Paper Folding and Cutting
About 6 min · Logical Reasoning · English
Time worked out from the lesson's 436 words at 150 words a minute, plus a minute for each question.
Paper folding and cutting is a spatial reasoning topic that tests your ability to visualize how a flat piece of paper transforms when folded, cut, and then unfolded. The concept is simple: you're shown a sequence of folds, a cut pattern, and must predict what the unfolded paper looks like.
Key ideas
- Folding creates layers: Each fold doubles the number of paper layers at that location. One fold = 2 layers, two folds = 4 layers (if folded in the same region), and so on.
- Cuts replicate across layers: A single cut through folded paper creates identical holes in every layer beneath. If you cut through 4 layers, you create 4 identical holes in corresponding positions.
- Symmetry is your compass: Folds create axes of symmetry. A vertical fold produces left-right symmetry; a horizontal fold produces top-bottom symmetry. Diagonal folds create diagonal symmetry axes.
- Unfold in reverse order: To predict the final pattern, mentally unfold the paper in the exact reverse sequence of how it was folded. Each unfold step mirrors the cut pattern across the fold line.
- Corner folds are special: Folding corners (triangular folds) creates radial or rotational patterns rather than simple mirror patterns. The cut position relative to the corner determines the final design.
Quick reference
- Layer count = Hole count: One cut through 4 layers → 4 holes when unfolded.
- Symmetry axis = Fold line: Vertical fold → left-right mirror; Horizontal fold → top-bottom mirror.
- Unfold in reverse order: Last fold made is first fold undone.
- Corner cuts → Centered patterns: Cutting folded corners produces designs near the paper's center.
- Edge cuts → Repeated boundary patterns: Cuts at folded edges create patterns near original edges.
Check yourself: 3 questions
1. A square sheet of paper is folded once vertically in half, and then a small circular hole is punched in the center of the folded paper. When the paper is unfolded completely, how many holes will appear?
2. A rectangular paper is folded in half horizontally, then folded in half vertically. A triangular piece is cut from one corner of the folded paper. When the paper is completely unfolded, how many triangular cuts will be visible?
3. A square sheet of paper is folded twice: first diagonally and then diagonally again. A small square notch is cut from the folded edge (not the corner). When unfolded, what pattern will the cuts form?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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