Have you ever thought about a multiplayer mode where each player has his own unit and soduku grid? Turns would be simotaneous and players would be unable to travel onto other grids. The winning player is the player that solved his puzzle first.
I have thought about this actually! I could be fun. There are a few challenges to overcome to make this workable:
1. The map. This is easy, as it could just be side by side versions of what is in the SP game.
2. True simultaneous action. For the best effect, the actions and movements of both players should be instantly updated on the other player's screen. I never play MP, so I don't know if this is how it already works, but I was under the impression that MP is still turn based, and not like an RTS. In any case, competitive Sudoku would need to be built on an RTS model, not turn-based -- especially since the Relams of Kylorin typically takes place in a single turn.
3. Fairness. The fairest way to use puzzles would be for the two players to try to solve the same puzzle. That way they could even spy on each other's progress to try to get a leg up. (Or even salt their map with temporary fake "solves" to throw off such spying!

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4. Content. The best way to manage this would be to generate random puzzles for each MP match, and have both players try to solve the same puzzle. I have found some python code that claims to generate Sudoku puzzles, but I'm not sure how good it is. I have a feeling that it may generate puzzles that do not have a unique solution. But I suppose that as long as both MP players are working the same puzzle, at least it creates no unfair advantage for one player or another. Anyway, I am still looking at this code sample and seeing if I can translate it into Civ style python.
In short, I like this idea and I think it is doable. Probably the type of thing I'd need help with, though, especially the MP aspect of it. (hint hint)