Problem 17 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
net-foldingpath-tracing
Leon has drawn a closed path on the surface of a cuboid. Which net (shown below) can represent his path?
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Answer: D
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Hint 1 of 3
On the real cuboid the path is one continuous loop, so on every fold edge the line must continue across without a gap.
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Hint 2 of 3
Walk along the path in each net and check that it leaves a face exactly where it re-enters the neighbouring face when folded.
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Hint 3 of 3
Reject any net where a path end stops at an edge with no matching segment on the face it glues to.
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Approach: match path crossings across every glued edge of the folded net
- A closed path on the cuboid is one loop, so where it crosses an edge of the net the two faces that join along that edge must each carry the line at the same point.
- In options A, B, C and E at least one path segment runs off an edge with no matching line on the face it folds against, breaking the loop.
- Only the segments in option D line up at every shared edge and close into a single continuous loop.
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