Problem 30 · 2021 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellationcasework
There are rectangular cards divided into 4 equal cells with different shapes drawn in each cell. Cards can be placed side by side only if the same shapes appear in adjacent cells on their common side. 9 cards are used to form a rectangle as shown in the figure. Which of the following cards was definitely NOT used to form this rectangle?
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Answer: E
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Hint 1 of 2
Cards join only when the touching cells match, so trace the shape sequence along each row and column of the assembled rectangle.
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Hint 2 of 2
Read the forced shapes from the given grid; one listed card has a cell pattern that can never fit.
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Approach: match each card against the forced grid pattern
- The assembled rectangle fixes which shapes sit in each cell because adjacent cards must agree on their shared edge.
- Reading those forced shapes, four of the candidate cards can occur somewhere in the layout.
- Card E has a cell arrangement that cannot fit anywhere, so it was definitely not used.
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