Problem 6 · 2024 Math Kangaroo
Easy
Counting & Probability
careful-countinggrid-counting
Alex hangs a poster on his kitchen wall. The wall has white and grey tiles of the same size (see picture). How many grey tiles are completely covered by the poster?
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Answer: B — 21
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Hint 1 of 3
A tile counts only if the poster hides ALL of it; skip any tile the poster just clips at the edge.
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Hint 2 of 3
Mark the block of whole tiles that sit completely under the poster.
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Hint 3 of 3
Among only those fully-hidden tiles, count the grey ones (the white ones don't matter).
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Approach: find the tiles completely under the poster, then tally just the grey ones
- First outline the tiles that the poster covers completely, ignoring tiles it only partly overlaps.
- These fully-hidden tiles form a grey-and-white checkerboard block.
- Now count just the grey tiles inside that block, one by one.
- That tally comes to 21 (B).
Mark:
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