X-Wing

An X-Wing pattern can be best understood through an example. Take a look at the example below! Within this pattern, there is a value that can be placed in the corners of a rectangle. In our case, the rectangle is highlighted with light gray, and the corners with medium gray. Observe that the value 8 is present in all four corners of the rectangle. Furthermore, in the rows of the rectangle, the value 8 is exclusively present in the corners, not in any other cell in the rows.

This pattern leads to the conclusion that the value 8 should be in opposite corners of the rectangle, either in the top-left and bottom-right, or in the top-right and bottom-left. The relationship, with the value in the opposite corners of the rectangle, can be depicted by connecting the opposite corners with lines, forming an X-shape, from which the name of this pattern is derived.

Here's why this works: Imagine what would happen if 8 were in the top-left corner of the rectangle? That would mean we could eliminate 8 from the top-right and bottom-left corners, so the diagonally opposite bottom-right corner would also be 8. The same logic leads to the conclusion that when the top-right corner is 8, then the bottom-left should also be 8.

This would mean that in both the first and last column, the value 8 is either in the fifth or the ninth row, so we can eliminate them from the other cells in these columns. In this example, we could eliminate them from the dark-gray cells. By eliminating 8 from the top-right cell, we get an immediate result with the remaining value 5.

Note that in this example, it was utilized that within the respective rows, the value was exclusively present in the corners, not in any other cell in the rows. Consequently, the value could be eliminated from the columns. In other Sudokus, if the values are exclusively in the corners for the columns, then the values can be eliminated from the rows.