Paper Folding and Paper Cutting for the Assam Police Constable (AB & UB) Exam
Paper Folding and Paper Cutting is a non-verbal reasoning topic of the SLPRB Assam Police Constable (AB & UB) examination in which a sheet of paper is folded one or more times and then a hole or a cut is made through the folded paper, and the candidate must find the pattern of holes that appears when the paper is opened out. A related form shows the punches already made in a folded paper and asks where the folds were. The topic tests the ability to picture the unfolded sheet and to mirror the cuts across every fold line. This page explains the two directions of the question, the folding method, worked examples, shortcuts and the common traps. The material follows the standard reasoning reference books used for Assam recruitment examinations and is reviewed before it is published.
What the Topic Means
When a paper is folded and a hole is punched through all the layers, then on opening the paper the hole appears as many holes, one for each layer that the punch passed through. The holes are the mirror images of one another across the fold lines. If the paper is folded once, one punch gives two holes; if folded twice, it gives four holes; and if folded three times, it gives eight holes, provided the punch goes through all the layers. The cuts on either side of a fold line are always mirror images, so the pattern is symmetrical about every fold.
The Two Forms of the Question
- Folding followed by cutting: the folds and the cut are shown, and the opened pattern must be chosen.
- Cutting followed by unfolding: the opened pattern is shown, and the position of the folds must be found.
- Counting the number of holes that result from a given number of folds and punches.
- Finding the shape of the cut after opening a paper folded along a diagonal.
A Step by Step Method
- Note how many times the paper is folded and along which lines.
- Note the position of the cut or hole on the folded paper.
- Unfold one fold at a time and mirror the hole across that fold line.
- Repeat the mirroring for every fold until the paper is fully open.
- Match the resulting pattern of holes with the options.
Worked Examples
Example one: a square paper is folded once along the middle and a hole is punched through both layers; on opening, two holes are seen, one on each side of the fold line, at equal distances from it. Example two: a paper is folded twice and a hole is punched through all four layers; on opening, four holes appear at the four corners of a rectangle. Example three: a paper is folded along the diagonal and a hole is cut near the fold; on opening, a V-shaped pattern of two holes appears, mirroring across the diagonal. Example four: a paper is folded into four and a corner is cut off; on opening, the corner is cut at all four places where the layers met. Example five: if a paper is folded and a shape is cut from the folded edge, then on opening a single large hole appears at the middle because the separate cut pieces join together.
How This Topic Appears in the Examination
The topic usually appears as two to four objective questions of one mark each. The common forms are to choose the opened pattern from four figures, to count the number of holes, and to find the fold line from the opened pattern. The options differ only in the position or the number of holes, so the candidate must unfold the paper in the mind carefully, one fold at a time.
Shortcuts and Speed Methods
- Count the layers first; the number of holes is the number of layers the punch passes through.
- Every hole has a mirror image across the fold line.
- Unfold one fold at a time and never jump straight to the final pattern.
- If the cut is on a fold line, the two half-holes join into one hole on opening.
- Check the symmetry of the option; the true pattern is symmetrical about every fold.
Common Mistakes to Avoid
- Forgetting that a cut on the fold gives a single hole and not two.
- Mirroring the hole in the wrong direction.
- Counting the holes without counting the layers the punch passes through.
- Choosing a pattern that is not symmetrical about the fold lines.
- Unfolding all the folds at once instead of one at a time.
Preparation Plan
- Practise by actually folding and cutting a paper a few times.
- Learn to count layers for one, two and three folds.
- Draw the mirror of a hole across a line every day.
- Solve ten questions a week and check each by unfolding step by step.
- Revise the standard patterns for folds along the middle and the diagonal.
More Practice Questions
- A paper folded once and punched through both layers; count the holes on opening.
- A paper folded twice and punched through all layers; find the pattern of four holes.
- A paper folded diagonally and cut near the fold; find the shape on opening.
- A corner cut from a paper folded into four; find the opened pattern.
- A paper folded and a shape cut on the fold line; find the number of holes.
Quick Revision Checklist
- Note the number of folds and their lines.
- Note the position of the cut.
- Unfold one fold at a time and mirror the hole.
- Remember that a cut on the fold gives one hole.
- Check that the final pattern is symmetrical.
Paper Folding and Spatial Reasoning
Paper folding and cutting is close to cubes and dice because both need a picture of a flat sheet or a solid object being changed in the mind. The skill of mirroring a hole across a line is the same as finding a water image or a mirror image, so practice in one topic helps the other. The best way to gain confidence is to fold and cut a real paper a few times and to watch how the layers behave; after that the mind can do the same folding without the paper.
Frequently Asked Questions
How many holes appear after folding and cutting?
The number of holes equals the number of layers the punch passes through, so one fold gives two holes, two folds give four and three folds give eight.
What happens if the cut is on the fold line?
The two half-holes made on either side of the fold join into a single hole when the paper is opened, so the count is one and not two.
How do I find the fold line from an opened pattern?
Look for the line about which the holes are mirror images of one another; the fold line is the axis of symmetry of the pattern.
Which way are the holes mirrored?
Each hole is mirrored across the fold line at an equal distance on the other side, and the same rule is repeated for every fold.
Is paper folding important for Assam Police?
Yes. The rule of layers and mirroring is simple and fixed, so the questions can be solved quickly once the method is practised.