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. This is because the blocks only exist in one direction so the technique cannot be applied to the sudoku cube along a different direction.The Sudoku Assistant uses several techniques to solve a Sudoku puzzle: Note however that any technique that specifically involves blocks, such as candidate line or multi-line, is not related to other techniques in this way. Naked triples, hidden triples, and swordfish are similarly related. In the same way naked pairs, hidden pairs, and x-wing are essentially identical techniques on this sudoku cube, merely applied along different axis directions. So single position and single candidate are really equivalent techniques. The same thing in a line along the z-axis is the single candidate technique. The single position technique in a row or column means that in this sudoku cube there is only one cell left in a line along the x- or y-axis that can be filled. Instead of writing a digit in a cell on the original sudoku grid, you merely colour in that cell in the layer for that digit in this sudoku cube.Ī solved sudoku then corresponds to a cube with 81 coloured cells, and along each of the three axes there is exactly one coloured cell in each line. Imagine you have 9 sudoku grids stacked on top of one another, forming a 9x9x9 cube. There is a neat relationship between the some techniques, which is not particularly useful unless you are writing a computer program, but it may be of interest anyway. Swordfish is merely 3 lines that have the candidates for a particular digit in the same three locations (or in just two of those three locations). However, their explanation of swordfish also goes on about pairs of cells, which is a special case. In their swordfish explanation they show you that x-wing is the 2-line equivalent of the 3-line swordfish. The other two lines that cross through those locations then cannot have that digit anywhere else. Any other candidates in those four cells are irrelevant. The point is that there are two lines that have the candidates for a particular digit in the same two locations (i.e. It has nothing to do with pairs, like their example seems to imply. Their explanation of X-wing is also somewhat confusing. This line has all its candidates for a digit in one block, therefore that block can't have that digit anywhere else. The way I spot the multi-line case is not by seeing the two lines they highlight in their explanation, but by spotting the other line going through the three blocks. It is really just a special case of their multi-line technique. The example of double-pair on that site unfortunately has the four relevant cells arranged in a rectangle, so it does rather make it look like an X-wing.
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