How to use x wing in sudoku

The Sudoku X-Wing pattern or technique is one of the most advanced techniques that can be applied to Sudoku puzzles from a medium difficulty level onwards. It is a very forthright method with a simply discernable pattern.

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How to use x wing in sudoku

The Sudoku X-Wing strategy is one of the most recurrent techniques that can be applied to Sudoku puzzles from a medium difficulty level onwards. It is a very straightforward technique with an easily identifiable pattern. It focuses on one single digit and its goal is to restrict the number of cells that can have that number as a possible candidate. Together with the Swordfish , the Sudoku-X-Wing technique is also a valuable strategy for any player to learn as it branches out into more complex patterns and techniques that are required to solve impossible puzzles. To be able to apply this technique, the player must find 2 rows or 2 columns where a single digit is a candidate in only two cells of each. These cells must be aligned by column and row, forming a square or rectangle when connected. The basic principle of this technique is simple. Since the digit has only two possible solutions in the rows or columns in analysis and each cell is directly affected by the others, the player can identify only two possible sets of solutions for the digit. That is, the pairs formed by the cells diagonally opposite to one another. By testing each set of possibilities on the grid, it becomes clear that whenever the Sudoku X-Wing technique is applied to rows, the digit in analysis cannot be a candidate to any cell of the columns connected to the base cells. Likewise, with X-Wing patterns on columns, it is impossible for the digit to be a candidate in the rows connected to the base pattern. According to the basic rules of Sudoku, every row and column must contain the numbers from 1 to 9 without repetitions. In the example above, it is clear that the number 8 has only two possible solutions within the highlighted columns.

We can be certain that 7 can be eliminated in the red circled cells. Print Version. I think, perhaps, I answered my own question: There is more than one solution to the puzzle; there are two.

If you can find a row that contains the same pencil mark in exactly two spots, as well as another parallel row that mirrors it — containing the same pencil mark in only the same two spots, then you can use this information to eliminate similar pencil marks in the columns passing through those spots. Because of this, we can safely assume that either the light blue cells or the dark blue cells must be 4s. Armed with this, let's zoom out all the way and shift our focus to the columns involved here indicated with arrows below. Based on what we said above, the 4s in these columns must exist where these two rows cross - that is, where the blue 4s are. Knowing that, all other 4s in the columns are not possible, and can be erased erase all the pink 4s. Of course, this whole concept can be rotated.

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How to use x wing in sudoku

This idea is completely analogous, logically, to pairs, triplets, etc. Here is the idea as an X wing : Consider any one candidate Consider any two distinct rows Let the candidate be limited to no more than two cells in each of these two rows Let this group of no more than 4 cells share exactly two columns The candidate is forbidden from all the cells in those two columns outside of those 4 cells Because of symmetry, one can exchange columns for rows in this rule. Note the following: All possible locations for 3's in row 9 are f9,h9. All possible locations for 3's in row 5 are f5,h5. Forbids 3 from f4,f8,h4,h6. To prove this technique, I prefer to use induction. This technique merely crosses the possible locations of a candidate in N rows with N columns. It is analogous to an Ntuple, which crosses the possible locations within a large container of N candidates with N cells. Got all that? I think I have used the Xwing rule sometimes, just didn't know what the community calls it.

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Never heard of this strategy and couldn't find any info about it on the web. In the trapezoidal like you explained, If 7 is present in cell A, then it can not be in cell B and vice versa. This removes the same 7s in the same place. It is nice to find methods to improve my game that I can follow and use. Great site for technique. X Wing Take a look at row number 2 and row number 4 in this puzzle. I believe the first question posed by colin pearce is a valid one and needs to be answered. Here is an example of combination 5. It seems that I was over-hasty with my comment on 2-Feb In this case, the number 5 repeats in cells r4c4, r6c4, r4c7 and r6c7. X-Wing is not restricted to rows and columns. It should be easier to spot in a game as we can concentrate on just one number at a time. Appreciate any help Andrew Stuart writes:. But how do you solve it? Blog Sudoku Techniques: X-Wing On the road to becoming a more proficient Sudoku player , learning several strategies and techniques to solve Sudoku puzzles more effectively is essential.

The Sudoku X-Wing strategy is one of the most recurrent techniques that can be applied to Sudoku puzzles from a medium difficulty level onwards. It is a very straightforward technique with an easily identifiable pattern. It focuses on one single digit and its goal is to restrict the number of cells that can have that number as a possible candidate.

And we also know the 4s cannot be on top of each other, because that would put two 4s in the same column. This is so much simpler than all those advanced strategies, so complex, which may or may not apply. If the solution for number 5 lies in one of the orange cells, which candidates can I eliminate? However, when the extra possibilities for the digit are restricted to one group, the player has a Finned X-Wing pattern. Trying both configurations reveals that, regardless of the final answer, the number 8 cannot be a candidate in the rows connecting to the base pattern. Combination 6 is also the complement of a pointing pair. Starting from 2 rows and eliminating in 2 columns Starting from 2 columns and eliminating in 2 rows Starting from 2 boxes and eliminating in 2 rows Starting from 2 boxes and eliminating in 2 columns Starting from 2 rows and eliminating in 2 boxes Starting from 2 columns and eliminating in 2 boxes. Same logic applies to C and D. We can remove the 7 s marked in the green squares. Blocks are not involved here. It isn't because "the blue boxes contain other 6s in the row".