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Academy11+

11+ Non-verbal reasoning · Topic explained

Paper folding and hole punching

Fold, punch, unfold: where do the holes end up?

The big idea

Every fold doubles the holes, and each new hole is a mirror image across the fold line.

Picture it

Paper snowflakes: one cut through folded paper shows up in every layer.

Key words

fold line
the crease: it works like a mirror line
layers
how many sheets thick the folded paper is
unfold
open it out, undoing the last fold first

Worked examples

  1. 1Warm-up

    Fold in half, punch one hole, unfold.

    • Two layers, so one punch makes two holes.
    • The second hole is a mirror image across the fold.
  2. 211+ standard

    Fold in half, then in half again. Punch one hole, then unfold.

    • Two folds make four layers.
    • So one punch makes four holes, one in each quarter.
  3. 311+ standard

    Fold the top down. Punch two holes, then unfold.

    • One fold, two layers: each hole doubles.
    • Two punches make four holes, mirrored top to bottom.
  4. 411+ standard

    Fold in half and punch a hole near the fold.

    • A hole close to the fold line…
    • …has its mirror image close to the fold on the other side.

The common mistake

The mistake

The unfolded paper has as many holes as you punched.

Instead

Each fold doubles the holes: one fold, two holes; two folds, four.

Why: The punch goes through every layer of the folded paper.

Where it comes up in the 11+

Paper folding and hole punching appear in GL NVR papers, and CEM-style tests use folding puzzles too.

The video

Video coming soon

We're making a short video that explains paper folding and hole punching step by step. Until then, everything it covers is on this page.

Free printable

Paper folding and hole punching worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Paper is folded in half once, and one hole is punched. How many holes when it's unfolded?

    • 2
    • 1
    • 4
    • 3
    Show the answer

    2

    Two layers, two holes.

  2. 2. Paper is folded in half twice, and one hole is punched. How many holes?

    • 4
    • 2
    • 3
    • 8
    Show the answer

    4

    Four layers, four holes.

  3. 3. What does the fold line act like?

    • a mirror line
    • a hole
    • an arrow
    • nothing
    Show the answer

    a mirror line

    Holes are reflected across it.