- #1

Warp

- 128

- 13

*Backstory begins:*

I presented this (classical, although reworded to be less ambiguous) problem on a particular discord server: "It takes Mark 3 hours to walk from town A to town B. It takes Julia 5 hours to walk from town B to town A. If they start walking at the same time, and assuming they walk at a constant speed, how long does it take for them to meet?" (This is classically presented as people painting a house, but I think this is much more unambiguous and easier to understand.)

After the discussion on that problem, and correct answers given, I noted that the generic solution (x*y)/(x+y) holds for any pair of times. Somebody noted that that's in fact the same formula as for calculating the total resistance of two resistors in parallel. We wondered if that's pure coincidence, and came to the conclusion that it probably isn't. That the two problems are actually related.

I then started wondering that since there's a formula for any number of resistors in parallel, if that other problem could be posed in such a manner that you could have any amount of times, and thus the parallel-resistors formula could be used.

A different such wording then occurred to me. Particularly: "There's a water hose that can fill a container in 3 hours, and another water hose that can fill it in 5 hours. How long does it take to fill the container if both hoses are used at the same time?" This version of the problem can easily be generalized to any amount of times, by simply increasing the number of simultaneous water hoses. (It also probably is conceptually closer to the parallel resistors.)

I then started thinking how difficult the problem would be if there were an infinite amount of hoses, but their contribution does not diverge? If the problem with just two hoses is tricky enough for someone (who hasn't dealt with this particular problem before), how much more difficult would it be if there are infinitely many hoses?

So I devised a non-trivial pattern for the hoses: "It takes the first hose 1 hour to fill the container, the second hose 4 hours, the third 9 hours, and so on." In other words, the square numbers. So the question becomes "how long does it take to fill the container if all the hoses are used at the same time?"

I thought this could perhaps be an interesting brain twister to think about, as it may not be immediately obvious that this is actually solvable using the parallel-resistors formula. (The sum of the reciprocal of squares is also non-trivial, although the result is well known. This is the so-called Basel problem. However, seeing that this is a case of the sum of the reciprocals of the squares might not be trivial.)

Backstory ends.

Backstory ends.

So I posted that problem in the forums, thinking that it would be a nice little mathematical puzzle.

My post was quickly removed and marked as "misplaced homework", and I got a warning (with 0 points, but nevertheless). I find this dumbfounding. Mind you, I'm in my 40's, and I graduated from university over 15 years ago. This was most certainly not "homework". I was not asking for an answer because I don't know it. I presented it as a mathematical puzzle.

I don't really understand what exactly counts as "homework", or why this kind of math puzzle is not allowed. How could have I known that this is "homework"? (And yes, I did read the guidelines. They don't really explain why this particular post of mine is classified as "homework".)