MC: Ping-Pong Cubes

[DavidM]

(05-27-2018 12:30 PM)ijabbott Wrote:  I suppose the only interesting part to me is whether there are any ping-pong cubes beyond 725^3...

As I recall some of Joe's previous challenges (and/or posted observations), I suspect a big motivator for him is answering that same question. Certainly it is a curiosity that there would exist a nicely-rounded quantity of 10 solutions, in relative close proximity, but then nothing else even close.

So if we simply look at answering that specific question, we very quickly find that a simple brute-force search will run for quite some time with no success. It is inevitable that optimizations need to be applied which will both speed up the test and limit the input to have any hope of being useful. Discovering the "arbitrary properties" of the numbers that can be ruled out (or in) becomes an imperative for any hope of speeding up the search (regardless of platform), and the more advanced mathematical minds here may even discover a proof of existence/nonexistence in the process (one can dream!).

I'm certainly not trying to tell you what you should find interesting, but rather trying to explain how some of us connect what you did find interesting to other aspects of the problem that you didn't. As time permits, I will continue to experiment with this challenge. It's my expectation that others will find a variety of optimizations long before I do, and I will celebrate with them when they do. That's the better part of this unique community that keeps me coming back -- the collective learning/sharing process (and the confirmation that I'm not the only person in the world who still appreciates these well-designed, geeky devices ).

Thanks for sharing your code and contributing to this puzzle!