Abseiling Puzzle

Here’s a classic puzzle. You are standing on the roof of a building which is 200 meters off the ground. There is a metal hoop hanging off the edge which looks sturdy enough to take your weight. Looking over the edge you can see that there is a small ledge with another metal hoop attached to it 100 meters below you.

You have a rope which is 150 meters long and a knife which is capable of cutting the rope. How can you successfully abseil down the building? Here’s a picture of the set up:

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There is a fairly neat solution: firstly cut the rope into a 50 meter piece and a 100 meter piece. Tie one end of the shorter rope to the hoop and tie a loop in the other end. Thread the longer rope through the smaller one and throw both over the edge like this:

Climb down your contraption to the ledge. Although you lose a little length because you tied a couple of knots, it should get you almost there because it should be only just shy of 100 meters in total. Once at the ledge you can pull on one end of the long rope until it comes free of the loop. You then have a rope which is exactly the correct length to get you to the ground.