Problem 6 · 2023 Math Kangaroo
Easy
Spatial & Visual Reasoning
tiling-tessellationspatial-reasoning
A grid should be cut along the black lines into several identical shapes, with no piece left over. Into which of the following shapes is it not possible to cut this grid in this way?
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Answer: D
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Hint 1 of 2
Count the cells of the grid; the number of cells in one tile must divide that total exactly.
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Hint 2 of 2
Even when the count divides evenly, also try to actually fit copies of the tile — the one that always leaves an unfillable gap is the answer.
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Approach: test which shape can tile the whole grid with no leftover
- First check the cell count: the number of cells in one tile must divide the total number of cells in the grid.
- For the shapes that pass that check, try fitting copies into the grid; most can be arranged to cover it exactly.
- The shape in option D can never be placed to cover the grid with no piece left over.
- So the impossible one is D.
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