The ‘Moving Sofa’ Problem

The "Moving Sofa" problem is a straightforward, commonplace issue that mathematicians are unable to resolve, despite their best attempts. Leo Moser put up the idea in 1966, and numerous mathematicians have since scratched their heads in an effort to find a solution without success.

The issue is quite straightforward to comprehend: in an L-shaped room of any size, what size couch can fit around a corner for a person moving into a new home? Although it isn't difficult, no one has been able to compute it for more than five years after the idea was put forth.

Though someone could always come up with a shape of a bigger area, depending on their proficiency in geometry, there are various ways to create a large enough item that could be turned around any L-shaped room. Currently, the Gerver couch, which Joseph Gerver proposed in 1992, is the largest design that might fit around a corner. There is still no method to verify that it is the solution, despite the fact that many mathematicians think it is.