14 June 2013

Rope length puzzle

Case A: Imagine you have a rope tightly wound around a basketball. How much more rope do you need for the rope to be one foot away from the surface of the basketball at all times? (as if it is tightly wound around an imaginary ball that has radius one foot more than the radius of the basketball). I do not need an exact answer now. Just imagine it.

Case B: Now imagine you have a rope tightly would around the equator of the earth (what, about 25,000 miles or so?). How much more rope do you need for the rope to be one foot away from the equator at all times? (as if the radius of the earth had increased by a foot). I do not need an exact answer now either. Just imagine it.

Now for the puzzle:
In which case do you think you need more rope – Case A or Case B? Any rough idea by how much?

Posted June 14, 2013 by Rajib Roy in category "Puzzles


  1. By Rajib Roy on

    Kerry Batts seems to have worked it out. As has Rupa Bamba (and surprised herself with the answer) πŸ™‚

  2. By Rajib Roy on

    The twins Debatri Chakraborty and Bijetri Chakraborty were equally surprised when they cracked it…

  3. By Rajib Roy on

    By now, all of you have figured it out – it takes exactly the same amount of extra rope. 2*pi*(1+r) minus 2*pi*r is 2*pi. Regardless of the value of “r”, the extra rope required is constant. The answer is quite unintuitive. This problem was first posed in 1702!! Three hundred years later, our intuition remains equally wrong πŸ™‚


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