A 600 foot Rope, and an 800 foot Drop

You find yourself trapped atop an $800$ foot tall building. The surrounding land is completely flat, plus there are no other structures nearby. You need to get to the bottom, uninjured, and can only safely fall about $5$ feet.

You look down the four walls; they are all completely smooth and featureless, except that one of the walls has a small ledge $400$ feet above the ground. Furthermore, there are two hooks, one on this ledge, and one directly above it on the edge of the roof. The only tools you have are $600$ feet of rope, and a knife. How do you get to the bottom?

Source: I got it from this puzzle collection, but I think it has been used in interviews.

• Can you throw the knife? – Rand al'Thor May 16 '15 at 22:34
• Can you make a loop and flick it off the hook when you get to the ledge? I haven't tried to flick a 400' length of rope but vertically the wave should travel fairly well. – Joffan May 16 '15 at 22:47
• @Joffan I had exactly the same idea, and must have been typing my answer based on it when you made that comment! :-) – Rand al'Thor May 16 '15 at 22:53
• I would offer the building superintendent the choice of 600 feet of rope or this fine knife if he'll let me use the elevator. – David Richerby May 17 '15 at 0:35
• I think my answer is best as it doesn't require olympian strength and endurance :p – Eamonn McEvoy May 18 '15 at 11:13

First, tie one end of the rope to the to hook and climb down to the ledge. Cut (without dropping) the rope that hangs below the ledge, then climb back to the roof carrying the extra rope that you cut. At the top, untie the rope from the hook.

You now have two lengths of rope: one that is 400 feet long and one that is 200 feet long. While you're on top of the roof, prepare the rope accordingly: Tie a small loop at one end of the 200-foot long rope. String the 400-foot long rope through the loop so that half of its length is on either side of the loop. Make sure that the loop is snug enough that the 400-foot long rope won't fall out by itself, but loose enough that you can pull the rope out later.

Now, tie the end of the 200-foot rope without the loop to the first hook. The 200-foot long rope lets you climb halfway to the ledge. For the remaining 200 feet, you carefully climb down the 400-foot rope, which hangs down 200 feet from where it is held by the loop. Once you get to the ledge, pull the 400-foot rope out of the loop, tie it to the second hook, and climb the rest of the way to the ground.

• Well played, I knew there was a cut-and-loop solution there somewhere. I'm still cutting at the door to get inside. Think how disappointed you'll be when the distance to the ground is actually 10' more than the distance to the ledge :-) – Joffan May 16 '15 at 22:55
• A very minor improvement to this answer: tie the ends of the 400-foot rope together, after threading it through the loop in the 200-foot rope. This makes it a lot safer to descend, since it ensures that both sides of the rope will descend the same distance. Once you're on the ledge, you can cut the loop to turn it back into a straight rope usable for making the final descent. – Trevor Powell May 17 '15 at 0:11
• Why the initial descent and climb? It seems all you accomplish out of that is turning your rope into a 200/400 split, but you can do that without ever leaving the roof! – The111 May 17 '15 at 1:18
• @The111 You're right, but I'm trying to exercise more and I'll take any excuse I can get. ;-) – Kevin May 17 '15 at 2:52
• @Joshua It still wouldn't be that difficult to figure out. You could simply fold the rope into thirds (or, if there isn't enough space on the roof, sixths) in order to find 200 feet of rope. Each fold would be 200 feet long when the rope is folded into thirds. – Kevin May 17 '15 at 21:33

If the rope is coarse enough, tie a variant of the sheepshank knot on the first hook and cut the middle rope (this makes it a kamikaze knot). Climb down to the ledge, shake your rope loose, retie, and climb down the rest of the way.

I think I have a simpler (albeit not very scientific) answer!

