![]() With this method we see that the blue color has more than one member in a sub-grid, therefore the blue We proceed around the grid in a like manner. I n this diagram we choose to start with row2 column2, and assign it color green, it's conjugates at row2 column3 and row6 column2 are then colored blue. The color must be the 'false' color, since this is impossible, or an illegal state.Īgain we provide a visual example to clarify the discussion.I Note: Whenever two cells within a group ( sub-grid, row or column), have the same color, this would indicate Some may even link together forming a chain of alternate true-false cell states, and these chains may exposeĬandidates which can then be excluded safely. ![]() The idea of the colors technique in essence then is to assign colors toįor any given sudoku there may be any number of these 'conjugate pairs' present at any given time. the two cells would have a conjugate, or opposing relationship, that is, ( This cell is highlighted in red ).Īn interesting little technique, basically used to try to narrow candidates only in two cells within a given Therefore by the xy theory, we can safely eliminate 5 from those cells within the group contained by A,B, and C. I n the diagram we have labeled cell A (root cell) containing. Of course it may be easier to visualize, refer to the diagram below: Note: If all 3 cells in an xy wing share the same candidates (namely x,y,z), then this would reduce to a ![]() Consequently one branch is assigned x and the other y, leaving the root without a Proof: If a root cell sharing a group with both branch cells has member 'z', then neither branch can beĪssigned 'z'. T hen any other cell which shares a group with both branch cells can exclude the z element that is common One cell ( the y 'root' with candidate xy), shares a group with the other two cells ( y 'branches'.Within they share three candidates in the form ( xy, yz, xz).However, there must not be more that three candidates in the pattern defining rows.Įxtends the x-wing theory to include three cells as follows: Note: As shown in this example, there does not have to be exactly 3 cells in each row (or column), there may be less. Other candidate 5's in these three columns (highlighted yellow) can be excluded safely. Three rows (three, five & seven) have candidate 5 in no more than three cells (only two cells each in this example-highlighted in blue), and these cells all share the same three columns (three, four & seven). Looking at the diagram we can observe the following: In this example we have highlighted all the possible values for our candidate (the number 5). (Therefore any other y's within those columns can be eliminated.)įinally, as it was true for the x-wing, the converse is also true ( that is interchange the words, rows and columns) ,Īnd the theory holds. Then y MUST be assigned exactly once (and only once ) in each of the three columns within these.No included column (within the rows) can contain more than one y.Candidate y must be assigned once in each row.Restricted to the same three columns within those rows and: Given a general puzzle with three rows that has candidate y, in each of the three rows: then y must be Similar to an x-wing pattern, the swordfish theory proceeds as follows. The columns shared are 6 and 9, thus any other 6's in those columns can safely be eliminated. Only rows 1 and 9 meet the x-wing criteria ( that is 6's appear twice within the rows and the cells also share the same columns). In this example we have highlighted all the possible values for our candidate (the number 6). (The converse of this theory also holds, that is interchange the words row and column above). Only appear once within each of the two rows, no column can have more than one y, and y willĪppear only once in each of the columns contained within the rows, and any other candidates If the number, say y, appears only twice in any given row, then we know it CAN only appear inįurther if y is also restricted to two columns (and no more than two columns), and since y can Given row, column, or sub-grid.) So for sudoku solutions with this method proceed as follows: (For one, we know that for any unique sudoku solution, the numbers 1-9 can only appear once in any ![]() Left corner and top right corner, which form an X, hence x-wing. To begin with the name X- wing refers to the top right corner and bottom left corner, or the bottom To solve Sudoku puzzles using this process, one must have recognition of number relationships They are slightly different from strategies such as elimination, CRME, lone rangers, etc, in that theyĭo not follow the standard sub-grid, row, column recognition patterns involved with the afore. These are very involved tactics and require extensive knowledge of Sudoku puzzle strategy., These Sudoku solutions techniques are for the serious Sudoku addict!
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