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Finally a solution to the Königsberg Bridge problem.
(sopuli.xyz)
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But the river running round the whole planet does not matter in this case.
You run into it on the planet backside and then need another bridge, right?
What about an opposite bridge where you cross under the river? Some sort of tubular subterranean structure. We could call them opposite bridges.
That would make the earth a donut lol and would work!
Won't be in Königsberg anymore though, so that bridge won't count