Problem of the Fortnight # 4

You are on top of a 40 meter high building. You have a 30 meter long rope, and you may not jump or fall. There are no windows or doors, the only way down is along the flat wall with a single solid ring at midpoint (20 meters from both roof and ground), to which you can attach your rope. You can cut and tie the rope as much as you like, disregard the length of the rope you spend on knots. How can you get to the ground safely?

Solution by Benjamin Burdett:

Cut the rope into a 20m and 10m segment. Make a noose on one end of the 10m rope, and tie the other end to the roof. Slip the 20m rope through the noose and use the resulting 20m rope to slide to the ring. Slip the 20m rope through the noose and use it to climb down.

OR....

Take the rope and cut it into three parts of equal length, 10m. Tie one end to the top of the building and tie the other two into a three-way knot such that when one end is pulled, the knot stays tight, but when the other end is pulled, the knot will come apart. Climb down on the steady part of the rope to the ring, pull on the unsteady part, and the knot will come undone. Tie the two 10m sections together and use it to slide to the ground.