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Problem of the Day #111: Albert’s rectangle July 8, 2011

Posted by Sreenath in : potd , trackback

Two points are chosen at random from the region bounded by the lines $x=0$, $y=0$, $x=1000$, and $y=1000$. These points are opposite corners of a rectangle with sides parallel to the axes. The expected value of the area of the rectangle can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.

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