I am not a mathematician but just a math puzzle enthusiast... I placed a month ago an adaptation of an old math problem on my site, see text below:
A high quality rubber band is fastened and hung from a horizontal pole with a cannonball at its end. Two facing ladybugs are crawling along this rubber band toward each other.
From their respective starting positions (8 cm apart -- see image), each small beetle crawls toward the other at a speed of 1 cm per second. However, in the length of time each beetle crawls 1 cm, the cannonball, thanks to the force of gravity, stretches the rubber band an additional 8 cm. Will the poor ladybugs ever meet? And, if yes, when? If not, why?!
(see the whole problem and solution at: https://www.archimedes-lab.org/monthly_puzzles_69.html )

My answer was that the beetles will meet after:
ln(n) + 0.5772156649 + 1/2n ≈ 4
that is approximately after exp^3.422784336 ≈ 30.65464915 sec.

But someone disagreed with me and posted a new solution:
exp^4 - 1 = 53.598... sec.

Who is right?

I would be very happy if a math expert would help me to settle this problem. Thanks in advance for your help!

Marie-Jo Waeber

Neither the gravity nor the bugs are not concerned with the fact that they became a part of a puzzle. They act independently of us puzzle fans, and the bugs meet when they meet: at the unique moment in time. Since the descrete solution depends on the two aforementioned factors (sequence and interval) it may only provide a numeric approximation to the real solution.

If interested you can look the attach file

-- Martin Gardner, Time Travel, (The Rubber Rope, ch.9 #1 p.111)

-- Martin Gardner, aha! Gotcha, (The Rubber Rope, p.145)

-- Graham & Knuth & Pasternick, Concrete Mathematics 1st ed, (6.3 p.260; 9.49 p.479)