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Solving Sudoku with logic?

  1. Jun 1, 2015 #1
    How to solve the attached Sudoku without computer or a guess?
     

    Attached Files:

  2. jcsd
  3. Jun 1, 2015 #2
    This sudoku does not have a unique solution, in-fact it has at-least 500 solutions, therefore it is not possible to solve it purely based on logic. (By this I mean you will have to make a choice.)
    How do I know it has at-least 500 solutions ? Click the solution-count button here. [I've done you the courtesy of typing out the sudoku.]
     
  4. Jun 1, 2015 #3
    I clicked the link and I filled up the entries then it gave me all numbers (1 to 9) in all blank cells!!!. So how many solutions?
     
  5. Jun 1, 2015 #4
    But I'd already filled the necessary squares for you ?
    Click the yellow "solution-count" button at the top right.
     
  6. Jun 3, 2015 #5
    yes I got it thanks. So what is the lowest number of clues that give a unique solution?
     
  7. Jun 3, 2015 #6

    HallsofIvy

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    If it has "at least 500 solutions" then it does not have a unique solution!

    Oops! I misread your response- you did say it does NOT have a unique solution.
     
    Last edited: Jun 3, 2015
  8. Jun 3, 2015 #7
    According to http://arxiv.org/abs/1201.0749, no solvable sudoko exists with less than 17 clues. Your sudoku is actually a 16 clue sudoku, because the 5 in the top right corner is redundant.
     
  9. Jun 4, 2015 #8
    What do you mean by redundant?
     
  10. Jun 4, 2015 #9
    He means you already know it is 5, it's not a useful information.
     
  11. Jun 5, 2015 #10
    Note that 17 clues does not guarantee a unique solution, but you need at-least 17, as the paper quoted by willem2 shows.
    It's actually only a 12 clue sudoku. You should be able to enter the remaining entries from this.
     
  12. Jun 5, 2015 #11
    Still, I don't understand why do you want to consider all entries on the right upper square redundant? Just because they are on 2 perpendicular lines?
     
  13. Jun 5, 2015 #12
    No. They aren't clues because you can solve the empty entries in the link from the given ones.
     
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