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They don’t need width for this do they? You could think of them as a set of points which have 0 area, but a region can still contain the points, so which set of points is overlapped by the most regions? I’m pretty sure U’ve got a bad idea there about width.

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They don't. But the post has chosen arbitrary "bands" to squeeze more counties in, rather than infinitely thin lines.

I must have missed the bit where he explained why a band of 700m or whatever was optimal

All the countries are present throughout the 700m band.

There are infinitely many infinitely thin lines that fit in that band and cover the countries.

Ahh yes, I missed the subtlety that Bulgaria and Slovakia overlapped

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