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Two players play a game using the interval $[0,33]$ on the $x$-axis. The first player randomly chooses a square of side length $s∈Z_+$ , which has a side that lies entirely on the interval. The second player randomly chooses a circle with radius $r∈Z_+$ , which has a diameter that lies entirely on the interval. After repeating choosing random squares and circles in this fashion, the players realize that the probability that the circle and square intersect is $1/2$. Let $S=\{(s,r):$ probability of intersection is $1/2 \}$ . Determine $\sum_{(s,r)∈S} (s+r)$.

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Somebody decided to turn to MSE to get their homework done and is rapidly posting it on the site by parts. –  Did Apr 2 '13 at 9:39
    
no,sorry, these are not my homeworks...but found those in an website and unanswered.so i wanted the answer immediately...extremely sorry if you get annoyed at my rapidness...forgive me ,please. –  sayan chaudhuri May 29 '13 at 8:47
    
"found those in an website and unanswered.so i wanted the answer immediately" makes no sense at all. What about not using the site as an automated cash machine? –  Did May 29 '13 at 10:49

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up vote 0 down vote accepted

12 is the correct answer. Think of minimum length of square required for an intersection and then compute it...

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