Fold and punch
A square of paper is folded, a hole is punched through every layer, and you pick the paper opened out. Here's how to see where every hole lands, without unfolding a thing.
Chapter 1
What are fold and punch questions?
A square of paper is folded, and a hole is punched right through it while it’s folded. You pick the picture of the paper opened out flat again.
The fold. The arrow shows which part folds over. The dashed line is the crease, where the paper bends.
The punch. The folded paper with its holes. The pale part is where the paper was before it folded over.
Each hole in the folded picture goes through every layer. The trick is working out where the extra holes land when the folded part swings back.
Open it out. Which shows the holes?
An NVR question from Rush, level 1.
Chapter 2
Solve it in 4 steps.
Here’s the question, one step at a time.
The question
Open it out. Which shows the holes?
An NVR question from Rush, level 1.
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Step 1
Count the layers.
The left half folds over onto the right, so the paper is two layers thick, and the punch goes through both. One hole through two layers makes two holes. Option 2 has only one: cross it out.
1 hole through 2 layers makes 2 holes.
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Step 2
The punched hole stays put.
The right half never moves: only the flap on top of it swings back. So the hole you can see is still exactly there when the paper opens, in the bottom right corner, pointing down. Option 5 has moved it up a row. Cross it out.
Still in the bottom right corner when it opens.
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Step 3
Its twin goes the same distance across.
The second hole is in the flap. Open the paper and the flap swings back over the crease, landing its hole on the same row, just as far from the crease. This hole is at the right-hand edge, so its twin is at the left-hand edge: the bottom left corner. Options 1 and 3 put it at the top. Cross them out.
Same row, same distance from the crease.
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Step 4
Mirror which way it points.
The twin is a mirror image. A mirror flips anything pointing at or away from the crease, but not along it. This triangle points down, along the crease, so its twin points down too. That’s option 4.
Down, along the crease, stays down.
Watch it open
Another question, with the same fold. The triangle near the crease points right, away from it, so its twin points left, away from it too.
The left half is folded over. Two holes go through both layers.
Open it. Each hole gets a twin across the crease.
The hole near the crease gets a twin just as near.
The hole at the far edge gets a twin at the other far edge. Same distance.
Four mistakes this question sets
| The mistake | Do this instead |
|---|---|
| Forgetting to open it. Option 2 shows only the hole you can see. But the flap folded over it was punched too. | Count the layers first: two layers, two holes. |
| Moving the punched hole. Option 5 looks neat, but both triangles sit a row too high. The punched one has moved. | Find the punched hole in each option. It must be in its own square. |
| Turning instead of opening. Option 3 puts the twin in the top left corner, pointing up. That’s the paper spun half way round. | Opening flips the paper over the crease. The twin stays on the same row. |
| Using the wrong crease. Option 1 puts the twin in the top right corner, as if the paper had folded top to bottom. | Mirror across the crease you’re shown. Here it runs down the middle. |
So it’s option 4. Two triangles in the bottom corners, the same distance from the crease, both pointing down.
Remember: Count. Holes stay. Mirror across.
Chapter 3
When it gets harder.
Rush folds the paper four ways, and its holes include triangles and L-shapes. The four steps still work every time. Here’s what changes.
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Across the crease, a triangle flips
Pointing at or away from the crease? The twin flips. Pointing along it? The twin doesn’t.
The top half folds down. The triangle pointing down, away from the crease, gets a twin pointing up. The one pointing right, along the crease, gets a twin pointing right. Trap: a twin that’s just copied, pointing the same way as its hole.
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Corner to corner
The crease slants, so a hole near the bottom left corner gets its twin near the top right.
The top right corner folds down to the bottom left. A slanted crease swaps directions in pairs, as on the reflection page: up comes back pointing left, and down comes back pointing right. It’s a flip, not a turn. Trap: a twin still pointing up.
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A third folds over
Only the strip under the flap is two layers. A hole there gets a twin; a hole outside it stays single.
The left third folds over. The L is under the flap, so it gets a twin: a backwards L. The circle went through one layer, so it stays single. Trap: giving every hole a twin out of habit, or copying the L without flipping it.
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Two folds: open the last one first
Two folds make four layers, so one hole opens into four. Unfold backwards, one fold at a time.
The right half folds over, then the top folds down. Open the top first: the twin points left, along that crease. Then open the right half: both get twins at the right-hand edge, flipped to point right. Trap: stopping after one fold, with only two holes.
Learn this by heart
Every fold in half doubles the layers, and the punch goes through them all. A third folded over doubles only the strip under the flap. Rush folds up to twice; the exam can fold three or four times.
- 1 fold2 holes
- 2 folds4 holes
- 3 folds8 holes
- 4 folds16 holes
Chapter 4: In the exam
A hole on the crease.
Rush never punches on a crease, but some 11+ papers do. It’s the one new rule, and the steps you know do the rest.
The left half folds over. Which shows it opened out?
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Step 1
Is a hole on the crease?
The circle sits right on the fold, so the punch cut half a circle out of the folded edge. Open it, and that half meets its mirror image: one whole circle across the crease, not two. Option 1 has two circles: out.
1 2 3 4 5 -
Step 2
Mirror the other holes as usual.
The triangle is at the right-hand edge, so its twin is at the left-hand edge, on the same row. Option 5 has no twin, and option 4 puts it beside the crease. Both out.
1 2 3 4 5 -
Step 3
Check which way it points.
The triangle points right, away from the crease, so its twin points left, away from it too. Option 2’s twin still points right: out. That leaves option 3.
1 2 3 4 5
So it’s option 3. One circle across the crease, and two triangles pointing away from it, one at each edge.
Remember: On the crease? One hole, not two.
Other ways the exam asks it
- More folds. Three folds make 8 layers and four make 16. Count them first, then open one fold at a time, last fold first.
- Where two creases cross. After two folds, a hole punched right at the corner where the creases meet opens into one hole in the middle of the paper.
- Other shapes. Check any shape that looks different in a mirror the way you check a triangle. A heart stays the same across an upright crease, but turns upside down across a flat one.
- Folds that don’t match. A third folded over and then folded in half, or a corner folded twice. Count the layers under each hole before you open anything.
Chapter 5
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Count the layers.
- The punched hole stays put.
- Its twin goes the same distance across.
- Mirror which way it points.
Remember: Count. Holes stay. Mirror across.
For parents.
What parents ask us about fold and punch.
Questions parents ask
How do you work out fold and punch questions?
Work out how many layers each hole went through, which tells you how many holes to expect. Then open the paper in reverse order, last fold first, giving every hole a mirror-image twin across each crease as it opens. Check the punched holes haven't moved and that every triangle points the right way.
Why does a hole near the fold end up near the fold?
Both layers are punched at once, so the hole in the bottom layer is exactly under the hole in the top one. When the paper opens, the top layer swings back over the crease and lands on the other side, the same distance away. So the two holes always sit symmetrically about the crease.
Is it worth practising with real paper?
Yes, a few times. Fold a square of paper, snip a small triangle through the layers with scissors, and ask your child to draw the open sheet before unfolding it. The triangle shows the flip that a round hole hides.
Are hole punch questions always one fold?
No. Rush's level 3 uses two folds, and papers can use three. Each full fold doubles the holes, 1, 2, 4, 8, and the method doesn't change: open the folds one at a time, last fold first.
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