1. Tie one end of the rope to the top hook and slide down to the bottom ledge.
2. Tie the other end of the rope to the hook on the ledge and then climb back up.
3. Once at the top, untie the top end of the rope from the hook.
4. Take a deep breath since what you are about to attempt is very ballsy (it helps if you think of yourself as Ethan Hunt from Mission Impossible)!
5. Make a poor man's climbing knot to abseil down the building.
6. Pull the rope taut so that you are holding it at an approximate 410 foot length.
7. Run towards the side of the building to gain sideways momentum and then abseil down running against the building.
8. In a circular motion, you'll swing right down past the ledge and then down towards the bottom of the building.
9. Once you've stopped swinging, lower yourself down to the floor and head towards the nearest pub to tell the lads about your courage!
10. Make a mental note to never again be trapped on top of tall buildings, maybe next time you won't have a handy rope, or a ledge with hooks attached to save you!
• +1 for chutzpah and for giving me an excellent mental image. – Kevin May 17 '15 at 21:35
• I think your arms would fall off – Mike Earnest May 18 '15 at 15:29
• @MikeEarnest: If the building was at least 400 feet wide, I think the principle could be adapted to keep G-loads reasonable. Cut the rope into a 400' piece tied securely at the ledge and very weakly at the top so it can barely support its own weight, and a 200' piece tied securely at the top. Get 200' from the support point while holding the shorter piece and swing down; grab the 400' piece as you pass it and release the 200' piece. At that point, absent friction, one would have sufficient horizontal velocity to swing in a circle around the lower attachment. – supercat May 27 '15 at 23:13
• @MikeEarnest: Horizontal velocity when hitting the ground would be irksome, but that can be dealt which much more safely than vertical velocity. – supercat May 27 '15 at 23:13

Cut the rope into a 200-foot piece and a 400-foot piece. Tie the 400-foot piece into a loop and tie the 200-foot piece onto some point of this loop, so you get a sort of spoon-shaped rope. Hang the loop (at the opposite point from where it meets the 200-foot piece) from the upper hook. Now when the loop is stretched straight - as it will be when downward force is exerted on it - the bottom of the 200-foot piece just reaches the ledge. Climb down to the ledge in this way.

Once you reach the ledge, make waves in the rope by jerking the end up and down, until the loop comes off the upper hook and the whole thing falls down to you. Hang the structure on the lower hook in the same way as you did on the upper one, and repeat the whole procedure.

• Why not tie a 10 foot loop instead? That way you have spare rope to work with and less weight in the loop so it will be easier to flick off. You also have extra rope to tie yourself to the ledge, allowing you to "stand" outward from the building and thus increase the amplitude of the waves you're generating. It will still require inhuman strength, but less so. – Móż Jan 30 '16 at 1:02
1. cut a 134m piece of rope, separate the strands (assuming 3 strands) and tie together to make a roughly 400m length.

2. Cut 3 2m pieces from the main rope, use these pieces to create a Purcell Prusik Knot Harness

3. Attach the remaining long rope to the hook using a Highway mans hitch

4. Tie the thin 400m rope to the 'dead end'.

5. Use the Prusik Knot Harness to safely descend the main rope.

6. Pull the thin rope to undo the highway mans hitch.

7. Repeat steps 2 - 5.

• This is the only answer that might allow you to survive the experience. The rest assume superhuman capabilities that are not more plausible than "just jump". Descending 150m of rope without climbing equipment would be almost impossible, doing it twice would exhaust anyone. Trad abseiling is hard as well as dangerous. Moving onto a narrow ledge right on the very end of a rope would be impossible, you would need 3-4m of rope stretch to allow you to stop without falling off the end of the rope. – Móż Jan 25 '16 at 11:48
• I'm pretty sure Mythbusters did a 'jail escape' comparing ropes made of sheets, toilet paper and hair, but the fun part was watching them climb ~15m down their "ropes" and how much that hurt them. – Móż Jan 30 '16 at 1:00

If it's a twisted or braided rope, you could separate the strands so you have two 600ft sections. Tie them together with good knots and you have more than enough rope to get you down safely.

You afix the knife on the roof ledge, off to the side (away from the main rope line). You tie yourself into one end of the 600ft rope, and you tie the other end to something at the top of the roof (not the hook). You belay yourself, carefully, straight down to the 400ft ledge. There will be approx 150-175ft of slack at this point. Hang onto the ledge as you pull all slack out. Cut the rope, but don't use all the slack to do so. Use maybe 50-100ft. Afix it to the hook at the 400ft point. Now, hold onto the top rope securely (maybe tie in or something) and swing such that you are able to either have the rope hit the knife and cut it, or merely wear it away from going over the ledge at the top. Eventually, the rope is cut and you fall a bit. Holding onto the 400ft rope segment that you now have, climb up your short rope back to the 400ft ledge. Afix the 400ft rope there, tie yourself in, untie yourself from the short rope, belay yourself down to the ground.

Simple. Just jump off the building and the split second you hit the ground you are uninjured and satisfied the requirement of the question. Being only able to safely fall 5 feet is irrelevant because it is not part of the stated requirement.

• This answer works why is it downvoted? Question didn't state had to be unharmed for any specific or minimum length of time. – David James May 18 '15 at 16:04
• Also, we don't know the angle of the walls. If the building is pyramid shaped, perhaps we can slowly slide down the walls to safety. – David James May 18 '15 at 16:31