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
big list - Which popular games are the most mathematical
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
graphviz - How to layout boolean combinatorics system with dot
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
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combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Continuous, Discrete Diagrams and Transitions. Applications in the
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
What is an example of a hard sounding math problem that's easy to
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
Cross-Blockchain Transactions: Systems, Protocols, and Topological
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Unexpected Electron Transport Suppression in a Heterostructured
combinatorics - Draw a line through all doors - Puzzling Stack Exchange
Applied Combinatorics - www.math.gatech.edu - Georgia Institute of
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