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玩数独,设计数独​

Play Sudoku, Design Sudoku

Advanced Solving Sudoku Technique: XY-Wing

5/10/2018

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​If you want to be a savvy Sudoku solver, this technique is a must to grasp: XY-Wing.

Simply speaking, when one square with candidates {X, Y} is in the same row, column, or box as two squares with candidate numbers {X, Z}, and {Y, Z}, candidate number Z can be eliminated from the squares in the same row, column, or box as these two squares.

​Candidate Numbers (or Candidate Values) of a blank/empty square is a list of ‘possible values’ or candidates for this blank/empty cell. Below is an example of using XY-Wing to refine the candidate values of R3C6. Empty Squares are marked with candidate values.

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For R5C5, 

  • If it takes number 4, R3C9 will have to take number 1;
  • If it takes number 8, R1C4 will have to take number 1.

​Either way, either R3C9 or R1C4 will be number 1.
​Therefore, R3C6 who is in the same row as R3C9 and at the same box as R1C4 cannot be number 1. We can safely remove number 1 from R3C6‘s candidate values. These above two possibilities rule out the possibility that number 1 could be in R3C6. We can safely remove number 1 from R3C6.

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How to find them?

  • Use basic methods to solve the Sudoku until no further blank/empty square can be inferred to be a number using basic methods (Sole Candidate and Hidden Single).
  • Write down the candidate values for every blank/empty square.
  • Apply interaction methods, Subset, SubsetPosition, X-Wing methods if necessary.
  • Check if one square with candidates X, Y is in the same row, column, or box, two squares with candidates X, Z and Y, Z. If there exists such a blank/empty square, we can eliminate candidate Z from the squares in the same row, column, or box as these two squares.

Try this hard Sudoku on 03/25/2018 to see whether you can apply XY-Wing as well as other Sudoku solving strategies to solve it?

​Sudoku on 03/25/2018 on www.createclassicsudoku.com

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Solve Hard Sudoku on 03/25/2018 in a step-by-step style

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