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In case anybody's wondering what Prolog is for. There you go.

Ha, well I used to teach Prolog and yes, you could solve it using Prolog but I think it would be horribly slow without Knuth's magic algorithm.

I think in this specific case the size is small enough that you could handle it -- 9! ~= 360,000.

But yeah, your point is well taken. On the logic programming side, ASP is probably a better fit.