The Math Factor Podcast

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1. Parallel Minded said,

   January 17, 2013 at 12:00 pm

   Spoiler alert: I am going to reason my way to a solution.

   The main problem is that you need to be able to lower yourself to the floor after whatever aerial preparation you do, but the lowering requires at least 40 feet of rope extending from the ceiling to where you can safely jump from.  If those 40 feet of rope are not then detachable from the ceiling, then you will have at most 60 feet of rope available for use which is not enough to reach the ground.  So, like it or not, you need to be able to detach the rope (the one you climb down) from the ceiling, after you have reached the floor.  Luckily, there are many ways to do this.

   As a first approach, although not a very satisfactory solution (unless you are really a knot expert), you could tie a fancy knot (surely findable in Ashley’s Book of Knots) to solve the problem: climb up, cut rope B, tie a complicated knot in rope A (using B also) which (1) will hold A together even after you cut part of A in the middle of the knot, but (2) can be released by pulling out B.  Then climb down A, give a tug on B, and pretty much all the rope is on the floor at your disposal.

   If you imagine the “tug on B” action being extended into pulling a long rope out of the “knot area”,  then the knot can be simplified:  You could make a loop at the top of rope A, and then make a long loop out of the remaining part of A together with B.  If you make the long loop so it goes through the loop at the top of A, then you can use that to reach the floor, where you could then untie the long loop and pull it out of the little ceiling loop.

   Similarly, you could go up, tie the two ropes together near the top (forming a little swing), then sit in the swing while you cut the ropes below the swing (without letting them drop), then tie the long ropes together to get a nearly 100 ft length, loop it through the swing, and climb down the pair of ropes (always splitting your weight evenly between them), and then at the bottom you pull the long rope out of the swing and use it to descend.  This solution seems simple enough that it might be what the puzzle author was thinking of.

   You would need to be unreasonably strong, or have some kind of harness you could attach to a hanging rope, to actually do any of these!  Most normal people need both hands to hold themselves up on a rope, and even if they are strong enough to hold on for an extended time with just one hand, they cannot easily tie knots with just the other hand….

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