Problem 2 · 2024 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationpath-tracing
A tile pattern is made up of a number of identical irregular pentagons. Which of the following tiles fits into the hole in such a way that a closed curve is formed?
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Answer: C
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Hint 1 of 3
Find where the curves on the surrounding tiles meet the edges of the empty pentagonal hole — those are loose ends.
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Hint 2 of 3
The inserted tile's arcs must connect to every loose end so the curve never just stops.
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Hint 3 of 3
Check each option by tracing: only one tile turns all the loose ends into a single unbroken closed loop.
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Approach: match the curve ends along the hole's edges
- On the edges of the empty pentagon, the surrounding tiles leave several curve ends sticking out.
- The tile dropped in must join to every one of those ends, or the curve would have a loose end.
- Tracing the five options, only one routes its arcs so that all ends connect.
- That tile seals everything into one closed curve, so the answer is C.
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