I don't know this particular puzzle, but whenever I see anything that might involve trial & error, I consider Dancing Links (https://en.wikipedia.org/wiki/Dancing_Links). Masak gave a talk on this to the London Perl Workshop >5 years ago. It is probably on line somewhere, but I have no idea where. He used Perl 6 in his examples, but the techniques were certainly obvious to me.

Regards,

John Davies

Update: having had a VERY quick look at the site (it's not something I want to get), my first thought is that it is a variant on the N queens problem. See, for example, Efficient N-Queen solution with Perl.