Paper Cutting: Types, Methods and Examples
Paper cutting is a non-verbal reasoning topic in which a paper is folded along one or more dotted lines and a part of it is cut or punched, and the candidate must decide how the paper will look when it is unfolded. The cut is reflected across every fold line, so the answer is found by reflecting the cut shape again and again until the whole sheet is opened.
This topic is asked in APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations because it tests the ability to imagine how folds and cuts produce a pattern of holes. It uses only a few fixed rules, so once they are clear the topic becomes quick and accurate. This article gives a complete deep-study revision of paper cutting: the basic terms, the core rules, the types of questions, the step-by-step method, the common mistakes and a practical preparation plan.
Basic Terms
- Fold: bending the paper so that one part lies on another.
- Crease: the line along which the paper is folded.
- Cut: a piece removed from the folded paper with a scissors.
- Punch: a small hole made in the folded paper.
- Unfold: opening the paper again to its full size.
- Layer: one thickness of the folded paper.
- Symmetry: the property of the final pattern that matches across each fold line.
- Reflection: the copying of the cut shape on the other side of a fold line.
- Fold line: the line about which the cut is reflected when the paper is opened.
- Pattern: the design of holes that appears after unfolding.
- Fold edge: the crease where two layers of the folded paper are joined.
- Punched hole: a hole made by pressing a tool through the folded paper.
- Mirror fold: a fold that makes the two halves of the paper match.
Core Concepts and Rules
- Every cut is reflected across each fold line when the paper is opened.
- The number of holes doubles with each fold in the simple cases.
- The shape of the hole stays the same; only its direction may reverse.
- The final pattern is symmetrical about every fold line.
- A cut made exactly on the fold line gives half a shape that joins when unfolded.
- A cut made near the edge gives holes near the corresponding edge.
- The distance of the hole from the fold line is the same on both sides after unfolding.
- When there are several folds, reflect the cut once for each fold, working from the last fold back to the first.
- When a paper has two folds, reflect the cut across both lines to get four copies in the simple case.
- The closer the cut is to a fold line, the closer together the resulting holes are.
Types of Paper Cutting Questions
The first type has a single fold and a simple cut. The second type has two or more folds, so the number of holes increases. The third type gives the folded paper with a cut and asks which unfolded figure results. The fourth type gives the unfolded pattern and asks where the paper was punched. The fifth type shows a paper folded several times and a shape cut out, and asks for the exact pattern of the opened sheet.
Steps to Solve a Paper Cutting Question
First, count the number of folds and note the direction of each fold line. Second, locate the cut and its position relative to the nearest fold line. Third, unfold the last fold and reflect the cut across that line. Fourth, continue unfolding one fold at a time and reflect the cut each time. Fifth, build up the full pattern of holes on the opened sheet. Finally, compare the pattern with the options and choose the one that matches in number, position and shape.
Examination Trends
In competitive examinations paper cutting usually carries two to four marks. Questions with one or two folds are the most common, and questions that ask for the unfolded figure are asked more often than questions that ask where the cut was made. Simple shapes such as circles, triangles and squares are used for the cut. Because the topic uses fixed rules and no calculation, a candidate who practises the reflection of the cut can answer these questions confidently in a short time.
Common Mistakes to Avoid
- Do not forget to reflect the cut across every fold line.
- Do not change the shape of the hole while reflecting it.
- Do not count the holes wrongly; the number usually doubles with each fold.
- Do not ignore a cut that lies on the fold line; it produces a joined shape.
- Do not place the holes at the wrong distance from the fold line.
- Do not confuse the folded paper with the unfolded paper.
How to Prepare This Topic
Begin by actually folding a square paper once and cutting a small shape, then open it and see the reflected pattern. Repeat with two folds and note how the number of holes increases. Then solve printed questions and mark the fold lines before reflecting the cut. After that, work on multi-fold questions and time yourself.
A useful method is to draw the fold lines on rough paper and reflect the cut with small arrows step by step. Another method is to fold a thin paper exactly as the question shows and punch it with a pencil to check the answer. Daily practice of fifteen to twenty questions for a few days makes the reflection rule automatic, and the same skill helps in paper folding and mirror image questions as well.
Quick Revision Tips
- Count the folds before anything else.
- Reflect the cut one fold at a time, from the last fold to the first.
- Keep the shape of the hole unchanged while reflecting.
- Remember that a cut on a fold line gives a joined shape.
- Check the number of holes against the options.
- Do not mix up the folded and unfolded views.
Final Revision Note
During final revision, fold a real paper once and twice, cut a shape and open it to see the pattern. Then solve printed questions by drawing the fold lines and reflecting the cut with arrows. If the number of holes in your answer is wrong, the mistake is almost always a missed reflection, so check the folds again. This practice makes the reflection rule second nature and turns paper cutting into a reliable source of marks.
Frequently Asked Questions
What is paper cutting in reasoning?
It is a non-verbal reasoning topic in which a folded and cut paper must be unfolded mentally to find the pattern of holes that results.
How many holes does each fold create?
In the simple cases the number of holes doubles with each fold, because the cut is reflected across the new fold line.
How do I find the unfolded pattern?
Unfold the paper one fold at a time and reflect the cut across each fold line, building the full pattern step by step.
What if the cut is on the fold line?
A cut on the fold line gives half a shape on each side, and the two halves join into a single hole when the paper is opened.
Which exams ask paper cutting questions?
APSC, ADRE, Assam Police, DHS, DME, SSC and Railway examinations ask paper cutting questions in the non-verbal reasoning section.