The great news is I've raised my Archaeology skill from 48 to 91 (I speak of course of WoW)! And as I was flying around to the various dig sites to do it, I implemented most of the entire core of the game, and it's now playable. It looks a bit like this:
As you can see, it currently tells you the rules. It's fairly difficult even like that... I mean, you win eventually, but it can take a while of back and forth and thinking. So I am pretty sure I'll do two modes: visible and hidden rules. I think hidden rules will be something of a nightmare, like 10 minutes and taking notes to get anywhere on it, unless it's a 3x3 with 2 rules or something. But a pretty solid logic puzzle.
And it mentions animals because the numbers are going to be different animals. The theme will be a zoo, and you have to arrange the cages to make the animals happy. Right now the animals look suspiciously like numbers, though.