Paper Folding

Predicting hole patterns when folded paper is punched and unfolded.

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Predicting hole patterns when folded paper is punched and unfolded.

Paper folding puzzles involve mentally simulating the process of folding paper, punching a hole through the folded layers, and predicting where the holes appear when the paper is unfolded. Each fold doubles the number of resulting holes, creating symmetric patterns.

holes_unfolded = reflect(punch_position, fold_axis)

Paper folded vertically with hole on left: holes appear on both left and right
Paper folded horizontally with hole at top: holes appear at top and bottom
Multiple folds create 4, 8, or more symmetric holes

How to recognize it

Identify the fold line (vertical or horizontal)
Note the punch position relative to the fold
Reflect the hole position across the fold line
For multiple folds, apply reflections in reverse order

Common mistakes

Forgetting to reflect across the fold line
Confusing which side of the fold has the hole
Not doubling holes for each fold layer

Step-by-step walkthrough

A square paper is folded in half vertically, then a hole is punched in the upper-left area. How many holes appear when unfolded?

Start with a flat square paper. The dashed line shows where it will be folded. The red dot marks where we will punch a hole.
Fold the paper in half along the vertical line. The right half (R) folds onto the left half (L), creating 2 layers.
Now punch a hole through the folded paper at the marked position. The punch goes through BOTH layers.
Unfold the paper. Since both layers were punched, there are now 2 holes - mirror images across the fold line.

Answer: Two holes: one on the left, one on the right (symmetric across the fold)

Practice guidance

Spatial Reasoning