Last reviewed 22 Sept 2026 · 5 min read
Unfold in reverse
A sheet is folded once or more, a hole is punched, and you must show the unfolded sheet.
Undo the folds in the reverse order of folding. At each unfold, every existing hole gains a mirror copy across the fold line just opened.
So folds turn one punch into holes — unless a punch lies on a fold line, when the two copies coincide and the count is lower.
Where the copies go
- Vertical fold (left over right): copies appear at the same height, the same distance on the other side of the vertical crease.
- Horizontal fold (top over bottom): copies appear in the same column, mirrored across the horizontal crease.
- Diagonal fold: copies are mirrored across the diagonal — a hole near the left edge becomes a hole near the bottom edge, not directly across.
A hole punched on the crease unfolds into a single hole straddling it.
Two folds
Fold left over right, then top over bottom, and punch one hole: unfolding the second fold gives 2 holes, and unfolding the first gives 4, arranged symmetrically about both creases. The final pattern always has the symmetry of the folds that were made — which is the quickest way to reject wrong options.
If the paper was folded once vertically, the answer must be left-right symmetric. Any option that is not can be eliminated without tracing a single hole.
Cuts instead of punches
A cut across a folded edge behaves the same way: each layer receives the cut, and unfolding mirrors it. A cut that removes a corner of the folded sheet removes every corner that lay under it — often producing a hole in the middle when the corner was at the centre of the sheet.
Transparent sheets
A related question gives three transparent sheets with patterns and asks what is seen when they are placed one on another. Here nothing is mirrored: the marks simply add up, and the answer is the option containing every mark from all three sheets, with none extra.
Worked examples
A square sheet is folded left over right and a hole is punched near the top-left of the folded sheet. How does the unfolded sheet look?
Solution. Two holes, at the same height, one near the left edge and one near the right — symmetric about the vertical crease.
A sheet is folded twice and one hole is punched. How many holes appear when unfolded?
Solution. 4, provided the punch does not lie on a crease.
A sheet is folded once and a hole is punched exactly on the fold. How many holes appear?
Solution. One, straddling the crease.
A sheet folded three times with one punch, none of the folds passing through it, gives how many holes?
Solution. 8.
A square is folded top over bottom and punched twice. Which options can be rejected at once?
Solution. Any option not symmetric about the horizontal centre line.
A square is folded along its main diagonal and a hole is punched in the middle of the upper triangle. Where are the holes when unfolded?
Solution. Two holes, mirror images across the diagonal — one in the upper triangle and one in the lower, at equal perpendicular distances from the crease.
A square is folded into quarters (left over right, then top over bottom) and the folded corner at the centre of the original sheet is cut off. What does the unfolded sheet show?
Solution. A hole in the middle of the sheet — all four layers were cut at the centre.
The same folded sheet has its outer corner cut. What is seen?
Solution. All four corners of the sheet are cut off.
Three transparent sheets carry a dot at top-left, a cross at centre and a line along the bottom. What is seen when they are stacked?
Solution. All three marks together — dot, cross and line — with nothing added or removed.
An unfolded sheet shows four holes, one in each quadrant, symmetric about both centre lines. How many folds and punches produced it?
Solution. Two folds and one punch — each fold doubling a single hole.