Those n candidates are not possible elsewhere in that same block, row, or column.īlock, row, or column, and those n candidates are not possible elsewhere in that sameīlock, row, or column, then no other candidates are possible in those cells.Ĭells can be identified for which the only possibilities are exactly three numbers, When n candidates are possible in a certain set of n cells all in the sameīlock, row, or column, and no other candidates are possible in those cells, then Can you find them?īy the way, can you find the hidden single 5? It's here.Īs for locked cells, there are two subset rules. There are several more locked candidates on this board. The same idea eliminates the possibility of 9s in the center block's top row,īecause in this case the only possible place for a 9 in the left center block is the top row. Row and demand that in the top right block the 1 must be in one of the two positions indicated in blue. We can eliminate it as a possibility (remove its mark) from the other cells in this row. The only possible locations for a 1 in the top left 3x3 block, then, is the third row.īut this means that, in the third row, the number 1 must appear in one of the red-circled cells - not onlyįor this 3x3 block but at all. In both the top row and the left-most column. In the example shown on the right, the location of the number 1 is already known (even if its exact location is still unknown), no other block may have that same number in the In this next technique, we useĪssigned to a given row or column of a specific block 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. The Sudoku Assistant uses several techniques to solve a Sudoku puzzle:
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