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Xyz wing sudoku strategy12/7/2023 ![]() ![]() This means that any cell that is seen by both r3c3 and r8c5 cannot contain the digit 5, so we eliminate 5 from r3c5. Thus, this is a Double Implication Chain and we showed that either r3c3=5 or r8c5=5. Similarly, by reversing the direction, if r8c55, then r3c3=5. When this happens, you know that the candidate MUST occur in that row or column because it cant appear anywhere else there, so it CANT occur elsewhere in that box. Now, if r3c35, then we have r3c3=1, which implies r7c3=1 and so r8c5=5. You can use Box/Line reduction if a candidate only appears two or three times in a row or column, and those candidates are also all in the same box. What does this XY-chain mean? Note that both ends of the chain involves the digit 5 as a candidate. The following example shows a XY-chain resulting in an elimination. Thus, the Z digit can be eliminated from the cells that see three cells forming the XYZ-Wing simultaneously. Therefore, either the Z digit is placed in the pivot or in the pincers if the pivot has an X or Y digit. The shortest XY-Chain is an XY-Wing with only 3 cells.Ī XY-Chain is both a Double Implication Chain and a Alternating Inference Chain. The XYZ-Wing technique is an extension of the XY-Wing technique. A very common and well-known 'human' solving. A thorough examination of the logic behind it, plus numerous examples. The other possible cells involved are R3C1, R7C2, R8C2 and R9C2 but none of them have a "3" as candidate.A XY-Chain is a chain of cells which each contain only 2 candidates.īecause the chain is entirely made up by bivalue cells, the link between the 2 candidates in each cell cause strong inference, which allows us to use weak inference between the cells. Explanation and demonstration of the XYZ-Wing Solving Technique in Sudoku. You can eliminate candidate "3" (Z) from all cells seen simultaneously by both pincers, in this case R2C1. The pincers are the green cells: R3C2 (93 or YZ) and R7C1 (37 or ZX). In Nice Loop notation, you must include the cell(s) with the eliminated candidates to complete the loop: You can write it like this in Eureka notation: Chain NotationĪn XY-Wing is a short chain. One of the pincers shares a row with the pivot, the other shares a column. candidate x in cell y is not set) to a result. A chain is simply a stream of implications that lead from a premise (e.g. A good strategy is to start with easy variants like Remote Pairs, X-Chains, or XY-Chains and advance from there. It starts by finding a cell with only two candidates (a bi-value. For beginners the variety (chaos) of techniques can be a bit overwhelming. Up to 5 eliminations are possible in this formation. XY Wing (sometimes called Y Wing) is another advanced technique for eliminating candidates. Each of the wings must share one candidate with the first cell, (thats part of sharing a unit) but of different values. One of the pincers shares a row or column with the pivot, the other shares a box. SubtypesĪlthough the logic behind the XY-Wing is always the same, subtypes have been introduced to help players to recognize these patterns more easily. The pincers have candidates XZ and YZ.Īny cell that can see both pincers can not longer contain a candidate for digit Z, because the pivot forces either of the pincers to contain this digit. The pivot contains candidates XY, which explains the name of this technique. The same reasoning also applies to Columns '3', '5' and '7'. Hence in Column '1' candidate 4 must be the solution in either A1, or D1, or F1, or J1 so it can be deleted in all the other cells of that column. The chain uses only 3 digits, symbolically named X, Y and Z. In the solution each row of the jellyfish must contain a candidate 4 and it must be in a different column in each of these four rows. The cell in the center is called the pivot. An XY-Wing is a solving technique that uses a short chain of 3 cells. ![]()
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