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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