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Problem 547

Posted: Sun Feb 14, 2016 5:12 am
by LaughingSkull
Not relying on random sampling, but instead on a calculus-based generalised solution for rectangles, the default case of n=3 yields for me a S(3) of a very slightly lower value than the one given in the problem's description. Precision errors on my part are out of the question, due to my calculation having been made on several distinct platforms. Mr. Euler, could you have erred?

Re: Problem 547

Posted: Sun Feb 14, 2016 9:10 am
by Animus
1.65135<S(3)<1.6514
Therefore S(3) is being rounded up to 1.6514.

Re: Problem 547

Posted: Sun Feb 14, 2016 8:14 pm
by LaughingSkull
Well, I got 1.6488, so apparently my method was incorrect altogether.

Re: Problem 547

Posted: Wed Jul 22, 2020 8:37 pm
by RagnarGrootKoerkamp
To clarify (since I only discovered this on my 3rd attempt): The problem asks for the average straight line distance between two random points in the hollow laminae, not the shortest distance within the hollow lamina itself.