How do Sudoku setters know they have filled just enough squares to give a unique solution?

sudoku
James P asked:

If they don’t fill enough squares, there will be multiple solutions; if too many, either there will be no solution at all (if a conflict arises) or they are making the problem easier than need be. Are there rules that describe the minimum number of filled squares to define a Sudoku (whether 3×3, 4×4 or bigger)?



Comments (4)    Posted in Mathematics    

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4 Responses to 'How do Sudoku setters know they have filled just enough squares to give a unique solution?'

  1. mom - September 13th, 2008 at 9:41 pm

    I have no idea, but I am addicted

  2. my.name.is.... - September 15th, 2008 at 4:00 am

    im guessing this is what makes the different levels easy medium hard etc.. the more numbers they leave behind the easier it will be for us..
    less number- the more trial and error we have to make..
    theres probably logic behind how many numbers to leave..
    clever buggers they are

  3. Luke - September 18th, 2008 at 2:56 pm

    Well i would think that making a sudoku is just as hard as doing one. I would think they start with a solution, all the squares filled, and carefully work backwards finding all possible leads. There must be a systematic approach and a computer program that creates soduko’s. I was going to try to program one when i was in programming, but found it way too big of a project.

    Found your question interesting enough, and maybe this site can help answer your question. My approach was obviously not the way they do it here.

    I didnt read it all.

  4. ignoramus - September 19th, 2008 at 4:13 pm

    If I am minded to fill a few minutes by filling in one of these puzzles ( usually the 3 x 3 size) , I always do a quick count of the number of pre-filled squares. Empirical observation indicates that 24 to about 28 filled squares is the usual count for a fairly difficult one that may take about half-an-hour to complete. 28 to 31 filled squares is of medium difficulty, and will take about 16 minutes on average. Anything more than 31 filled means a very easy one that should be completed in under 10 minutes.

    As a general rule, therefore, I would suggest that a setter aims at between about 24 and 32 filled-in squares, and that less than 24 will raise the possibility of more than one solution, although it might be difficult to determine precisely for any individual case, short of trying it out.


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