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Almost Locked Candidates
This article describes a Sudoku solving technique that is currently being actively developed by the Sudoku community. As the technique gets further developed by the community, the technique itself may receive substantial revisions. The name of this technique may also be changed in due time.
The Almost Locked Candidates, or ALC, technique refers to a line-box intersection and a set of digits S such that:
- An Almost Locked Set (ALS) for the set of digits S exists in the line outside the intersection; and
- An ALS for the set of digits S exists in the box outside the intersection.
Then the following eliminations can be made:
- If all the cells in the line that are not in the intersection or the line-ALS contains no digits from S, then the digits from S can be eliminated from the cells in the box that are not in the intersection or the box-ALS.
- If all the cells in the box that are not in the intersection or the box-ALS contains no digits from S, then the digits from S can be eliminated from the cells in the line that are not in the intersection or the line-ALS.
The ALC technique is best illustrated by using a example.
In the above grid, each cell marked XY means that it has the candidates X and Y, and each cell marked / means that it does not have X or Y as candidates. Now, if r1c4=X, then all the candidates for Y in row 1 are being confined in box 1. This triggers a Locked Candidates move, resulting in Y being eliminated from all cells in box 1 that are outside the intersection. But this also means that r2c1=X, so all the cells marked * cannot contain the digits X or Y. A similar deduction can be made if r1c4=Y. Therefore, in both cases, we can safely eliminate X and Y from all cells marked *.
X, Y and Z can be eliminated from all cells marked *.
This page was last modified 18:25, 12 April 2007.