Problem 8 · 2019 Math Kangaroo
Easy
Counting & Probability
careful-counting
Laura wants to colour in exactly one 2 × 2 square (a block of four little squares) somewhere in the figure shown. How many ways are there for her to do that?
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Answer: D — 8
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Hint 1 of 3
Every 2×2 block is pinned down by just one cell: the one in its top-left corner.
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Hint 2 of 3
Slide the block around and mark each spot where all four of its little squares stay inside the shape.
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Hint 3 of 3
Count those marked spots carefully so you do not double-count or miss one.
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Approach: count valid top-left corners for a 2×2 square
- Each placement of the 2×2 square is decided by which cell is its upper-left corner, provided all four cells lie inside the figure.
- Going through the shape cell by cell, there are exactly eight spots where a full 2×2 square fits.
- So Laura has 8 ways (D).
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