What field of mathematics deals with these types of problems?

Geometry?

But I want an easier solution with fewer steps I can be sure I’ve gone through ever opinion. Similar the the mathematics of knot theory, can this rope be untied.

Also similar to packing problems. Yes I can measure them but can I be sure I’ve gone through ever opinion?

Topology.

I don’t see how knot theory and topology are related to this problem. Topology, for example, would allow me to bend the red shape to fit through smaller gaps. There aren’t any knots in the diagram either.

@PhiNotPi Without delving into this too deeply, it strikes me as some sort of manifold problem. You don’t think so?

I think of the moving sofa problem which to some extent also deals with the same concepts. The main question of both is “Can this shape fit through an obstacle course?”

Wikipedia says that the sofa problem is “discrete geometry,” whatever that means.

I’m in agreement it’s a geometry problem. I know you said you weren’t concerned with this particular problem, but just for posterity’s sake, yes, the red block can easily be rotated through that obstacle course. In fact, if it represented a couch on casters then it could travel to the right then down to exit A or to the left, down and then up to exit A. The only way it can’t leave the room is by passing between the X and the backward L shaped partitions.

I“m interested in where you came across this question? Mathematics aside, the question appears to be a test to determine one’s visual acuity for solving common sense spatial problems.

@PhiNotPi
Thanks, I was thinking about this problem when moving so the moving sofa problem is 100% what I was getting at

I wonder if you know of where I can read more on these types of problems?

Also I didnt mean it was like knot theory just there are ways to know if something is knoted or not without loads of complex maths

@inunsure Indeed there are simple solutions. I posted my analysis of what routes would accommodate the couch after simply printing the graphic, then making a cutout of the red rectangle and sliding it through the room without hitting any partition. That’s actually maths in action, and a Hell of a lot simpler than the geometric proof the problem would require.

One additional point on moving couches. If the couch is in the room, and it wasn’t built there , nor was the room built around it, it will more than likely come out in some fashion. Standing it on end may be the fashion. I’ve been there, done that. It’s how I got the couch in and out. And on end, it had to be slowly tilted back down to clear the top of the door.

@ETpro
Sadly im looking for something more general for all problems like this. like i said i dont really care about that one i posted.

I have a few ideas of some general statements that i can say for all these types of problems but not a proof. im guessing its np hard with an infinite amount of solutions.

@inunsure Sorry. Can’t help. Your guess sounds likely.