Problem 12 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationgrid
Which of the five shapes cannot be placed on the large square so that it only lies on white squares? (The five shapes A–E and the patterned large square are pictured with the question.)
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Answer: D
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Hint 1 of 2
Look at where the white squares actually sit on the big board, then try to slide each shape around so all of its squares land on white.
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Hint 2 of 2
Four of the shapes can be tucked onto a run of white squares; hunt for the one shape whose squares are forced to grab a black square no matter where you put it.
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Approach: try to fit each shape onto only white squares
- A shape works only if you can lay it down so every one of its squares sits on a white square of the board.
- Slide each shape A–E around the board: four of them can be placed on a stretch of white squares with no black square underneath.
- Shape D is the only one that always lands on at least one black square wherever it goes, so it cannot sit only on white squares — the answer is (D).
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