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.
Single fold, punch
very commonOne half fold, one or two punches, four figure options.
How to solve: Mirror each punch across the fold line; same height for a vertical fold.
Example: Q. Folded left over right, punched once near the top-right. Holes after unfolding?
2 holes at the same height, one near each side.
Quarter fold, punch
very commonTwo folds at right angles, then a punch.
How to solve: Undo the second fold, then the first; 4 holes per punch placed symmetrically about both centre lines.
Example: Q. Folded into quarters and punched once near the open corner. How many holes?
4, one near each corner of the sheet.
Diagonal fold
commonA corner-to-corner fold makes a triangle.
How to solve: Reflect across the diagonal: (x, y) → (y, x) for the top-left to bottom-right diagonal.
Example: Q. Folded along the main diagonal, punched near the middle of the left edge. Where is the other hole?
Near the middle of the bottom edge.
Strip (partial) fold
occasionalThe fold line is not through the centre.
How to solve: Double only punches inside the folded strip.
Example: Q. Left quarter folded over; punches on the doubled and the single part. Holes?
2 + 1 = 3.
Three folds
occasionalQuarter fold followed by a diagonal, or three half folds.
How to solve: 8 holes per punch; undo the last fold first.
Example: Q. Halved, halved again, then folded along a diagonal; one punch. Holes?
Punch on a crease
occasionalThe punch mark is on the edge where the paper bends.
How to solve: Copies across that crease merge into one hole.
Example: Q. Quarter fold punched at the folded corner. Holes?
Hole count only
commonText question: number of folds and number of punches.
How to solve: H = p × 2ⁿ for full folds; adjust for strip folds and crease punches.
Example: Q. Folded in half three times, 2 punches. Holes?
Layers after a three-way fold
occasionalThe sheet is folded into three equal strips.
How to solve: 3 layers; each later full fold doubles it.
Example: Q. Folded into three strips, then in half. Layers?
Cut and unfold
commonA shape is cut from a folded edge or corner instead of a punch.
How to solve: The cut opens into a shape symmetric about each fold line; mirror it in reverse order.
Example: Q. A half-circle is cut from the folded edge of a sheet folded once. What opens out?
A full circle centred on the crease.