Paper Folding & Cutting

Paper Folding and Cutting is a topic where a square paper is folded one or more times and then a cut is made. You have to find what the paper looks like when it is unfolded. It is a visual and spatial topic that requires practice to master.

Basic Concept:

When a paper is folded and a cut is made, the cut appears on both the folded layers. When unfolded, the cut appears as a mirror image on the other half too.

Simple Example:

• Take a square paper
• Fold it in half (left to right)
• Cut a small triangle from the folded edge
• Unfold it - you will see TWO triangles, one on each half (mirror images of each other)

Types of Paper Folding & Cutting Questions in SSC CGL:

Type 1 - Single Fold and Cut Paper is folded once and a cut is made. Find the unfolded pattern.

Example: 

Square paper folded from right to left (vertical fold). A circular hole is punched in the upper left area. When unfolded - the hole appears on BOTH left and right sides at the same height (mirror image).

Logic:

• Fold creates 2 layers
• Cut goes through both layers
• Unfolding reveals 2 identical cuts as mirror images

Type 2 - Double Fold and Cut Paper is folded twice (first horizontally then vertically or vice versa) and then a cut is made.

Example: 

Step 1 - Fold square paper from bottom to top (horizontal fold) 

Step 2 - Fold again from right to left (vertical fold) 

Step 3 - Cut a triangle from the corner

When unfolded - you get 4 triangular cuts, one in each corner of the paper (because 2 folds create 4 layers).

Logic:

• 1 fold = 2 layers = 2 cuts when unfolded
• 2 folds = 4 layers = 4 cuts when unfolded
• 3 folds = 8 layers = 8 cuts when unfolded

Number of Cuts Formula: Number of holes/cuts after unfolding = 2^n Where n = number of folds made

Example: 

1 fold = 2^1 = 2 cuts 2 folds = 2^2 = 4 cuts 3 folds = 2^3 = 8 cuts

Type 3 - Diagonal Fold and Cut Paper is folded diagonally (corner to corner) and a cut is made.

Example: 

Square paper folded diagonally (bottom left to top right). A cut is made on the folded edge. When unfolded - the cut appears symmetrically on both sides of the diagonal.

How to Solve Paper Folding & Cutting Questions:

Step 1 - Carefully observe the direction of each fold (left to right, top to bottom or diagonal). 

Step 2 - Note the position of the cut on the folded paper. 

Step 3 - Mentally unfold the paper one fold at a time. 

Step 4 - Remember - each fold creates a mirror image of the cut on the other side. 

Step 5 - The final unfolded pattern should be symmetric along the fold lines.

Important Rules:

Rule 1 - The unfolded pattern is always symmetric along the fold line.

Rule 2 - The number of cuts doubles with each fold.

Rule 3 - Cuts made on the folded edge (crease) appear as one connected cut when unfolded.

Rule 4 - Cuts made away from the folded edge appear as separate holes when unfolded.

Rule 5 - Diagonal fold creates diagonal symmetry in the final pattern.

Quick Tricks:

Trick 1 - Always trace the fold direction first before thinking about the cut position.

Trick 2 - Use actual paper to practice - physically fold and cut to verify your mental answers.

Trick 3 - The final answer must always be symmetric. If your answer is not symmetric - it is wrong.

Trick 4 - Count the expected number of holes using the formula 2^n before checking options.

Important Tips:

• This topic requires strong visual imagination - practice daily with real paper
• In exam, eliminate options that are not symmetric first
• 1 to 2 questions come from this topic in SSC CGL every year
• Paper folding questions look difficult but the symmetry rule eliminates wrong options quickly
• Practice at least 10 questions daily with actual paper folding