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    Hi Guys,
    I was having a bit of difficultly in engaging with a problem pertaining to Buffon's Needle. Essentially, the question is to find the ratio of needles crossing a line when the needles are thrown randomly, exactly the same as in the classic Buffon's Needle experiment. However, the change is that the floor is composed of square tiles, instead of slats. What would the ratio of the number of needles thrown to the number of needles crossing a line be?
    Any help would be much appreciated!
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    Can the length of the needle be larger than the side-length of the square? Which solution(s) to Buffon's Needle Problem are you familiar with?
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    As a little hint: Under what circumstances will the needle cross a line? How can you parametrise the position of the needle in such a way that it is easy to calculate whether the needle lies across a line? (As a check, if you're working with the solutions for a needle longer than a side-length, if the length of the needle is x and the side length L, then if x > L \sqrt2 the probability is 1, because the "worst possible" way it can land is diagonally across a square.)
 
 
 
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