Fifteen meters of rope for a twenty-meter drop. At first glance, the numbers do not add up.
The rope that falls short
Riddle statement
A climber is standing on a ledge 20 meters above the ground.
He has:
- a 15-meter rope;
- a knife;
- a secure anchor ring beside the ledge;
- another anchor ring exactly 10 meters below.
Beside the lower ring is a secure foothold from which he can handle and secure the rope.
Assume that he can cut, knot, manipulate, and descend on the rope safely, and that the length consumed by knots is negligible.
How can he reach the ground?
Show solution
Solution
Answer: cut the rope into two sections: one 5 meters long and the other 10 meters long.
First stage: reaching the lower anchor ring.
- Secure one end of the 5-meter section to the upper metal anchor ring.
- Make a closed loop in the rope itself at the free end of that section. This is not another metal ring: it is simply a strong rope loop hanging 5 meters below the ledge.
- Pass the 10-meter section through this loop, but do not tie it. Center the rope so that two equal 5-meter ends hang down.
- Descend the fixed 5-meter section until you reach the rope loop. From there, continue downward using both ends of the doubled rope together. They extend another 5 meters and reach the secure foothold beside the lower anchor ring.
The climber has now covered the first 10 meters: 5 meters on the fixed short section and 5 meters on the two ends of the long section.
Second stage: recovering the rope and reaching the ground.
Once safely supported beside the lower ring and no longer placing weight on the long rope, pull one of its two ends. Because the 10-meter section passes through the loop without being tied to it, it slides freely. Keep pulling until the opposite end passes through the loop and the entire 10-meter section has been recovered.
The short section remains above, but it is no longer needed. Secure the recovered rope to the lower metal anchor ring and descend its full 10-meter length to the ground.
Key idea: the long rope is first used doubled, as two equal 5-meter ends, and is then recovered and reused at its full length.