Problem 18 · 1998 AJHSME
Hard
Geometry & Measurement
symmetryspatial-reasoning
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Answer: B — Choice B.
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Hint 1 of 2
First settle how MANY holes appear: the paper was folded twice, so the punch went through 2 × 2 = 4 layers. The answer must show exactly 4 holes — that alone rules choices out.
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Hint 2 of 2
Unfold in reverse order, and each time you open a fold the holes copy across the crease line like a mirror. Undo the last fold first.
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Approach: count layers for the number of holes, then mirror across each crease
- Two folds stack the paper into 2 × 2 = 4 layers, so the single punch pierces 4 spots — look only at choices with exactly four holes.
- Unfold in reverse. Undo the last fold (left-to-right): the hole in the upper area mirrors across the vertical crease, making a left/right pair. Then undo the first fold (bottom-to-top): both holes mirror across the horizontal crease, making the bottom copies.
- The result is four holes placed symmetrically — matching choice B.
- Why this transfers: every fold-and-punch is two questions in one. Count holes = 2^(number of folds), and locate them by reflecting across each crease as you unfold in the opposite order you folded. Folding is just mirroring.
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