Paper Folding & Cutting
🔒 Log in to trackA folded sheet is punched or cut, and you must predict the unfolded pattern. Unfold in reverse order, reflecting every hole across each fold line; count layers first (p × 2ⁿ for full folds) to eliminate options, then match positions. Diagonal folds swap the two coordinates; partial folds double only what the flap covers.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
36 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (36 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Fold once, punch a hole
very commonA sheet is folded in half, a hole is punched, and you pick the unfolded sheet.
Every hole has a mirror twin on the other side of the fold line.
The twin is at the same height for an up-down fold line.
A sheet is folded left over right. One hole is punched near the top-right. How do the holes look after unfolding?
The fold line is the middle line
The mirror twin is on the left, equally far from the fold
Both are at the same height: 2 holes, one near the top of each side
Fold twice into quarters
very commonA sheet is folded twice at right angles, then punched.
Unfold in reverse order.
Each hole makes 4 holes placed evenly around both middle lines.
A sheet is folded in half twice and one hole is punched away from the creases. How many holes are there after unfolding?
Each fold doubles the layers
2 × 2 = 4 layers, and the punch goes through all
Total = 4 holes
Diagonal fold
commonA square is folded along a corner-to-corner line to make a triangle.
The hole's twin is its mirror image across the diagonal.
A point on an edge moves to the matching point on the next edge.
A square sheet is folded along the diagonal from top-left to bottom-right. One hole is punched at the middle of the left edge. Where is the other hole?
The diagonal works like a mirror
The left edge reflects onto the top edge
The twin is at the middle of the top edge
Fold only part of the sheet
occasionalOnly a strip of the sheet is folded over, not the whole half.
Count layers in each part.
Two layers give 2 holes, one layer gives 1 hole.
The left quarter of a sheet is folded over onto the rest. One hole is punched through the two-layer part and one through the single-layer part. How many holes are there?
Two-layer part: 1 punch gives 2 holes
Single-layer part: 1 punch gives 1 hole
Total 2 + 1 = 3 holes
Three folds
occasionalA sheet is folded three times, then punched.
Each fold doubles the layers.
Number of holes = 2 × 2 × 2 = 8 for each punch.
A sheet is folded in half, in half again, then once along a diagonal. One hole is punched away from all creases. How many holes?
Three folds: 2 × 2 × 2 = 8 layers
The punch goes through all 8 layers
Total = 8 holes
Hole on a crease
occasionalThe hole is punched right on the folded edge.
Twins across that crease fall on the same spot.
They join into one hole.
A sheet is folded in half twice and punched exactly at the corner where both creases meet. How many holes?
This corner is the centre of the sheet
All four copies fall on the same spot
They join into 1 hole
Count holes only
commonNo picture. It gives the number of folds and punches and asks for the holes.
Holes = punches × 2 for each fold.
Check for partial folds or holes on creases.
A sheet is folded in half 3 times and 2 holes are punched, away from the creases. How many holes are there?
3 folds: 2 × 2 × 2 = 8 layers
Each punch makes 8 holes
2 punches: 2 × 8 = 16 holes
Count the layers
occasional"How many layers are there after the folds?"
Start with 1 layer.
Multiply for each fold.
A sheet is folded into three equal strips, then folded in half. How many layers are there?
Three strips: 3 layers
Fold in half: 3 × 2
= 6 layers
Cut a shape from the fold
commonA shape is cut out of the folded sheet instead of a hole.
The cut opens into a shape that is the same on both sides of each fold.
Unfold in reverse order.
A sheet is folded once. A half-circle is cut with its flat side on the fold. What shape appears after unfolding?
The fold line acts like a mirror
The half-circle is joined with its mirror twin
They make a full circle