Problem 547

[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?

[Animus]

1.65135<S(3)<1.6514
Therefore S(3) is being rounded up to 1.6514.

[LaughingSkull]

Well, I got 1.6488, so apparently my method was incorrect altogether.

[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.