UPDATE: I changed the image to reflect an actual X-Wing. As a matter of fact, this is the puzzle that I posted a couple of days ago under the “daily Sudoku” page.
Here is a quick explanation for the “X-Wing” technique. Suppose you reach the following position and you can’t go any further:
You look at columns 4 and 7 and you search for cells where digit 1 is a candidate. You find that only R4C4, R4C7, R8C4 and R8C7 have 1 as a candidate. So all 4 of those cells that belong to columns 4 and 7 (2 different columns) belong to 2 different rows (4 and 8 ). Now, digit 1 must be somewhere in both columns 4 and 7 – but if it must be in rows 4 and 8 then digit 1 can be erased from rows 4 and 8 except of course from R4C4, R4C7, R8C4 and R8C7.
So, this technique doesn’t solve a cell. It only eliminates candidates from some cells, which could help you solve the puzzle. But in this case, it indirectly solves R4C9=9 (you eliminate 1 from there).
That was X-Wing. Swordfish is a more complex version. Basically, you’re looking for any number of columns (let’s say “n” columns) that can have your chosen digit in up to “n” different rows. Then you can erase that chosen digit from other cells in those rows.
I’m terrible at explaining things. This only proves it. 🙂 lol