Single Vertical Fold - Basic

Single Vertical Fold problems involve folding a square paper vertically (left to right or right to left), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the vertical fold line. These problems test your understanding of reflection symmetry across a vertical axis.

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Introduction to Single Vertical Fold - Basic

Single Vertical Fold problems involve folding a square paper vertically (left to right or right to left), then punching one or more holes through the folded layers. After unfolding, the holes appear in symmetric positions about the vertical fold line. These problems test your understanding of reflection symmetry across a vertical axis.

Prerequisites

Understanding of reflection symmetry Basic visualization of folds Concept of vertical axis Layer counting (folded paper has 2 layers)
Why This Matters: Single Vertical Fold problems are essential for paper folding reasoning. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Single Vertical Fold - Basic Problems

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Step 1: Identify the fold direction - vertical fold means the paper is folded either left-to-right or right-to-left

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Step 2: The fold line becomes the axis of symmetry - it runs vertically through the center

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Step 3: Note the hole position(s) on the folded paper

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Step 4: When unfolded, each hole creates a mirror image across the fold line

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Step 5: A single hole punched through 2 layers creates 2 holes in the unfolded paper

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Step 6: The distance of each hole from the fold line remains the same on both sides

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Step 7: Combine the original hole positions with their reflections to get the final pattern

Pro Strategy: Draw the vertical fold line as the axis of symmetry. For each hole on the folded paper, reflect it across the fold line to find holes on the opposite layer. Count layers to determine number of holes.

Example Problem

Example: A square paper is folded vertically from left to right. A hole is punched near the top-left of the folded paper at (30, 25). What is the pattern when unfolded? Solution: Step 1: Fold direction: vertical (left to right) Step 2: Fold line is at the vertical center (x = 50 on a 100x100 paper) Step 3: Hole position on folded paper: (30, 25) Step 4: When unfolded, the right layer hole stays at (30, 25) Step 5: The left layer hole mirrors across x=50: (30, 25) reflects to (70, 25) Step 6: Result: Two holes horizontally aligned at (30, 25) and (70, 25) Answer: Two holes horizontally aligned in the upper portion

Pro Tips & Tricks

  • Vertical fold = horizontal symmetry in hole pattern (holes appear left and right of the fold line)
  • The distance from the fold line remains constant for mirrored holes
  • If a hole is exactly on the fold line, it creates only ONE hole when unfolded
  • For 'left to right' fold, the left layer folds over the right layer
  • For 'right to left' fold, the right layer folds over the left layer - symmetry is the same
  • Mirror formula for vertical fold: x' = W - x (where W is paper width, x measured from left edge)

Shortcut Methods to Solve Faster

Hole at (x, y) on folded paper → unfolded holes at (x, y) and (W - x, y)
Vertical fold axis equation: x = W/2
Mirror formula: x' = W - x (for 0 to W coordinates)
Two holes are always horizontally aligned (same y-coordinate)

Common Mistakes to Avoid

Confusing vertical fold with horizontal fold (horizontal fold creates vertical symmetry)
Forgetting that the fold creates 2 layers, so 2 holes unless punched on fold line
Using wrong mirror formula (should be W - x, not x ± something)
Not accounting for the direction of fold (left-to-right vs right-to-left gives same result)

Exam Importance

Single Vertical Fold - Basic is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
INSURANCE
2-3 questions

Ready to Master Single Vertical Fold - Basic?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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