3 ms·

That strikes me as extremely unlikely. I think the complexity class of Sudoko is NP-Complete (a quick google confirms it's not exactly NP but very close: http:

• Natsu 16y ago
  I usually solve them by hand without guess and check, though occasionally, you get down to where there are pairs of values where you have no choice but to try one and see what works (or maybe I just need to figure out more constraints to use).
• thret 16y ago
  Sudoku are designed so that there is always a correct move that does not require guesswork.
  • crux_ 16y ago
    That is not true. They're typically designed to be unambiguous (only one correct solution), so in that sense there is always a 'correct' move. However, finding that correct move is exactly as hard, in the computational sense, as finding the solution to the entire puzzle. > . . . | . . . | . 1 2 > . . . | . . . | . . 3 > . . 2 | 3 . . | 4 . . > ------+-------+------ > . . 1 | 8 . . | . . 5 > . 6 . | . 7 . | 8 . . > . . . | . . 9 | . . . > ------+-------+------ > . . 8 | 5 . . | . . . > 9 . . | . 4 . | 5 . . > 4 7 . | . . 6 | . . . There should only be one solution. Enjoy yourself, and remember: No guessing! (Source: http://en.wikipedia.org/wiki/Algorithmics_of_sudoku#Exceptionally_difficult_Sudokus_.28hardest_Sudokus.29 http://en.wikipedia.org/wiki/Algorithmics_of_sudoku#Exceptio...)
    • thret 16y ago
      Well, an ambiguous Sudoku is like a 12 line sonnet... It isn't computationally relevant but even if trial and error were a simpler approach I feel like that is not in the spirit of the game. Sudoku is a number maze, the goal is to backtrack. Also I refuse to attempt something that is supposedly too difficult for humans to solve, I'm incapable of quitting puzzles and don't relish spending the next X hours proving it can be done :)
      • crux_ 16y ago
        I believe the above puzzle has only one valid solution.
    • jws 16y ago
      9x9 grid of digits with an ambiguous solution is not a Sudoku. It is part of the definition. Within the set of initial grids that have unambiguous solutions there are ones which require guessing or backtracking, these are generally not considered proper Sudokus and are not presented to humans to solve. A Sudoku is not a destination, it is a journey.
      • T-hawk 16y ago
        If a Sudoku has one and only one solution, then it is always solvable without guessing or backtracking. It just might not be within the scope of the human brain. There exist (many) configurations where every cell is influenced by every other, so to solve any one cell essentially requires a simultaneous solve of the entire puzzle. There's no theoretical reason a human couldn't do that too; it's a problem simply of computational capacity not fundamental approach.
        • crux_ 16y ago
          How would you structure a program to solve such a puzzle without having it generate and test potential solutions along the way?
• deleted 16y ago
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• pieceofpeace 16y ago
  Glenn Flower has written an (open source) program that solves using constraint propagation only. It does solve some of the hardest Sudoku's. He discusses the strategies used here: http://www2.research.att.com/~gsf/sudoku/ http://www2.research.att.com/~gsf/sudoku/
  • crux_ 16y ago
    From the first paragraph of your link: > The solver uses depth first and/or breadth first with constraint propagation to prune the search That would be backtracking. Further, the purpose of many the constraint techniques seem to be aimed at creating puzzles that are amenable to humans, not solving them. The article itself states that for solving, backtracking with fewer constraints performs better.
    • pieceofpeace 16y ago
      You are right that "the purpose of many the constraint techniques seem to be aimed at creating puzzles that are amenable to humans, not solving them" I shared the link because I found his sudoku generator and the constraint methods interesting. > That would be backtracking. Let me quote the first para in full: The solver uses depth first and/or breadth first tree search with constraint propagation to prune the search for the next best move (forms of forward checking.) There are space/time tradeoffs between depth/breadth first search and the constraints used; sudoku(1) has options to control the combinations. The common characteristic for all constraints, here and elsewhere, is that they avoid trial and error. Its fine for a computer to guess and backtrack but a definite breach of puzzle manners to require a human to do so. I could be wrong but, yes, it does use backtracking to find the constraint that can give a number for an empty cell but it never has to change a number it has put in a cell. That differs from the trial and error approach that moves forward by guessing values and checking if it leads to a valid solution.
      • crux_ 16y ago
        The constraint-finding is for generating puzzles that are easy, hence the comment about puzzle manners.