You’re locked on the roof of a building that’s 800 feet tall, and you want to reach the ground uninjured. You can safely fall only about 5 feet. The walls of the building are completely smooth and featureless, except that one wall has a small ledge that’s 400 feet above the ground. There’s a hook on this ledge, and another hook directly above it at the edge of the roof.
You have 600 feet of rope and a knife. How can you reach the ground?
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Cut the rope into lengths of 400 and 200 feet. You can do this by simply folding it into thirds or by measuring it against the building (tie one end to the top hook, climb down 400 feet to the ledge, cut the rope at that point, and climb back up).
Now tie a loop in one end of the 200-foot rope. Pass the 400-foot rope through this loop so that half its length lies on either side.
Tie the other end of the 200-foot rope to the top hook. The compound rope is 400 feet long, which is long enough to reach the ledge. Once you’re there, pull the 400-foot rope through the loop, tie it to the lower hook, and descend to the ground.
That’s from Puzzling Stack Exchange. See “Stealing the Bell Ropes.”
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