it. A hole near the fold stays near the fold; a hole near the outer edge lands near the opposite outer edge.

Doing it in reverse order matters when there are two folds. Unfold the last fold first, then the first fold, and the positions come out right every time. Children who try to picture the finished sheet in one leap tend to mirror across the wrong line.

Do it once with real paper. Fold a sheet, punch it with an actual hole punch, and open it out slowly so your child watches each hole gain its partner. Most children stop guessing after a single demonstration, because the doubling and the mirroring stop being abstract rules and become something they have seen happen.

Three worked examples

In each one the dotted line is the fold line. Cover the options, predict the answer, then check.

Example 1 · One fold, one punch

Solving rule: one fold doubles one hole into two, mirrored across the fold line
A square folded in half with one hole punched
A square of paper is folded in half along the dotted line, the left half onto the right. One hole is punched through both layers. What does the paper look like when it is opened out?
A
B
C
D
E
Show the answer and the elimination, step by step

Count first. One fold makes two layers, so one punch must give exactly two holes. That removes A, which still has one hole, and E, which has four.

Then check the mirror line. The fold is the vertical centre line, so the second hole must be directly across from the first, the same distance from that line. C mirrors downwards across a horizontal line, which is the wrong axis. D puts the second hole on the same side of the fold, close to the right-hand edge, which is not a mirror image at all.

B has two holes at the same height, equally far from the centre fold, so B is correct.

Example 2 · Two folds, one punch

Solving rule: unfold the folds in reverse order, mirroring across each line in turn
A square folded twice into a quarter, with one hole punched
A square is folded in half bottom to top, then in half again left to right, leaving a small square a quarter of the size. One hole is punched through all the layers, where shown. What does the full sheet look like unfolded?
A
B
C
D
E
Show the answer and the elimination, step by step

Count first. Two folds make four layers, so one punch gives exactly four holes. That eliminates A and B, which have two, and D, which has three.

Undo the last fold first. The last fold was left to right down the vertical centre line, so the hole gains a partner mirrored across that vertical line, giving two holes in the top half of the paper.

Then undo the first fold. That one was bottom to top across the horizontal centre line, so both holes gain partners mirrored downwards, giving four holes arranged in a neat rectangle, symmetrical about both centre lines. E has four holes but they are scattered with no symmetry, so C is correct.

Example 3 · One fold, two punches

Solving rule: every punch doubles, so count punches times layers
A square folded in half upwards with two holes punched
A square is folded in half along the dotted horizontal line, the top half folding down onto the bottom half. Two holes are punched through both layers. How does the paper look unfolded?
A
B
C
D
E
Show the answer and the elimination, step by step

Count first. Two layers and two punches give 2 × 2 = 4 holes. A has two and B has three, so both are out.

Now mirror across the fold. The fold line is horizontal and across the middle, so each hole gains a partner the same distance above the line as the original is below it. The hole close to the fold produces a partner close to the fold; the lower hole produces a partner higher up.

D has four holes but it has reflected them left to right instead of top to bottom. E mirrors in the right direction but measures the distances from the top edge instead of from the fold line, so its holes sit too close to the edge. C is the true mirror image, so C is correct.

Free printable practice

Fold and punch is easy to practise at home with nothing more than paper and a hole punch, and it is worth doing before the drilling starts. Fold a sheet, let your child predict the pattern out loud, then open it and check together. Once predictions are reliable, move to written questions where the paper stays in the imagination.

Pip's free 24-question Non-Verbal Reasoning practice paper is a printable PDF with a full worked answer key, and it includes spatial-style puzzles alongside the 2D reasoning families. Every other subject is on the 11+ printables page, also free and with no sign-up.

Related question types: nets and cubes for folding a flat shape into a solid, cube rotation for turning a solid, and the full spatial reasoning guide for all eight types.

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All eight spatial reasoning question types in one place, with diagrams, the solving rule for each and which exams test them.

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Paper folding FAQ

How do fold and punch questions work?+

A square of paper is folded one or more times, a hole punch goes through all the layers, and the paper is opened out. You are shown drawings of the opened sheet and pick the one with the holes in the right places. It is question type 6 of the eight spatial reasoning types used in 11+ style papers.

How many holes does each fold make?+

Every fold doubles the number of layers, so it doubles the number of holes. One fold gives two layers and turns one punch into two holes; two folds give four layers and four holes; three folds give eight. Two punches through a twice folded sheet give eight holes in total. Counting is usually enough to eliminate two or three options.

Which way do the holes mirror?+

Across the fold line, and at the same distance from it. Undo the folds in reverse order, last fold first: each time you undo one, every hole you already have gains a partner on the other side of that line. A hole close to the fold produces a partner close to the fold, and a hole near an outer edge produces one near the opposite outer edge.

Is this the same as CAT4 figure analysis?+

The skill is the same. The CAT4 tests figure analysis, which is fold and punch style visualisation, as part of its spatial work. The CAT4 itself is a cognitive abilities test used inside schools rather than an 11+ entrance exam, and we cover that distinction on our CAT4 spatial reasoning page.

Is there a free printable for fold and punch practice?+

Yes. Pip publishes a free 24-question Non-Verbal Reasoning practice paper as a printable PDF with a full worked answer key, and free printable papers for every other 11+ subject, with no sign-up. You can also make your own in seconds with a sheet of paper and a hole punch.

What is the difference between paper folding and 3D shape folding?+

Paper folding folds a flat sheet flat again and asks about holes. 3D shape folding, also called nets and cubes, folds a flat shape up into a solid and asks which faces end up opposite or which cube the net makes. They use related visualisation but different rules, and nets and cubes has its own page.

How much practice does a child need for this type?+

Less than most types. Fold and punch is highly learnable, and many children go from guessing to reliable in one sitting once they have seen a real sheet unfolded. A short set of questions a few times, rather than a long drill, is usually enough.