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2017 Math Kangaroo

Problem 12

Problem 12 · 2017 Math Kangaroo Medium
Spatial & Visual Reasoning paper-cuttingfolding

Bob folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like this. Along which dotted line has Bob folded the paper beforehand?

Figure for Math Kangaroo 2017 Problem 12
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Answer: C
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Hint 1 of 2
Count the holes: four holes from one punch means the paper was in four layers.
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Hint 2 of 2
Four layers come from folding twice, along both centre lines.
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Approach: four holes need four layers, i.e. folds along both centre lines
  1. One punched hole makes one hole per layer of paper.
  2. Four holes mean the paper had four layers when punched.
  3. Four layers come from folding along both the horizontal and the vertical centre line.
  4. That double fold is shown by the cross in choice C.
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