UP Police Constable · Bite-size lessons
Paper Folding & Cutting
About 7 min · Mental Aptitude / IQ / Reasoning · English
Time worked out from the lesson's 487 words at 150 words a minute, plus a minute for each question.
Paper Folding & Cutting questions test your spatial visualization and mental rotation abilities. In UP Police Constable exams, you'll be shown a sequence of diagrams: a paper being folded one or more times, then punched or cut at specific points. Your task is to predict how the paper will look when fully unfolded. These questions can be solved quickly once you master the pattern-recognition technique.
Key ideas
- Fold multiplication principle: Each fold doubles the number of layers. One fold creates 2 layers, two folds create 4 layers, three folds create 8 layers. A single punch through all layers creates holes equal to the number of layers.
- Symmetry along fold line: When paper is folded and punched, the resulting holes appear symmetrically on both sides of the fold line when unfolded. The fold line acts as a mirror axis.
- Sequential folding matters: The order of folds determines the final pattern. Fold left-then-up produces a different result than fold up-then-left, even with identical punches.
- Rotation vs reflection: When a paper is folded diagonally, holes reflect diagonally. When folded horizontally or vertically, holes reflect along that axis. Corner folds create rotational patterns.
- Punch position tracking: Mark mentally where the punch is relative to edges and previous fold lines. This position replicates across all layers when unfolded.
Quick reference
- 1 fold = 2 holes; 2 folds = 4 holes; 3 folds = 8 holes (for single punch through all layers)
- Fold line = symmetry axis — holes mirror across it
- Diagonal fold = diagonal symmetry; horizontal fold = horizontal mirror
- Draw mental grid: mark fold lines on imaginary paper while reading question
- Eliminate options violating basic symmetry before detailed analysis
Check yourself: 3 questions
1. A square piece of paper is folded once in half and then a small triangular piece is cut from one corner as shown. When the paper is unfolded, which pattern will appear? [Description: A square paper is folded in half vertically. Then a small triangle is cut from the bottom-right corner of the folded paper.]
2. A rectangular paper is folded twice - first in half horizontally and then in half vertically. A circular hole is punched through all layers. How many holes will appear when the paper is completely unfolded?
3. A rectangular piece of paper is folded three times. First, it is folded in half along its length, then folded in half along its width, and finally folded diagonally. A semicircular cut is made along the longest folded edge. After unfolding completely, how many semicircular cuts will be visible and what will be their arrangement?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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