# Pole, rope, and chasm

You come across a chasm. It's perfectly smooth, 50m deep, and 50m across, and too wide to go around.

You have a pole that is 40m long, and as much rope as you need.

How do you get across the chasm?

There's an anchor point at the top of both sides. You have average human size and capabilities. The pole is solid and rigid and weighs relatively little. You can tie a rope securely anywhere along its length.

(A family member asked me this. I don't know where she got it, but I guess it was circulating in her school)

• Is the pole hollow? How far/high can I jump? Could I throw one of the rope ends across the chasm? Apr 14 at 17:06
• Clarification: the chasm cannot be infinitely deep
– smci
Apr 15 at 2:52
• @smci the question specifies the depth of the chasm
– JQL
Apr 15 at 6:15
• Sorry, I somehow misread that
– smci
Apr 15 at 10:39

With the edits in place

Considering one has infinite rope:

Tie the end of the rope to the anchor point on your side. Throw enough of the rope to hit the bottom of the chasm. Use that to descend down safely. Then from the ground up fill an area of the chasm with as much roping material needed for one to safely walk across.

• This is the intended answer. Nice. Apr 14 at 17:14
• Just for the record I didn’t know about this problem before hand, I honestly just worked it out from scratch.
– PDT
Apr 14 at 18:22
• I never for a moment thought you did! Apr 15 at 0:54
• I know I am being to practical, but Rot13(V qb jbaqre gubhtu ubj ybat vg jvyy gnxr n crefba jvgu "nirentr uhzna fvmr naq pncnovyvgvrf." gb svyy gung punfz jvgu ebcr.) :-) Apr 15 at 7:09
• @Retudin we can estimate (rot13) Yrg'f nffhzr n 50zz ebcr. Fanxr vg onpx naq sbegu npebff gur punfz. Lbh'q arrq gb trg onpx naq sbegu 1000 gvzrf sbe rnpu ynlre naq 1000 ynlref. Ohvyq hc ynlref gb raq hc jvgu n gevnathyne pebff frpgvba, mreb jvqgu ng gur gbc. N 45° fybcr fubhyq or BX: znqr bs 4 ynlref gur fnzr jvqgu, gura erqhpr gur jvqgu ol 200zz sbe gur arkg 4 ynlref, rgp. gb trg n fgnvepnfr. Gur nirentr jvqgu vf gura 50z, juvpu lbh unir gb jnyx 1000×1000 gvzrf. Ng 5z/f jnyxvat cnpr gung'f 1 zvyyvba frpbaqf be nobhg 11½ qnlf gb jnyx gur qvfgnapr naq ynl bhg gur ebcr. Apr 15 at 15:54

Use the pole as a bridge

Depending on the particulars of the anchor point, you might be able to build a cable-stayed bridge that suspends the 40m pole horizontally over the chasm despite being supported from one side only. This would require an anchor point above the lip of the chasm, or would require mounting the pole below the lip of the chasm and keeping it perfectly perpendicular to the chasm wall so it doesn't slip. Alternatively, you can just build a cantilever bridge with 39m of the pole extending out into space, counterbalanced by a massive amount of rope piled on top of the remaining 1m as a counterweight.

Once the one-sided bridge is properly supported, you just need to shimmy to the end of the pole while carrying some rope, and throw a lasso the remaining 10m or so to snag the other anchor, which is within reasonable throwing range. Once you have a rope around the opposite anchor, you can either build a rope bridge between both anchors, or descend to the bottom and climb back up.

• I love it. I was hoping folks would come up with some creative alternatives. Apr 18 at 16:58