Paper Folding
Brief Theory Overview
Paper Folding is a non-verbal reasoning topic that tests your spatial visualization ability. A question shows a sequence of folds made on a transparent square paper and then one or more holes are punched on the folded paper. You have to mentally unfold the paper and pick the unfolded pattern (answer figure) that matches the exact position, shape and number of holes. The key is to reverse the folding sequence step-by-step and mirror-locate every punched hole on all layers that were beneath it.
Always remember:
- Count the total layers under the punch – each layer gets one identical hole after unfolding.
- Work backwards from the last fold to the first; sketch tiny marks on rough sheet if needed.
- Use symmetry – diagonal folds create 45° hole lines, edge-to-edge folds create mirror pairs.
- Eliminate options that have extra holes, missing holes, or wrong symmetry; you can often solve by “odd one out” visual scan.
Multiple-Choice Questions
Easy (1-8)
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A square paper is folded once along the vertical middle line and a hole is punched at the centre of the folded edge. How many holes will appear on the fully opened sheet and where?
- A) 1 hole at centre
- B) 2 holes, both on vertical mid-line
- C) 2 holes, both on horizontal mid-line
- D) 4 holes, one in each quadrant
AnswerCorrect: Option B. Explanation: Single fold doubles the paper; centre punch goes through 2 layers → 2 symmetric holes on the original vertical mid-line.
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A paper is folded in half top-to-bottom (horizontal fold) and a hole is punched at the top-right corner of the folded rectangle. The unfolded sheet will show holes at:
- A) top-right only
- B) top-right & bottom-right
- C) top-right & top-left
- D) top-right & bottom-left
AnswerCorrect: Option B. Explanation: Horizontal fold mirrors top onto bottom; punch at top-right appears on both top-right and bottom-right.
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A square paper is folded along both diagonals one after another and a hole is punched at the centre of the folded triangle. How many holes after full unfolding?
- A) 1
- B) 2
- C) 4
- D) 8
AnswerCorrect: Option C. Explanation: Two diagonal folds create 4 layers; centre punch → 4 symmetric holes along the diagonals.
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A paper is folded once corner-to-corner to form a right-triangle. A hole is punched at the midpoint of the hypotenuse. Unfolded pattern shows:
- A) 1 hole at centre
- B) 2 holes on a diagonal
- C) 2 holes on vertical mid-line
- D) 4 holes
AnswerCorrect: Option B. Explanation: Single diagonal fold → 2 layers; midpoint of hypotenuse maps to two points on the original diagonal.
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After a vertical fold, a hole is punched on the top-edge exactly at the mid-point. The opened sheet has:
- A) 1 hole
- B) 2 holes on top edge
- C) 2 holes on bottom edge
- D) 2 holes, one each on left & right edges
AnswerCorrect: Option B. Explanation: Fold doubles left-right; midpoint of top edge becomes two midpoints on the original top edge.
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A paper is folded twice—first vertically, then horizontally. One hole is punched at the centre of the folded square. Total holes on opening?
- A) 2
- B) 4
- C) 6
- D) 8
AnswerCorrect: Option B. Explanation: Two folds create 4 layers; centre punch → 4 holes forming a 2×2 square pattern.
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If after folding a paper into half, a circle is punched at the folded edge 2 cm from the crease, the unfolded sheet shows:
- A) 1 circle 2 cm from edge
- B) 2 circles each 2 cm from opposite edges
- C) 2 circles each 4 cm apart on same side
- D) 4 circles
AnswerCorrect: Option B. Explanation: Fold creates mirror; distance from crease remains 2 cm on both mirrored positions.
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A square sheet folded along a diagonal once; a hole is punched at the right-angle vertex of the resulting triangle. The unfolded sheet has:
- A) 1 hole at a corner
- B) 2 holes at two corners
- C) 2 holes at centre
- D) 4 holes at all corners
AnswerCorrect: Option B. Explanation: Right-angle vertex is the folded corner; punch appears on two opposite corners of original square.
Medium (9-18)
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A paper is folded sequentially: left half over right, then bottom half over top. A hole is punched 1 cm from the new top-right corner. How many holes and where after unfolding?
- A) 2 holes near top-right & bottom-left
- B) 4 holes near four corners
- C) 4 holes near top-right, top-left, bottom-right, bottom-left
- D) 1 hole only
AnswerCorrect: Option C. Explanation: Two folds create 4 layers; punch near top-right corner maps to all four original corners.
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A paper is folded in zig-zag fashion: first vertical half left→right, then the folded rectangle folded top→bottom, then again left→right. A hole is punched at the centre of the final folded strip. Total holes on opening?
- A) 4
- B) 6
- C) 8
- D) 16
AnswerCorrect: Option C. Explanation: Three folds → 8 layers; centre punch → 8 holes arranged in 2×4 grid symmetry.
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A square is folded along both diagonals and then along the vertical mid-line. A hole is punched at the intersection point of all folds. The unfolded sheet shows:
- A) 4 holes on diagonals
- B) 6 holes
- C) 8 holes
- D) 16 holes
AnswerCorrect: Option C. Explanation: Three folds create 8 layers; punch at common centre → 8 holes.
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After folding a paper such that point A meets opposite point C (diagonal), a triangular hole is cut along the folded edge. Unfolded pattern shows:
- A) 1 triangle at centre
- B) 2 triangles mirror on diagonal
- C) 4 triangles around centre
- D) 8 triangles
AnswerCorrect: Option B. Explanation: Single diagonal fold; cut on edge → 2 mirrored triangles on that diagonal.
