So, I thought of this question a while ago and haven't found a clear answer for it yet. Here's the question:
Suppose you have a rope that is tied to two ends of a room. You can tangle the rope however you want, but the rope must stay in the room at all times, must remain in the 2nd dimension (on the ground), and cannot cross itself at a point more than once.
Now, you are on one side of the room and want to cross the rope to get to the other side. In order to cross the room, you can only move diagonally where a rope intersects itself. For example, if you have the rope like this:
-|- (the | is one rope, and the -- is the other rope)
then you can only move in one of two ways, either from the top left to the bottom right (or vice versa), or from the top right to the bottom left (or vice versa). Your goal is to make it to the other side of the room while only crossing the rope intersections diagonally in this way.
I have played around with lots of ways to tangle the rope, but I haven't yet found a configuration that will let me pass to the other side of the room.
So, is there a way you can tangle the rope that will let you move to the other side of the room? Or is it impossible to cross the tangled rope? If so, why?
(P.S. I'm not very knowledgeable in the world of mathematics lingo, so if possible, could you try to answer my question in simpler words? Thanks!)
