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My work on XOR is currently in limbo. I don't have quite enough time to give it the kind of focus and concentration that it needs. Know that I have found some very interesting patterns that can do some very interesting things. So, I got to playing a little bit with the data set found here: [url=http://www.jaderat.com/sudoku/sudo3_latins.html]Sudo3 Latins[/url] That data can be used be used to generate a sudoku grid if you set it up like Algorithm X. You know, approach it like a cover-all problem. The way I did it is akin to a charging rhino - it just goes until it can't go anymore. Sometimes it makes it to the end, and sometimes it runs out of possibilities. Not smart at all, but it does work all the way through about 1/3 of the time. Then I started exploring using that data for solving sudoku. More rhino. Here is a starting grid. It is a minimum 17 sudoku puzzle. [code] 7 8 2 . . . . . . . . . 3 . . 1 . . . . . . . . . . . . . . 5 . . . 2 . . 9 . . 8 . . . . 1 . . . . . 3 . . 6 . 3 1 . . . . . . . . . 4 . . 8 9 . . . . . . . . . [/code] Start with that, plug it into the data set, and see what possibilities pop out. So, my rhino has a full data set, and decides to have a go at 1. Anything that is not a 1, gets pruned out. Out of what's left, only the ones that match 1 are kept. After all that, there are 10 possibilites left. My rhino doesn't know which way to go. Not the smartest rhino. Then 2, which ends up with too many possibilites. And so on for 3, 4, 5, 6, and 7. Then my rhino had a go at 8. And things got interesting. After pruning and matching, only one possibility was left. My rhino just solved for all of the 8's in the grid. [code] 7 8 2 . . . . . . . . . 3 . . 1 . 8 . . . 8 . . . . . . . . 5 . . 8 2 . . 9 . . 8 . . . . 1 . 8 . . . 3 . . 6 . 3 1 . 8 . . . . . . . 4 . . 8 9 8 . . . . . . . . [/code] How awesome is that? Now, if rhino were to have a go at 9, he would be left with one possibility and all 9's would be solved in the grid as well. (For this particular puzzle, solving for all 8's and 9's is as far as my rhino can get. But I did check and naked singles and hidden singles can solve the rest.) I did check a handful of other grids and the above technique was able to completely solve without any other techniques. Solving sudoku puzzles in 1/9 chunks at a time. Heh.
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