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Free guide · Spatial reasoning · 3 min read

How to solve paper folding questions

Paper folding: unfold backwards

Punched holes mirror across each fold line as you unfold, last fold first. Count layers, mirror holes, and the answer is arithmetic.

Updated

A sheet is folded, punched, and unfolded — which pattern results? The untrained eye simulates forward and drowns. The method runs BACKWARDS: start from the punched state and undo one fold at a time; each undo mirrors every existing hole across that fold line and doubles the count.

One fold = one mirror

Undoing a right-onto-left fold reflects every hole across the vertical center line and ADDS the mirrored copies. Two punches through a single fold make four holes: the originals plus their mirror twins, symmetric about the fold line.

Count before you look

Holes multiply by 2 per fold (when every punch pierces all layers): 1 fold → ×2, 2 folds → ×4. Compute the expected count FIRST and discard every option with the wrong number of holes — usually all but two options die on arithmetic alone.

The strategy

  1. Count folds F and punches P. Expect P × 2^F holes.
  2. Eliminate options with the wrong hole count.
  3. Undo the LAST fold first: mirror all holes across its line.
  4. Undo the remaining fold. Check the final pattern's symmetry axes match the fold lines.

Common traps

  • Forgetting one unfold — the too-few-holes option.
  • Mirroring across the wrong axis (vertical fold, horizontal mirror).
  • The unmirrored option: your punches where you punched them, and nowhere else.

Speed · ~45s/item: Count → eliminate → mirror runs in 30–60 seconds; forward simulation cannot compete.

Worked example

Made by the same generator and answer checker as the practice questions, at middling difficulty, but never served in a test. Commit to an option before you reveal — the pick is yours alone and is never recorded.

The sheet is folded and punched as shown. Unfolded, which pattern results?

Reveal the answer

The answer is E.

Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the left half is folded onto the right), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 2 punch(es) through 2 layers become 4 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.

Try it yourself: 4 practice questions

Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.

Question 1 · Easy

The sheet is folded and punched as shown. Unfolded, which pattern results?

Reveal the answer

The answer is E.

Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the left half is folded onto the right), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 1 punch(es) through 2 layers become 2 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.
Question 2 · Easy

The sheet is folded and punched as shown. Unfolded, which pattern results?

Reveal the answer

The answer is C.

Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the left half is folded onto the right), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 1 punch(es) through 2 layers become 2 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.
Question 3 · Easy

The sheet is folded and punched as shown. Unfolded, which pattern results?

Reveal the answer

The answer is B.

Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the right half is folded onto the left), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 1 punch(es) through 2 layers become 2 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.
Question 4 · Easy

The sheet is folded and punched as shown. Unfolded, which pattern results?

Reveal the answer

The answer is E.

Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the top half is folded down onto the bottom), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 1 punch(es) through 2 layers become 2 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.

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Questions people ask

How do you solve a paper folding question?

Unfold backwards, last fold first. Each fold you undo mirrors every hole across that fold line and adds the copies.

How many holes will there be?

Each fold doubles the holes when the punch goes through every layer: one fold gives two, two folds give four. Count first and rule out options with the wrong number.

How long should a paper folding question take?

About 30 to 60 seconds: count, rule out, then mirror.

Will paper folding questions be on the free test?

Maybe. The free test gives spatial reasoning 4 of its 20 questions, spread across 9 different question types, so any one test may or may not include this kind.

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