Problem 12 · 2010 Math Kangaroo
Medium
Spatial & Visual Reasoning
paper-cuttingfolding
A paper strip is folded three times in the middle. It is then opened again and looked at from the side, so that one can see all 7 folds from the side at the same time. Which of the following views is not a possible result?
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Answer: D
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Hint 1 of 2
Folding a strip in the middle three times makes 7 creases when reopened.
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Hint 2 of 2
Look at the up/down pattern of creases; one of the pictures breaks the rule of what folding can make.
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Approach: check the crease (mountain/valley) pattern
- Folding in the middle three times and reopening leaves seven creases, each either a peak (mountain) or a dip (valley).
- Repeated centre-folding forces a fixed symmetric mountain/valley pattern, so most of the pictures match a real fold while one cannot occur.
- The view that no sequence of centre folds can produce is D.
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