On the ECLiPSe website, you can find a model for sudoku. Given you read some documentation about ECLiPSe, you can turn this file into a model for multi-sudoku. I've made some small modifications resulting in the following quick-and-dirty solution:
I "borrowed" the model of the sudoku from Joachim Schimpf, so credits to him. Furthermore note that this answer does not advice to use ECLiPSe over another tool. I'm simply more familiar with the Prolog toolchain when it comes to constraint programming. But if you are more into C++, Gecode will do the trick with approximately the same (or even better) performance.
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The last two "matrices" show the solution for the two Sudoku's. As you can see (I haven't checked it fully), they share a block (the same output), and all sudoku constraints are valid. A more convenient representation of the solution is shown below:
Evidently there are other AI techniques to solve problems. A technique that is commonly used to tackle hard search and optimization problems is evolutionary computing: one starts by filling in the sudoku allowing some values to be wrong, then at each time step they aim to fix one or more fields. Sometimes they introduce new errors in order to find a valid solution eventually.
To fit a genetic algorithm to your problem. You could do something like the following. Create for every 3x3 or 9x9 sudoku a local correct solution. These are the chromosomes. Put them in one data structure. Thats an individual. Create a bunch of them to form a generation. Evaluate every individual by the constraints its violating. Calculate corresponding probability. Recombine the individuals, mutate some chromosomes, repeat.
You could see it as combination of local and global optimization. Since you would need some kind of greedy algorithm (or whatever you want to use to solve the local sudoku) to find a local, and the GA to find the overall global optima. I think it would not make sense to only use the GA and try to solve this Problem. I implemented a GA on a combinatorial Problem recently and without local optimization the results were, most of the time, quite terrible.
When I saw this cache I knew it would take me forever to solve it so I put a call out to the gang - "Who is good at sudoku?". Well turns out swed31 is really good at them so he took it on and solved it in about an hour. Wow! Today the Michigan Big Dip gang stopped on our way to breakfast. Didn't take too long to track it down. Thanks for the cache!
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This game shows a sudoku puzzle to the students with not enough numbers to allow it to be solved. For each question the student correctly answers an additional number is slotted into the puzzle to make it easier to solve. ff782bc1db
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