Don't burn these ropes

[Jimmy Snyder]

You are at the top of a 400 meter cliff with a 300 meter rope and there is a ring attached to the cliff at the top to which you can secure the rope. There is a second ring in the cliff at the 200 meter mark. No long distance untying, you can't untie the rope at the top when you are in the middle, but you can climb down that rope to the bottom of the cliff. You can't unravel the rope, it won't be strong enough if you do.

I found this riddle on the net with no answer. I have a solution, but I don't know if is the answer that the original poser requires.

Hint: Assume that the cliff face is very smooth.. End of hint.

 

[Hurkyl]

This sounds very much like the old puzzle where you are in a high room on stilts and there are two ropes hanging from the ceiling.

*does some thinking*

And the same general idea seems to work.

I don't see how your hint helps.

Solution:

Cut off a 100 foot portion, tie one end to the ring at the top, and make a small noose in one end.

Thread the other 200 foot portion of rope through the noose, so the noose is in the middle.

You can now use the rope to climb down to the middle of the cliff.

Tie one of the ends of the 200 foot length of the rope to the ring in the middle, and pull it out of the noose. You can now use that length of rope to climb to the bottom.

End solution.

 

[Jimmy Snyder]

This sounds very much like the old puzzle where you are in a high room on stilts and there are two ropes hanging from the ceiling.

*does some thinking*

And the same general idea seems to work.

I don't see how your hint helps.

I don't know that one.

 

[Hurkyl]

I don't know that one.

https://www.physicsforums.com/showthread.php?t=151408

 

[Jimmy Snyder]

Looks the same. The hint is so you don't become one with a crag.

 

[country boy]

Is this the solution you had in mind?

Cut the rope into 100 and 200 ft lengths. Tie the 100 piece to the top ring. Make a small loop at the end of the 100 ft piece. Pass the 200 ft piece through the small loop and knot its ends together. Pull the knot to the farthest distance, ~ 200 ft from the top ring. Lower the ropes and climb down to the middle ring. Untie the knot, which is now on the lower end, and tie one end of the 200 ft piece to the middle ring. Lower the 200 ft piece and climb to the ground.

In practice the small lengths needed for the knots and loop may cause this simple solution to be short on rope, and there is the question about how to secure yourself at the middle ring while you untie the knot. However, a little extra rope past the knot to tie to the middle ring before untying the knot, together with a minor falling distance, will allow it to work.

 

[Jimmy Snyder]

Is this the solution you had in mind?

Cut the rope into 100 and 200 ft lengths. Tie the 100 piece to the top ring. Make a small loop at the end of the 100 ft piece. Pass the 200 ft piece through the small loop and knot its ends together. Pull the knot to the farthest distance, ~ 200 ft from the top ring. Lower the ropes and climb down to the middle ring. Untie the knot, which is now on the lower end, and tie one end of the 200 ft piece to the middle ring. Lower the 200 ft piece and climb to the ground.

In practice the small lengths needed for the knots and loop may cause this simple solution to be short on rope, and there is the question about how to secure yourself at the middle ring while you untie the knot. However, a little extra rope past the knot to tie to the middle ring before untying the knot, together with a minor falling distance, will allow it to work.

This is a good solution. When I first saw the problem, I wondered why they gave you so much rope. Now I see that they had a solution different from the one I came up with.

Very well, now do the problem starting with 210 feet of rope.

 

[Strilanc]

I don't see how we can do that without pushing the limits of the problem.

Eg. I'm pretty sure you could rig up a system which would release the top of the rope when you took your weight off of it upon reaching the middle hook. You could also unravel the rope (but make sure you always have the equivalent of a full rope's support) and use the loop mechanism to get almost all of the rope down to the middle hook.

 

[country boy]

Eg. I'm pretty sure you could rig up a system which would release the top of the rope when you took your weight off of it upon reaching the middle hook. You could also unravel the rope (but make sure you always have the equivalent of a full rope's support) and use the loop mechanism to get almost all of the rope down to the middle hook.

This is outside the scope of the original puzzle, but still interesting.

A simple mechanism such as you suggest would be a loop with a stick through it. Under tension the stick is held against the ring and supports you and the rope. When the rope is relaxed the stick falls out and the loop can be pulled through he ring.

There are knots that will do the same thing, i.e., hold under tension but undo when the rope is relaxed and shaken (the utility of these depends somewhat on the rope material).

Other crazy solutions:

1) Bungee. Tie knot to top ring, climb down and tie knot at middle ring, climb back up and untie knot, run along cliff and jump, pull in some rope during arcing fall, then swing to stop a little short of the bottom of cliff. If still alive, climb remainder to ground.

2) On asteroid. Forget about the rope and just jump, or push off, toward bottom of cliff.

 

[Jimmy Snyder]

My apologies to all. Hurkyl's solution is probably the only good one. The solution I thought I saw was based on a geometry mistake on my part. I don't know any good solution to the 210 foot rope problem and since I'm the one that posed it, that would make it null and void.