i worked feverishly on this neopets game a couple years ago, writing a solver in Java that eventually shot towards the top. i eventually stopped running it when it became clear that the puzzle maxed out at 100: this was a big anticlimax. you can't really see who has the best solver, since a lot of people got to 100. and no doubt at all that it's all computer programs solving the puzzles. no human could get anywhere close.
i don't have most of the old levels, but here's what level 74 looked like:
i also had a python script to scrape the page, and another to submit the solution.
there's a version of this puzzle at:
http://www.hacker.org/modulo/
it's almost exactly the same, except here the difficulty ramps up without limit, the high scores are permanent, and computer program use is encouraged. people who have written solvers should try running them there -- the forum explains how it works.
as for the algorithms i used -- well, it would be no fun to give away all the secrets
one thing for sure, it's a puzzle with serious depth. my final codebase was about 4000 lines of java. my ultimate solver combined a series of optimizations and pruning techniques, each shaving off an exponent from the solve time, just to have another exponent added by going a few levels higher.
adum