X-wing Logic

X-wing logic in Sudoku gets its name from the fact that occasionally two rows will contain only two occurrences of a candidate number, and those occurrences happen to share the same two columns; in other words, their arrangement forms a rectangle or square, and interconnecting lines drawn along the diagonals would make an “X” shape. The wing part of the term comes from the fact that only one of the two diagonals is possible, but we don’t know which one yet. See the graphic below.

If you look at the second and eighth rows, you can see how 4 is an option only in the second and fifth cells. These four 4s have two rows in common and two columns in common, which means that either the upper-left and lower-right cells are the correct locations, or the upper-right and lower-left cells are the correct locations. To satisfy the row requirement for a 4, one and only one of these can be true. In light of this, we can safely erase any other occurrence of a 4 in the second and fifth columns. See the resulting partial puzzle below.

In the picture above, you can see how we’ve kept the four original 4s, indicated by the arrows, and removed any other 4 from the second and fifth columns.