Non-Verbal Reasoning • Topic 3 of 5

Paper Folding & Cutting

A sheet is folded one or more times, a hole is punched, then unfolded — predict the pattern of holes. Each fold doubles the holes by reflecting them across the fold line. Work backwards: unfold the last fold first, mirroring every punch across that crease.

Each fold doubles the holes

When you punch through a folded sheet, every layer gets a hole. Unfolding mirrors each hole across the crease — so one punch through a sheet folded once gives two holes, folded twice gives four, and so on.

folded · 1 punch → unfolded · 2 holes
Holes appear symmetrically about every crease. Folds = 1, 2, 3 → holes = 2, 4, 8 for one punch.
Method: unfold in reverse. Start from the final folded state and undo the last fold first, reflecting every hole across that crease; repeat back to the flat sheet. The number of holes for one punch is 2^(number of folds).

✅ Solved examples

1. A sheet folded once (in half) with one punch gives how many holes when opened?
Two (mirrored across the fold).
2. Folded twice, one punch — holes on opening?
Four (each fold doubles).
3. Folded three times, one punch?
2³ = 8 holes.
4. Holes appear how, relative to the fold line?
Symmetrically (mirror images across each crease).

✏️ Practice — try these, take hints as needed

1. Folded once, two punches — holes opened?
Each doubles.
2×2.
—
4
2. Folded twice, one punch?
2².
—
—
4
3. Folded four times, one punch?
2⁴.
—
—
16
4. Punches are placed how on opening?
About the crease.
—
—
Symmetrically
5. To solve, you unfold in which order?
Reverse.
—
—
Last fold first

📝 Topic test — 8 questions

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