Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $\sum_{(s,r)∈S} (s+r)$.

share|improve this question

closed as off-topic by Jonas Meyer, Davide Giraudo, JChau, Daniel Rust, Micah Dec 13 at 18:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jonas Meyer, Davide Giraudo, JChau, Daniel Rust, Micah
If this question can be reworded to fit the rules in the help center, please edit the question.

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

1 Answer 1

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...

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.