Problem 22 · 2025 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellationarea
Julio wants to make the shape shown in the top picture on the right. He has several of each of the five tiles shown in the bottom picture on the right. The tiles must be placed next to each other without overlapping. What is the smallest number of tiles he must use?
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Answer: C — 13
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Hint 1 of 2
To use as few tiles as possible, you want each tile to cover as much of the cross as it can, so reach for the biggest tiles first.
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Hint 2 of 2
The straight parts of the cross are easy to cover with the large rectangle and big triangle; the pointy arm-tips are what force you to use the small triangles.
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Approach: cover the big areas with big tiles, the tips with small ones
- Fewer tiles means each tile should cover as much as possible, so fill the wide straight parts of the cross with the largest tiles (the long rectangle and the big triangle).
- The four slanted arm-tips are too thin for the big tiles, so each tip has to be finished with the small triangle pieces — these are unavoidable and set the limit on how low the count can go.
- Packing the big tiles in the body and the small triangles at the tips, with no overlaps, covers the whole cross in 13 tiles, and no arrangement does it in fewer, so the answer is (C) 13.
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