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combinatorics - Draw a line through all doors - Puzzling Stack

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I saw the following problem on 4chan and couldn't solve it: It's very likely to be some kind of troll (no solution). I'm hoping to see some rigorous proofs that disprove the existence of such a l
combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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combinatorics - Draw a line through all doors - Puzzling Stack
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