Problem 14 · 2013 Math Kangaroo
Medium
Spatial & Visual Reasoning
net-foldingfoldingspatial-reasoning
The five shapes pictured were cut out of paper. Four of them can be folded to form a cube. For which shape is this not possible?
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Answer: C — Shape 3
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Hint 1 of 2
Imagine folding each net up around a cube; track where each square lands.
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Hint 2 of 2
Four of them wrap correctly — one has two faces fighting for the same spot.
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Approach: mentally fold each net
- A net folds into a cube only if its six squares cover all six faces without overlap.
- Folding each pictured net, four of them wrap neatly onto the cube.
- Shape 3 forces two squares onto the same face, leaving one face bare.
- So Shape 3 cannot be folded into a cube.
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