TITLE: Whats the mathematics behind this type of taking the rope out puzzle.
QUESTION [6 upvotes]: I know there has to be a way to solve this puzzle with math.  I have included a picture, because I don't know the proper terms for this puzzle.  I have included two pictures, I believe they are the same problem, along the lines of the famous joke of empty the bucket and the problem as been reduced to the previous solution.  I am sorry if this is a repeated question, as I have no idea the proper terms to search for a solution or explaining paper.  Also, I don't know how to properly tag this question.


ps. Ok, get is getting cold here and I have spent to much time trying to solve this that I am dreaming about it.  Any help would be great.

REPLY [3 votes]: The main idea I would use to attack this type of puzzle is that of linking number. There are various different bits of the metal you can picture as loops. If the rope has non-zero linking number with any one of those loops, you need to find a way of changing that, usually by going round the end of something. I can't see the position of the rope well enough in the pictures to actually attempt these ones.