Pattern Completion (Reverse)
Pattern Completion (Reverse) problems give you what you see through a folded transparent sheet and ask you to determine what the original pattern was before folding. These are the inverse of basic overlay problems and require working backwards from the superposition to the original pattern.
What You'll Learn
Introduction to Pattern Completion (Reverse)
Pattern Completion (Reverse) problems give you what you see through a folded transparent sheet and ask you to determine what the original pattern was before folding. These are the inverse of basic overlay problems and require working backwards from the superposition to the original pattern.
Prerequisites
How to Solve Pattern Completion (Reverse) Problems
Step 1: Identify the fold type and fold line from the problem
Step 2: Note what pattern is visible through the folded sheet
Step 3: Understand that visible pattern = original pattern + reflected pattern
Step 4: Decompose the visible pattern into two mirror-image halves
Step 5: The pattern on one side of the fold line is the original
Step 6: The pattern on the other side is its mirror image (reflection)
Step 7: Therefore, the original pattern is one of these two mirror halves (usually the one that could have been drawn originally)
Example Problem
Example: A transparent sheet is folded vertically through the center. Through the folded sheet, you see a complete butterfly with its wings spread. What was the original pattern? Solution: Step 1: Fold is vertical through center (x = 100) Step 2: Visible pattern = complete butterfly Step 3: This visible pattern is the superposition of original + reflection Step 4: A complete butterfly has left wing and right wing Step 5: For it to appear complete, one wing must be original, the other its reflection Step 6: Therefore, the original pattern was HALF a butterfly (one wing) Step 7: The other half was created by reflection through the fold Answer: Half a butterfly (one wing)
Pro Tips & Tricks
- The visible pattern is always symmetric about the fold line
- The original pattern is one half of that symmetric pattern
- Patterns touching the fold line appear at the same location (they are original, not reflected)
- Patterns not touching the fold line appear in pairs (original + reflected)
- To reconstruct original: take the visible pattern and remove reflections
- The original pattern must be such that when reflected, it creates the visible pattern
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Pattern Completion (Reverse). Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Pattern Completion (Reverse) is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Pattern Completion (Reverse)?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: