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2019 Math Kangaroo

Problem 13

Problem 13 · 2019 Math Kangaroo Hard
Spatial & Visual Reasoning tiling-tessellation
Figure for Math Kangaroo 2019 Problem 13
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Answer: E — Square E.
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Hint 1 of 2
The two given pieces have a fixed number of black and white cells; any buildable square must match that count.
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Hint 2 of 2
Try to tile each option with the two pieces; one of them is impossible.
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Approach: match piece shapes and shading to each target
  1. The two pieces together cover the 16 cells of a 4×4 square with a fixed pattern of black and white cells.
  2. Four of the option squares can be assembled from the two pieces (allowing rotation).
  3. Square E has a black/white arrangement the two pieces cannot produce.
  4. So the answer is E.
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