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MarieJo W.
guest

Dec2707, 01:04 PM (EST) 

"Puzzle involving exponential"

Dear Puzzle Friends, 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.archimedeslab.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! MarieJo Waeber 

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MarieJo
guest

Dec3007, 01:08 PM (EST) 

4. "RE: Puzzle involving exponential"
In response to message #2

>Beside the difference that arises in discretization process, >I believe the solution posted have some inconsistencies. And >at a first look in absence of tons of ingenuity like >Archimedes brain we must resort in calculus or to solve >numerically. > >If interested you can look the attach fileDear mpdlc, Thanks for your help... I had a look at your attached file and find it very complete. Can I post your answer on my site? I wonder, however, if there isn't a simpler way to help the visitors to understand the problem with clear stepbystep examples or references. My site is first of all intended for general interested people (puzzle math fans), I just want to put a 'spark' in the visitors' mind by giving them indications/information where to find the math tools to solve particular problems. The visitor should afterwards be able to understand and solve the problem by himself. Best wishes, MarieJo


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Pierre Charland
Member since Dec2205

Jan1908, 11:18 PM (EST) 

7. "RE: Puzzle involving exponential"
In response to message #0

I have some references concerning a variation of this problem (one worm walking the length of a stretching rubber band).  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)
AlphaChapMtl 

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