Recycled anecdote from the last time this was discussed on HN:<p>While a student, I looked after the apartment of a friend of mine, who was overseas.<p>When he moved there, we were _just_ able to eke his sofa around the last corner from the stairwell and through the door to his apartment. Just. After much cursing and several failed attempts.<p>So, what does a good (cough) friend do while the owner is overseas?<p>Get some hardwood mouldings/trimmings/whatever you call those long, thin pieces of wood typically put where wall transitions to ceiling or floor and nail them to the exterior doorframes, making both door openings perhaps 3/8" or so narrower, paint them in the color of the doorframe, sit back and wait.<p>Then, years later, as he is about to leave town, moving company comes along and everything runs smoothly until one item remains. The sofa. Obviously, it got in - so it'll (as obviously) come out.
Only it doesn't.<p>We (everybody except the owner and the moving guys were in on the joke) managed to keep a straight face for several minutes.<p>The moving guys even laughed as they (eventually) left, mollified by a bottle filled with a Scottish export product which we'd kept on hand to ensure no feelings were hurt afterwards.
If anyone hasn't read or has forgotten Douglas Adams 'Dirk Gently's Holistic Detective Agency' then I warmly recommend it. It includes, iirc, The Sofa Problem and the solution is classic Adams and all HNers will love it! :)
Gibbs's computational approach is really interesting [1]. Keep the sofa still and move the corridor, and the optimal sofa shape is the intersection of all (well n, since it's a numerical approximation) the corridor shapes as they sweep around.<p>[1] <a href="https://www.researchgate.net/publication/311900489_A_Computational_Study_of_Sofas_and_Cars" rel="nofollow">https://www.researchgate.net/publication/311900489_A_Computa...</a>
Kudos to the animation illustrator [0]. See also [1]. I'm collecting these for reasons.<p>[0] <a href="https://en.m.wikipedia.org/wiki/User:Rocchini" rel="nofollow">https://en.m.wikipedia.org/wiki/User:Rocchini</a><p>[1] <a href="https://news.ycombinator.com/item?id=15549197" rel="nofollow">https://news.ycombinator.com/item?id=15549197</a>
This problem seems tame and uninteresting compared to the real-life 3D case.<p>Last christmas, I was moving a sofa on my mother-in-law's home, and it was stuck in the corridor. She told me "i seem to recall that you have to raise this side a bit". I replied something to the effect "no way, i am a mathematician and there's no way that this can possibly make a difference".<p>Of course she was right. I could only move the sofa by rotating it in 3D <i>just so</i>, so that the slightly protruding arm and leg could pass one after the other.<p>So the real question, not dealth with in the wikipedia page, is: what is the largest sofa that we can move through a unit corner, allowing it to rotate in 3D ?
Somewhat related, but more counterintuitive and "solved": <a href="https://en.wikipedia.org/wiki/Kakeya_set" rel="nofollow">https://en.wikipedia.org/wiki/Kakeya_set</a>
Nice numberphile vídeo on the subject:<p><a href="https://youtube.com/watch?v=rXfKWIZQIo4" rel="nofollow">https://youtube.com/watch?v=rXfKWIZQIo4</a>
Would proving this advance our knowledge in some related field such as mathematical topology? Since the values have already been brute forced (but unproven) there really isn’t any direct practical application for knowing the solution
Numberphile did a great video on this topic <a href="https://youtu.be/rXfKWIZQIo4" rel="nofollow">https://youtu.be/rXfKWIZQIo4</a>