Problem 11 · 2013 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellation
Ralf has many equally big plastic plates, each a regular pentagon. He glues them together edge to edge to form a complete ring (see picture). Out of how many plates is the ring made?
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Answer: C — 10
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Hint 1 of 2
Each pentagon turns the ring by a fixed angle as you go around.
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Hint 2 of 2
The ring closes after the turning adds up to a full 360° (going around twice for pentagons).
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Approach: turning angle around the ring
- Gluing regular pentagons edge to edge bends the chain by 36° at each joint.
- To come back to the start the bends must total 360°, needing 10 plates.
- So the ring uses 10 plates: C.
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