![]() Only one remains in a cell, so then we know that cell's value. Once all the singles have been found, I usually start marking. Then it is also not possible anywhere else in the same row/column. Then it is also not possible anywhere else in the same block.Īnd it is not possible anywhere else in the same block, When a candidate is possible in a certain block and row/column,Īnd it is not possible anywhere else in the same row/column, Row/Column Range Checking ("locked" candidates) examples This idea is more fully discussed mathematically in The 12 Rules of Sudoku. If a candidate k is possible in the intersection of A and B but not possible elsewhere in A, then it is also not possible elsewhere in B. Using "A" and "B" here for some number of rows, columns, cells, or blocks, then we have: Most people do this step without actually making any marks.įirst of all, if the rules discussed below sound pretty much the same, it's because they are all just permutations of the same Cross-hatch scanning is generally all that is necessary for "easy" puzzles. This process, referred to as cross-hatching, is repeated for each row and each column. "hidden" by the presence of the other marks. The 5 in this cell is called a "hidden single" because it can only be in this single location, and that fact is Since a number can only appear once in any given column or row and must appear exactly once inĪny given 3x3 block, the easiest place to start is to first checkįor cells that must hold a value because no other cell in a 3x3 block can hold that number.įor example, in this case the number 5 is excluded from all but one cell in the top center 3x3 block. But in that top middle block only one cell can hold a 5. In that cell the numbers 4, 5, 6, and 8 are all possible. The dots in the cell in row 3, column 5, indicate that You should always start a Sudoku by finding all the hidden singles. Despite the name, hidden singles are far easier to find than naked singles. There is only one possible cell for a candidate. There is only one possible candidate for a cell a hidden single arises when This situation can arise for one of two reasons. When a candidate k is possible in only a single cell ofĪ row, column, or block, then that cell must be k. Hypothesis and proof and a sort of depth.Īll of these techniques are based on identifying all the possible "candidates" for a cell (indicated by marks)Īnd then eliminating them one by one until only one possibility remains in a given cell.Ĭross-Hatch Scanning (looking for singles) When all that fails, the Sudoku Assistant resorts to ![]() Almost-locked set analysis can be extended to grids, where itĪnd also to what I am calling almost-locked ranges. What I'm calling 3D Medusa analysis, includingĪnalysis. You can practice this strategy by installing the SudokuCoach application on your Android™ device.The Sudoku Assistant uses several techniques to solve a Sudoku puzzle: ![]() In the example if candidate 9 were the solution in F7, then candidate 4 would be the solution in F6, 5 in E7, 8 in E9. ![]() The group of four Cells would then contain only three possible Candidates that can each be the solution in only one Cell of the group, leaving one Cell of the group without solution. Indeed, if this Candidate were the solution in a Cell outside of the group and if that Cell saw all the Cells of the group where this Candidate is present, then it would eliminate all occurences of this Candidate from the group. In any Cell outside of the group that can see all the Cells of the group where it is present. See all the other Cells of the group where it is present, except for one of those Candidates, then this Candidate can not be the solution If one can identify a group of four Cells containing various combinations of only the same four Candidates and if each of these four Candidates can ![]()
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