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Hi, I recently came across the famous Buffon's needle problem (http://en.wikipedia.org/wiki/Buffon%27s_needle), and there is no doubt that the problem as well as its answer are elegant. However, the problem I have in mind, is slightly modified. The original problem deals with parallel lines separated by fixed distance (say, m). What if there are squares of side m instead of just parallel lines? How will this affect the probability? I scratched my brain over this, but could not come up with anything. Can some genius crack this for me?

Regards, Salil

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    $\begingroup$ Laplace is the genius you require - mathworld.wolfram.com/Buffon-LaplaceNeedleProblem.html $\endgroup$
    – dke
    Commented Aug 8, 2010 at 15:32
  • $\begingroup$ The expected number of lines crossed is equal to the expected number of vertical lines crossed plus the expected number of horizontal lines crossed. $\endgroup$
    – Steven Landsburg
    Commented Aug 27, 2017 at 23:38

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This is solved in Fifty Challenging Problems in Probability with Solutions, the 1965 book by Frederick Mosteller (Problem #54). A very good book to have around in any case.

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    $\begingroup$ hmmm... 54th problem in 50 challenging problems ... :-)) Thanks! $\endgroup$
    – Salil
    Commented Aug 8, 2010 at 17:22
  • $\begingroup$ Yes, there are 56 in total. The book's at my office, so I can't tell you more than that right now, but I can look up the detailed answer tomorrow if you need me to. $\endgroup$
    – Thierry Zell
    Commented Aug 8, 2010 at 18:03
  • $\begingroup$ no no ... I will get the book in my college library. Thank you very much for that reference! $\endgroup$
    – Salil
    Commented Aug 8, 2010 at 18:08

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