Problem 18 · 2015 Math Kangaroo
Stretch
Spatial & Visual Reasoning
compositionspatial-reasoning
Some of the small squares on each of the square transparencies have been coloured black. If you slide the three transparencies on top of each other, without lifting them from the table, a new pattern can be seen. What is the maximum number of black squares which could be seen in the new pattern?
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Answer: D — 8
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Hint 1 of 2
Stacking the see-through sheets makes a square black wherever any sheet is black there.
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Hint 2 of 2
Slide them so the black cells overlap as little as possible, then count the covered squares.
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Approach: overlay the transparencies and count the black cells
- Each sheet is transparent, so a cell looks black if it is black on at least one of the stacked sheets.
- Lining the three sheets up so their black cells barely overlap covers as many squares as possible.
- Together the black cells can cover 8 of the 9 squares, leaving just one clear.
- The maximum number of black squares is 8.
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