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2025 Math Kangaroo

Problem 16

Problem 16 · 2025 Math Kangaroo Hard
Spatial & Visual Reasoning tiling-tessellationcomposition

Eva puts these two identical pieces together to make a figure. Which of these figures can she not build?

Figure for Math Kangaroo 2025 Problem 16
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Answer: E
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Hint 1 of 2
The two identical pieces can be flipped and turned - try fitting them into each shape.
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Hint 2 of 2
Four shapes can be tiled by the two pieces; the odd one out is the answer.
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Approach: try to tile each shape with the two identical pieces
  1. Each given piece is a fixed shape; you may rotate or flip it.
  2. Try assembling each option from exactly two copies.
  3. Four of them work, but the arrow shape in option E cannot be formed.
  4. So Eva cannot build E.
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