Paper folding and hole punching is one of the most reliably recurring non-verbal reasoning patterns in GL-style 11+ papers, and it is also one of the most learnable. A square of paper is folded once, twice or three times, a hole (or holes) is punched through the folded stack, and the child must picture the sheet opened flat and choose where every hole ends up. It looks like a test of imagination, but it is really a test of method. Non-verbal reasoning rewards a systematic approach more than any other 11+ subject, and children who learn to unfold the paper on purpose, one crease at a time, routinely overtake classmates who rely on a lucky mental snapshot.
What the question actually looks like
The question stem shows a small sequence of pictures: a plain square, then the same square folded (the fold might be in half top-to-bottom, side-to-side, or corner-to-corner along a diagonal), sometimes folded a second or third time, and finally the folded shape with one or more punched holes shown as filled circles. Beneath sit five multiple-choice options (A to E) showing the fully unfolded sheet with different hole arrangements. Only one is correct. In a GL non-verbal reasoning paper you should expect several of these, and in reasoning-heavy regions where NVR carries a large share of the marks, getting this family right can noticeably lift a child's GL paper score.
The method: unfold backwards, one crease at a time
The single reliable technique is to reverse the folding in the exact opposite order it was done, mirroring the holes across each fold line as you go. Never try to jump straight to the finished sheet in your head. Work like this:
- Find the last fold line. That is the crease you will open first. It is usually the visible straight edge where the paper was doubled over.
- Reflect every hole across that line. Each punched hole produces a mirror-image partner an equal distance on the other side of the crease. The holes are always symmetrical about the fold.
- Repeat for the previous fold. Open the next crease and mirror all the holes you now have — the originals and the new copies — across that earlier fold line.
- Keep going until the paper is flat. When every fold is undone, count your holes and match the pattern to an option.
A quick sanity check keeps you honest: each unfold at most doubles the number of holes. So one punch through paper folded n times gives a maximum of 2 to the power n holes — one fold up to two holes, two folds up to four, three folds up to eight. If your chosen answer has an impossible count, it is wrong before you even look at the positions.
A worked example
Suppose a square is folded in half left-over-right, then folded again bottom-up, and a single hole is punched near the centre of the small folded square. Unfold the last fold (the bottom-up one) first: the one hole mirrors upward across the horizontal crease, giving two holes, one above the other. Now unfold the first fold (left-over-right): those two holes each mirror across the vertical crease, giving four holes arranged in a neat rectangle, symmetrical about both the horizontal and the vertical centre lines. Two folds, one punch, four holes — exactly 2². The correct option will show that balanced four-hole rectangle, and any option with three or five holes, or with holes bunched on one side, can be eliminated instantly.
Diagonal folds: the tricky variation
When the fold is along a diagonal, the mirror line is that slanting crease rather than a horizontal or vertical one. Holes reflect across the diagonal, so a hole near one corner lands near the opposite side, not straight across. Children find diagonal reflections harder because the eye wants to slide holes horizontally. The fix is the same disciplined step: identify the crease, then reflect perpendicular to it. Practising a handful of diagonal-fold questions separately, until the slant feels natural, pays off quickly.
Reference: holes by folds
| Number of folds | One punch gives up to | Typical symmetry to expect |
|---|---|---|
| 1 fold | 2 holes | Mirror across a single line |
| 2 folds | 4 holes | Symmetrical about two lines |
| 3 folds | 8 holes | Repeating, balanced grid pattern |
Two punches simply double these figures again, so keep the count in mind as your first filter on every question.
The classic traps
- Mirroring across the wrong fold line. Always unfold in reverse order — last crease first. Reflecting across the first fold before the last scrambles the pattern.
- Losing count of layers. A hole punched through several layers reappears once per layer. Undercounting is the commonest slip; the 2ⁿ check catches it.
- Reflecting the distance carelessly. The mirror hole sits the same distance from the crease as the original. A hole close to the fold has its partner close to the fold too.
- Ignoring symmetry. Every correct answer is symmetrical about each fold line. If an option is lopsided, it is a distractor.
How to practise this type
Little-and-often beats long marathons. Fold real scrap paper and punch it with a pencil so your child sees the mirror image appear in their hands — the abstract clicks fast once it is physical. Then move to paper: do ten questions, mark them together, and review every error out loud with one question, "which fold line did I mirror wrongly?" Our free NVR worksheet sets isolate this exact pattern so it can be drilled on its own, the full NVR types list maps the whole territory, timed mock papers rebuild exam pace, and the revision hub sequences it alongside rotations and reflections so confusable types are learned side by side. Everything is free.
Frequently asked questions
How many holes can appear?
At most two to the power of the number of folds, per punch. One fold gives up to two holes, two folds up to four, three folds up to eight. Extra punches multiply that total again.
What is the single best technique?
Unfold backwards. Open the last crease first and mirror every hole across it, then repeat for each earlier fold until the sheet is flat. Never try to picture the final sheet in one leap.
Why are diagonal folds harder?
The mirror line is slanted, so holes reflect across the diagonal rather than straight across. The method is identical — find the crease, reflect perpendicular to it — but it needs a little extra practice to feel automatic.