Problem 3 · 2017 Math Kangaroo
Easy
Spatial & Visual Reasoning
tiling-tessellation
Anna has four identical building blocks that each look like the one shown (a straight strip of three squares). Which of the shapes in the options can she not form with them?
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Answer: E
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Hint 1 of 2
Each block covers three squares in a straight line; four of them cover twelve squares.
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Hint 2 of 2
A shape can be built only if it can be cut into straight 1×3 pieces — try tiling each one.
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Approach: tile each shape with straight triominoes
- The block is a straight strip of three squares, so four blocks cover 12 squares total.
- Each pictured shape has 12 squares, so the test is whether it splits into four straight 1×3 strips.
- Four of the shapes can be cut into such strips; the remaining one cannot be tiled this way.
- That shape is (E).
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