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Paper Folding & Cutting

Agniveer (All) · Logical Reasoning

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Core Concept

Read this first — the foundation of the topic

→Core Concept

When paper is folded and cut, the cuts create symmetric patterns when unfolded. Each fold creates a mirror effect. The number of holes depends on how many times the paper was folded

💡Key Rules

First, count the number of folds carefully. Each fold doubles the number of holes. One cut on a paper folded once = 2 holes. One cut on a paper folded twice = 4 holes.

Second, holes appear symmetrically around fold lines. Third, the position of holes mirrors across each fold line. Fourth, the shape of holes remains the same, only position changes.

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL typically asks 1-2 questions on this topic. Questions show 2-4 folding steps followed by cutting. You get 4 answer choices showing different unfolded patterns. The cuts are usually simple shapes - circles, triangles, or small squares.

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Shortcuts

Use these to save 30–60 seconds per question

Use the 'Fold Count Formula' - Number of holes = 2^(number of folds) × number of cuts. For symmetry, imagine drawing lines where folds occurred. Holes must appear symmetrically on both sides of these imaginary lines.

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Worked Example

Solve this step-by-step before moving on

1

Step 1

Count folds = 2 folds (vertical + horizontal)

2

Step 2

Count cuts = 1 cut (one circle)

3

Step 3

Apply formula = 2^2 × 1 = 4 holes

4

Step 4

Determine positions - Original cut was at top-right of folded paper. When unfolded, holes appear at all four corners (top-right, top-left, bottom-right, bottom-left) due to symmetry around both fold lines.

5

Step 5

Verify symmetry - Draw imaginary vertical and horizontal lines through center. Holes are symmetric around both lines. Advanced Trick: For complex folding, trace the cut position backwards through each fold. Start from the final cut position and mirror it across each fold line in reverse order. Common Mistake: Students often forget to account for all folds or miscalculate symmetry. Remember that each fold creates a new axis of symmetry. Also, don't confuse the number of paper layers with the number of holes. Focus on fold lines, not thickness.

🔑 Key Points

Each fold doubles the number of holes created by cuts
Holes appear symmetrically around all fold lines
Formula: Number of holes = 2^(folds) × number of cuts
Position of holes mirrors across each fold axis
Shape of cut remains same, only position multiplies
Count fold steps carefully before applying formula
Draw imaginary lines at fold positions to check symmetry
Work backwards from cut to unfold position step by step

📌 Exam Facts

SSC CGL typically includes 1-2 paper folding questions per exam
Maximum folds shown in SSC questions is usually 3-4 folds
Most common cuts are circles, triangles, and small rectangles
Questions always provide exactly 4 answer options showing unfolded patterns
Each fold creates one axis of symmetry in the final pattern
Corner cuts are the most frequently tested cutting positions
Questions are worth 2 marks each in SSC CGL Tier-I
Time allocation should be maximum 1 minute per question

🚀 60-Second Revision

Remember: Each fold doubles the hole count from cuts
Formula: Holes = 2^(number of folds) × cuts made
Trick: Holes must be symmetric around all fold lines
Method: Count folds first, then apply symmetry rules
Trap: Don't confuse paper thickness with number of holes
Speed tip: Eliminate options that violate symmetry immediately

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