Problem 20 · 2020 Math Kangaroo
Medium
Spatial & Visual Reasoning
Logic & Word Problems
paper-cuttingfoldingcasework
Amelia has a paper strip with five equal cells, each containing a different drawing, as shown in the figure. She folds the strip so that the cells overlap in five layers. Which of the following sequences of layers, from top to bottom, is not possible to obtain?
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Answer: A — ★, □, ■, ○, ●
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Hint 1 of 2
Folding a strip reverses the order of the cells that flip over; track which symbol ends on top.
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Hint 2 of 2
Test each listed stack against an actual fold — one ordering can never arise.
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Approach: simulate the folds
- Folding the five-cell strip so all cells overlap forces certain symbols to keep their relative order and others to reverse.
- Checking each option against a real folding, four of them can be produced.
- The ordering in A cannot be obtained by any folding, so it is the impossible one, choice A.
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