X-Wing in Sudoku - The Definitive Advanced Elimination Technique

An X-Wing is established under the following conditions. For a specific digit (say, 4), in both Row A and Row B, the candidates for 4 exist in only Column X and Column Y. In this case, 4 must go in either Column X or Column Y in Row A, and likewise in Row B. Furthermore, due to column constraints, if Row A places 4 in Column X, then Row B must place it in Column Y, and vice versa. In either case, Columns X and Y are guaranteed to have 4 placed in them, so 4 can be eliminated from all other cells in Columns X and Y (those not in Rows A or B).

The name X-Wing comes from the X shape formed when you draw diagonal lines connecting the four candidate cells. The cells at Row A-Column X, Row A-Column Y, Row B-Column X, and Row B-Column Y form a rectangle, and its diagonals draw an X. The digit will be placed in two cells along one of these diagonals (which diagonal is undetermined). Once you can visually recognize this pattern, your discovery speed improves dramatically.

To systematically find X-Wings: (1) For a specific digit, list all rows where that digit's candidates appear in exactly 2 cells. (2) Among those rows, look for a pair where the candidate column positions match. (3) If such a pair is found, the X-Wing is established, and you can eliminate candidates from the corresponding columns' other cells. Column-based X-Wings work the same way (just swap rows and columns). Accurate pencil mark maintenance is essential - missed updates cause X-Wings to go undetected.

X-Wing is a 2-row by 2-column pattern, but extending it to 3 rows by 3 columns gives you the Swordfish. If a digit's candidates across three rows are contained within a total of 3 columns, that digit can be eliminated from other cells in those 3 columns. Further extending to 4 rows by 4 columns yields the Jellyfish. These are generalizations of X-Wing with the same logical basis, but the increased pattern complexity makes them significantly harder to spot.