Problem 13 · 2014 Math Kangaroo
Hard
Spatial & Visual Reasoning
paper-cuttingtiling-tessellation
A square is cut into four pieces. Which shape can you not make with these four pieces?
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Answer: D
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Hint 1 of 3
The four pieces never change, so every shape you build with them must take up the same amount of space as the square.
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Hint 2 of 3
Pretend the pieces are puzzle pieces and try to slide them inside each shape, turning and flipping as needed.
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Hint 3 of 3
Four of the shapes can be filled with no gaps; one shape always leaves a gap or an overhang.
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Approach: try to fit the same four puzzle pieces into each shape and find the one that won't go together
- The square is cut into four set pieces, so any shape made from all four covers exactly the square's worth of space.
- Treat the pieces like a puzzle and try to fill each answer shape, allowing turns and flips.
- Shapes A, B, C, and E can each be filled neatly with the four pieces.
- Shape D is the one that cannot be built from these four pieces.
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