Problem 16 · 2023 Math Kangaroo
Hard
Spatial & Visual Reasoning
tiling-tessellationspatial-reasoning
A building block is made up of five identical rectangles (shown). How many of the patterns shown below can be made with two such building blocks without overlap?
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Answer: D — 4
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Hint 1 of 2
Two blocks cover 5 + 5 = 10 small rectangles, so only patterns with 10 cells are possible.
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Hint 2 of 2
For the right-sized patterns, try to split them into two of the given S-shaped blocks.
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Approach: check cell count, then attempt a two-block tiling of each pattern
- Each building block is 5 cells, so two of them cover 10 cells — only patterns with 10 cells can work.
- Testing those patterns, exactly four of the five can be split into two of the S-shaped blocks without overlap.
- So the answer is 4.
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