Posted: Sun Feb 13, 2011 10:51 am Post subject: Least square method
I remember that when I was young, now I am sixty years old, I used the least square method to solve a crystal structure in radiocrystallography. I am wondering if it is possible to use such a technique to find new 17 given sudokus.
JPS, I only have dim recollections of crystallography, but while crystallographers look for planes of alignment, Sudoku puzzles require digits to be misaligned in every possible direction. Can you elaborate a little on where you sense the parallels and what values we might plug into the least squares method please?
At first sight it seems you're looking to reduce the solution path using probabilities – is that right?
[Edit] Now the penny's dropped! You're a month and a half or so early and are talking of the cellular squares method.
This is an interesting subject. But viewing a puzzle crystallographically, a solution has zero entropy. Real crystals formed at finite temperature have a finite density of defects. Here defects aren't allowed!
I have not studied Sudoku solver methods: only the one described in The Ruby Programming Language, which is basically to always guess on the cell with the least number of legal possibilities. For large puzzles it doesn't do so well, however (for example, 36x36). It tends to get into dead ends from which it takes millions of iterations, or more, to extract itself.
I think what you propose is more of a long-range order sort of thing: throw down cell values then "anneal out the defects". Since there is so much long-range order in Sudoku, I'm not sure how well this would work...
Anyway, I need to see some of the other threads to see what people describe.
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