Problem 28 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
net-folding
Leon has drawn a closed loop on the surface of a cuboid. Which net cannot show his loop?
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Answer: C
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Hint 1 of 2
A loop on a closed surface must enter and leave every face it crosses — on the net, the curve's pieces must join up when faces are folded.
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Hint 2 of 2
Check each net for a curve that fails to close into a single loop when the cuboid is reassembled.
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Approach: fold each net and test loop closure
- A valid loop crosses shared edges consistently and closes into one continuous curve once the net is folded.
- Tracing the arc segments across the shared edges of each net shows whether the ends meet.
- Net C's segments cannot be joined into a single closed loop on the folded cuboid.
- So the impossible one is C.
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