Ruthrobin,
You are right, of course, that there is an important difference between taking a short cut to a solution by writing a computer program, and simply asking someone else to provide the solution. The fact is, though, all of these Listener numerical puzzles have, or ought to have, an ideal, elegant solution path that is reachable without computer assistance.
Here I took the lazy route, as I did with Radix's 'Boxes' puzzle from a few months ago, of writing a short program that just sifted through all the various possibilities to come up with the answer. The fact that this is not the ideal, intended solution path is a point in its disfavour.