combinatorics - Draw a line through all doors - Puzzling Stack Exchange

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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 Exchange
combinatorics - Draw a line through all doors - Puzzling Stack
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
What is the toughest puzzle book? - Quora
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
combinatorics - Draw a line through all doors - Puzzling Stack
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Combinatorial encoding of odors in the mosquito antennal lobe
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
big list - Which popular games are the most mathematical
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Jigsaw puzzle design of pluripotent origami
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Spin-Layer and Spin-Valley Locking in CVD-Grown AA′- and AB
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
trigonometry - 2018 January Challenge: Prove inequality in
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
combinatorics - Draw a line through all doors - Puzzling Stack
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Can you solve this? 5 room puzzle challenge
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
I've been trying to solve this puzzle for years everytime I have some
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