Fun Math Problem 'Cussed Ladders'

[AlexFekken]

(09-19-2017 03:54 PM)Gerson W. Barbosa Wrote:  For practical purposes it's better to use a numerical solver than those beautiful (and lengthy) exact solutions.

If this was about actual ladders then I would agree.

But the aim of a puzzle is to stretch mind and in that scenario I prefer, and get a lot more satisfaction from, an exact solution (or even just finding out if an exact solution is possible) and preferably finding it without the help of a machine.
Otherwise you could just get some (usually obvious) lower and upper bounds for the solution and use a generic numerical solver after writing out the equation to solve (in this case basically 1/h1 + 1/h2 = 1/h, which we already had from the first puzzle). Now where's the fun in that?

And in this particular case there was also the explicit challenge: "This one will require that you use your calculator--as well as your head". Not true... :-)