Cherchez Le Électron

The following results were obtained by manually seeding starting positions into an optimizer, then manually fine tuning the optimizer results to account for obvious symmetries and to reduce optimizer noise. A useful strategy for the asymmetric cases in this problem is to start with a plausible solution centered on the origin and then move the entire group of cups around to maximize the total probability covered.

Note that n=5 and n=8 are offset from center, moving the asymmetrical perimeter cups towards the peak of the probability distribution to maximize total probability. With n >7 it gets harder to increase probability significantly and it seems likely that the optimal cup locations will tile the plane in center-hexagonal formation with increasingly small offsets from center, with offsets approaching zero as n becomes large.

Note: I have updated my answer for n=6 after seeing better answers from Tom Keith and Jenny Mitchell – thanks!

Cherchez Le Électron

2 thoughts on “Cherchez Le Électron

    1. Overseer says:

      Hi – it’s just my own python optimizer moving the (x,y) offsets of all the center points around the same amount after seeding center points of likely configurations . I looked at modifying a circle packing optimizer like circifly, but that’s not necessary here.

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