X-Wing: two rows and the same two columns
Updated
You have checked the quieter moves, and one digit is still drawing a rectangle. Two rows. In each row the digit has exactly two homes, and the homes are the same two columns. Whatever order the rows take, both columns get used. The digit cannot appear in either column anywhere else.
This page is only that rectangle. It places nothing by itself. After the deletion, you go back to naked singles or hidden singles.
When to use it
Singles, pairs, pointing, and triples have nothing left to place or delete, and one digit still shows the rectangle. On Calmtile this is an Expert step. On this board, follow 7 through rows 2 and 6. In both rows, it has exactly the same two places left.
Where to look
Ignore the other candidates at first. Follow one digit. Here it is 7, in row 2 and row 6, columns 2 and 5. The two columns sit in different boxes, which is why the rectangle is wide enough to see, and why it is not also a box-line of one row.
Row 2 is filled except at r2c2, r2c5, and r2c9. Column 9 already holds a 7 at r8c9, so r2c9 cannot be 7. That leaves r2c2 and r2c5.
Row 6 is filled except at r6c2, r6c5, and r6c8. Column 8 already holds a 7 at r4c8, so r6c8 cannot be 7. That leaves r6c2 and r6c5.
Both rows reserve column 2 and column 5 for 7. Each corner’s full list is 6, 7, and 9. The 7 is only one of them.
The step
- Find a digit with exactly two homes in one row.
- Find a second row where the same digit has exactly those two columns, and no third.
- Delete the digit from both columns, in every row except the two you found.
- Leave the four corners alone. They still hold the digit, and they may hold others.
On this board, r3c2 is one cell that loses 7. It is not a corner. The corners stay as they are: each of r2c2, r2c5, r6c2, and r6c5 can still be 6, 7, or 9.
Turn the picture a quarter-turn and you have the column version. Two columns each keep the digit in only the same two rows. The same rule then removes it from those two rows, outside the columns.
Digit 7 in row 2 and row 6 sits only in column 2 and column 5. Each corner can also be 6 or 9.
What the step does not do
It does not fill a corner with 7. The first time I met one of these, I tried to. Each corner has three candidates, and the rectangle does not choose. It also does not tell you which row takes which column. It only says both columns are spent, so the rest of those columns lose 7.
If a deletion leaves a cell with one candidate, place it afterward as a naked single. If it leaves a digit with one home in a house, place it as a hidden single. Those are earlier checks, used again on a quieter grid.
Easy to misread
The four corners do not have to contain only 7. On this board every corner can still be 6, 7, or 9, and the rectangle is valid anyway. What matters is that 7, the digit you are tracing, has no third column in either row.
A third home in either row breaks the pattern, even if the four corners look neat. A rectangle of cells that merely can hold 7 is not enough. The rows must have no other home for it.
Next
When you are not sure which of these checks to try, the order on the next page is there to keep beside you.