Sudoku probability

jimbo2907 · Posted: Tue Mar 13, 2007 11:43 am Post subject: Sudoku probability

Hi all, i am finishing a dissertation on sudoku and i am looking for a bit of help analyzing the results.

I have a puzzle generator generating minimal puzzles and a solver using several weighted techniques to determine a difficulty rating (e.g Naked single in Row/Col/Grid = 1 Triplet in Row/Col?Grid =4). I have also analyzed the clue density by row/col/grid, this has been done by counting the number of clues and if it is below 3 it is counted as a "Sparse" row/col/grid.

What i wanted to do is to check the probability of a puzzle with a higher number of sparse R/C/G having a corresponding higher difficulty level

Puzzle difficulty/No of clues/Sparse Row/Sparse Col/Sparse Grid/Total

51 30 3 3 4 10
166 28 1 3 1 5

I am looking to prove\disprove the expectation that a puzzle with a higher number of sparse areas should result in a higher difficulty level. I have the results of several runs in an excel sheet if anyone can help

Thanks

daj95376 · Posted: Tue Mar 13, 2007 5:11 pm Post subject:

I suggest that you go here and see how your rating system compares to one that's drawn a lot of attention elsewhere for hard puzzles. Then, you can check out the threads on Inferior, Ulterior, and Superior puzzles there as well. This should give you an excellent range of puzzles for ranking comparisons.

My puzzle generator fills a grid and then searches for a valid puzzle with the most number of unknown candidates. Although this has proven to be reasonably successful in producing difficult puzzles, it doesn't come close to the extreme puzzles generated by using a diagonal pattern for clue locations ... combined with looking for the right combination of clues to fill that pattern.

jimbo2907 · Posted: Tue Mar 13, 2007 7:24 pm Post subject:

Thanks daj95376, but i'm happy with the generator/rating side of things(Just as well ... report is due in 3wks) I was looking for a bit of help applying probability/correlation to the results

Smile