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A paper is folded once so that the bottom-right corner lands exactly on the top-left corner. A hole is punched 3 cm below the top edge of the folded paper. After unfolding, the holes will be:
- A) 3 cm below top-left & 3 cm above bottom-right
- B) both 3 cm below top edge
- C) both 3 cm above bottom edge
- D) 4 holes
AnswerCorrect: Option A. Explanation: Diagonal fold maps corners; distance from top edge becomes mirrored 3 cm positions.
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A rectangular paper is folded in half twice—first along length, then along width. A hole is punched at the new geometric centre. The unfolded sheet contains:
- A) 1 hole
- B) 2 holes
- C) 4 holes forming rectangle
- D) 8 holes
AnswerCorrect: Option C. Explanation: Two folds → 4 layers; punch → 4 holes at centres of each quadrant.
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A paper is folded into an accordian (fan) of 4 equal vertical strips. A hole is punched through all layers at the mid-height of the 2nd strip from left. Unfolded sheet shows:
- A) 4 holes in 2nd strip
- B) 4 holes alternating strips
- C) 8 holes
- D) 2 holes
AnswerCorrect: Option B. Explanation: Accordian fold doubles layers; 4 strips → 8 layers but punch in 2nd strip appears in every alternate strip due to back-and-forth folding.
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A square paper is folded corner to mid-point of opposite side (forming a trapezium). A hole is punched at the acute-angle vertex. Unfolded pattern has:
- A) 1 hole
- B) 2 holes
- C) 4 holes
- D) 8 holes
AnswerCorrect: Option C. Explanation: Special fold creates 4 symmetric positions; punch → 4 holes.
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After folding a paper into a small square by consecutive half-folds, a corner of the final square is clipped off. The unfolded sheet shows:
- A) 1 clipped corner
- B) 2 clipped corners diagonally
- C) 4 clipped corners
- D) 8 clipped corners
- E) (Note: 4 options only)
AnswerCorrect: Option C. Explanation: Two folds → 4 layers; clipping corner → 4 symmetric missing corners on original square.
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A circular paper is folded in half along a diameter, then again along a perpendicular diameter. A hole is punched at 1 cm from the circumference along the second crease. Unfolded circle shows:
- A) 2 holes
- B) 4 holes forming square
- C) 4 holes on cross
- D) 8 holes
AnswerCorrect: Option C. Explanation: Two perpendicular folds → 4 layers; punch near rim along crease → 4 holes on the cross diameters.
Hard (19-25)
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A paper is folded in the sequence: diagonal (top-left→bottom-right), then vertical mid-line, then horizontal mid-line. A hole is punched at the centroid of the final folded triangle. How many holes after unfolding?
- A) 4
- B) 6
- C) 8
- D) 16
AnswerCorrect: Option C. Explanation: Three folds → 8 layers; centroid punch → 8 symmetric holes.
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A square paper is pleat-folded: top 1/4 down, bottom 1/4 up, then whole paper folded left-to-right. A hole is punched at the intersection of the two inner pleat creases. The unfolded sheet shows:
- A) 4 holes
- B) 6 holes
- C) 8 holes
- D) 12 holes
AnswerCorrect: Option C. Explanation: Pleat + vertical fold → 8 layers; punch at inner crease intersection → 8 holes.
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A paper is folded such that it forms 16 layers by 4 consecutive half-folds. A tiny hole is punched through the top-left corner of the folded wad. After unfolding, the number of holes is:
- A) 8
- B) 12
- C) 16
- D) 32
AnswerCorrect: Option C. Explanation: 4 folds → 16 layers; each layer receives one hole → 16 symmetric holes.
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A paper is folded into a paper-boat (classic origami) having 8 layers at the bottom tip. A hole is punched exactly through that bottom tip. The fully opened sheet shows:
- A) 4 holes
- B) 6 holes
- C) 8 holes
- D) 10 holes
AnswerCorrect: Option C. Explanation: Boat fold creates 8 layers at tip; punch → 8 holes radiating symmetrically.
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A square is folded along both diagonals, then each triangular flap is folded to the centre, creating 8 layers. A hole is punched at the centre. Unfolded pattern shows:
- A) 4 holes
- B) 6 holes
- C) 8 holes
- D) 16 holes
AnswerCorrect: Option C. Explanation: Final fold yields 8 layers; centre punch → 8 holes.
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A paper is rolled into a cylinder and then flattened; the flattened strip is folded in half. A hole is punched at the midpoint of the folded strip. After unrolling, the sheet shows:
- A) 2 holes
- B) 4 holes in rectangle
- C) 6 holes
- D) Infinite holes
AnswerCorrect: Option B. Explanation: Roll+flatten creates 2 layers, then fold → 4 layers; midpoint punch → 4 symmetric holes forming rectangle corners.
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A paper is folded in a way that 3 vertical and 3 horizontal accordian folds intersect, producing 16 small squares. A hole is punched in the 3rd row 2nd column square. The unfolded sheet shows:
- A) 4 holes
- B) 8 holes
- C) 12 holes
- D) 16 holes
AnswerCorrect: Option B. Explanation: Accordian folds create 8 effective layers due to back-and-forth; punch appears in 8 mirrored squares.
Shortcuts & Tips
- Layer Count = 2ⁿ (n = number of fold lines that pass through the punch zone).
- Mirror Rule: Every hole’s position is reflected across each fold line; draw faint mirror lines on rough sketch.
- Corner-Cut Trick: If a corner is clipped after n folds, expect 2ⁿ symmetric missing corners.
- Eliminate Options:
- Count total holes first—eliminate any option with fewer or more.
- Check symmetry axis—holes must appear mirrored across every fold line.
- Time Saver: For >3 folds, note that holes form equidistant grid or diagonal crosses; pick the option showing perfect grid/diagonal regularity.
BETA
