A rectangle over the shaded row
In a grid of unit squares, the entire middle row (the th) is shaded. A rectangle is chosen uniformly at random from all axis-aligned rectangles made of grid cells. The probability that it contains at least one shaded square equals for an integer ; find .
Show hints (2)+
- The shaded row spans all columns, so only the rectangle's vertical range matters: does it include the middle row?
- Count line-pairs that fail to span it (both above or both below): .
Answer
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2023
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Asked at: Jane Street, Two Sigma