Paper Folding & Paper Cutting
Paper Folding and Paper Cutting is a very common non-verbal reasoning topic of the ADRE 3.0 Grade IV paper. In this type of question a sheet of paper is folded once or more than once, and then one or more holes are punched or one or more pieces are cut out. The candidate has to find the pattern that appears on the paper when it is unfolded again. The whole topic depends on a single idea: when a folded paper is unfolded, every hole is reflected across the fold line, so each cut produces an image on the other side of the fold as well. If the paper is folded several times, each fold doubles the number of holes, and the holes are mirrored across every fold line in turn. Understanding this reflection is the key to solving every question of the topic.
Meaning of Paper Folding and Cutting
The question shows a square or rectangular sheet that is folded along one or more lines, and then a small shape such as a circle or a triangle is punched out or cut away. The figure of the folded paper with its holes is given, and the candidate must select the option that shows the correct unfolded sheet. The folds may be vertical, horizontal or diagonal, and the punch may be at any place on the folded paper. The answer must show all the holes in their correct positions, and no extra hole and no missing hole is allowed.
Important Rules of Folding and Cutting
- Every hole is reflected across each fold line when the paper is unfolded.
- A single fold doubles the number of holes made by one punch.
- Two folds increase the number of holes to four times the original.
- The distance of a hole from the fold line is the same on both sides.
- A punch on the fold line produces a single hole that lies on the crease.
- A punch near the outer edge produces holes near the outer edge in the unfolded sheet.
- If the fold is diagonal, the holes are mirrored along the diagonal.
- The number of holes is always a power of two when only full folds are used.
- Cutting a piece from the folded edge produces a notch on the edge of the unfolded paper.
- The shape of every hole is the same as the shape that was punched.
Types of Questions
Some questions fold the paper once and punch a single hole, which is the simplest form. Some fold the paper once and punch two holes, so the unfolded sheet has four holes. Some fold the paper twice, once vertically and once horizontally, and then punch, producing four holes. Some questions fold the paper into a triangle by a diagonal fold and punch near the diagonal. A few questions cut a piece from the folded edge instead of punching a hole inside, and there the candidate must find the shape of the notch on the outer boundary of the unfolded sheet.
How to Solve a Paper Folding Question
- Count the number of folds and note the direction of each fold.
- Count the number of punches or cuts on the folded paper.
- Multiply the punches by two for each fold to get the total holes.
- Mark each hole and reflect it across the fold lines one by one.
- Compare the resulting pattern with the options and reject any excess or missing hole.
Worked Examples
If a paper is folded once along the middle and a single hole is punched on the folded paper, then on unfolding there will be two holes, placed at equal distances on the two sides of the crease. If the same paper is folded twice, first in the middle and then again in the middle, one punch will produce four holes arranged in a square. If the paper is folded along a diagonal and a hole is punched near one corner, the unfolded sheet will show two holes placed symmetrically about the diagonal. If a piece is cut from the folded edge, the unfolded sheet will have the same notch repeated on both sides of the crease.
How This Topic Appears in the Examination
Paper folding and cutting is usually asked as a small group of objective questions carrying one mark each. The figures are simple and the arithmetic needed is only the doubling of the number of holes, so the main skill is careful imagination. Candidates who lose marks usually do so because they place the holes in the wrong positions rather than because they count wrongly. A little practice with a real piece of paper while learning quickly builds the imagination needed to answer without it in the examination hall.
Memory Tips
Remember the simple rule that each fold doubles the number of holes. Always draw the fold line clearly before placing the reflected holes, because a clear fold line prevents a wrong reflection. Fold the paper mentally in the order in which it was folded, and unfold it in the reverse order, reflecting the holes at each stage. When a punch lies on the fold line, remember that it makes only one hole, not two. If the number of holes in the options differs from the number you calculated, that option can be rejected at once.
Common Mistakes to Avoid
- Forgetting to reflect the holes across every fold line.
- Placing the holes at unequal distances from the crease.
- Treating a punch on the fold line as two separate holes.
- Reflecting the holes in the wrong direction for a diagonal fold.
- Choosing an option with the right number of holes but the wrong arrangement.
How to Prepare This Topic
- Learn the rule that each fold doubles the number of holes.
- Use a real sheet of paper to fold, punch and unfold while learning.
- Practise at least fifteen questions every day.
- Draw the fold lines on rough paper before placing the holes.
- Time yourself so that each question takes less than a minute.
Additional Solved Examples
If a square sheet is folded along the middle vertically and a hole is punched at the top-left corner of the folded half, then on unfolding the holes appear at the top-left and the top-right corners of the square. If a round hole is punched exactly on the folded edge, then on unfolding the hole appears as a single round hole on the crease, and not as two. If a paper is folded into four equal parts and a hole is punched at the centre of the folded packet, the unfolded sheet shows four holes arranged in a square. If a triangular piece is cut from the fold line of a folded sheet, the unfolded sheet shows a diamond-shaped opening formed by the two mirrored triangles.
Advanced Tips
When the number of folds is large, first fix the total number of holes by doubling, and use that number to eliminate options before worrying about positions. In diagonal folds, the two halves of the unfolded sheet are mirror images about the diagonal, so a hole above the diagonal has a partner below it at the same distance. When a question cuts a piece from an edge, treat the removed piece as a hole of the same shape, because the missing part of the paper is what appears in the answer. If two options have the same number of holes, compare them hole by hole, starting from the corner nearest the punch; the correct option will match at every point.
Related Non-Verbal Topics
Paper folding and cutting is closely related to Mirror Image and Water Image, Figure Analogy and Pattern Completion. Mirror image also uses the idea of a reflection, and paper folding is simply a reflection across a fold line instead of across a mirror. Figure analogy often uses a folded and unfolded figure as the model pair. Pattern completion asks for the missing part of a design, which is like finding the missing holes after unfolding. Practising these topics together makes the idea of reflection familiar and easy to apply.
Quick Revision Checklist
- Each fold doubles the number of holes.
- Reflect the holes across every fold line.
- Keep equal distance from the crease on both sides.
- A punch on the fold line makes only one hole.
- For diagonal folds, mirror the holes along the diagonal.
- Reject options with the wrong number or wrong position of holes.
Frequently Asked Questions
What is a paper folding and cutting question?
It shows a paper folded and then punched or cut, and asks you to find the pattern of holes that appears when the paper is unfolded.
How many holes does one punch make after folding?
Each fold doubles the number of holes, so one punch after one fold gives two holes, after two folds gives four holes and so on.
What happens if the punch is on the fold line?
A punch exactly on the fold line gives a single hole lying on the crease when the paper is unfolded, not two separate holes.
How do I handle a diagonal fold?
For a diagonal fold, reflect the holes across the diagonal line, so a hole above the diagonal has a partner below it at the same distance.
How much time should each question take?
A paper folding question should take less than a minute once the rule of doubling and reflection is firmly understood.