Every technique so far has lived inside one region. A square cornered by its row, column and box. A number with one home left in a box. Two squares in the same column agreeing on the same two candidates. In each case you could draw a ring around nine squares and everything that mattered was inside it.
This one doesn't work like that, and that's the whole reason it's the sixth technique rather than the second. The pattern is four squares sitting at the corners of a rectangle, in four different boxes, as much as seven rows apart. There's no region you can draw a ring around. You have to hold two columns in your head at once and compare them.
The pattern itself is simple. The jump is agreeing to look for something that isn't in one place.
An X-wing is one digit whose only remaining homes in two different columns are the same two rows — which means the rest of both of those rows can't have it.
Why four corners rule out anything at all
Take a digit — a 6, say — and find every square in some column where it could still go. If there are exactly two, you've got a column with a 6 in one of two places. That alone is worth nothing; you can't act on it.
Now find another column where the 6 is also down to two homes, and where those two homes are on the same two rows as the first column's. Four squares, at the corners of a rectangle.
Here's the argument, and it's the sentence the whole technique rests on.
Each of those two columns needs a 6. The first column's 6 goes in the top row or the bottom row. Whichever it takes, the second column's 6 has to take the other one, because two 6s can't share a row. So between them, those two columns put a 6 in the top row and a 6 in the bottom row — one each, always, whichever way round it falls.
And a row holds one 6. If the top row's 6 is already committed to one of these two columns, then no other square in that top row can be a 6. Same for the bottom row.
That's the elimination. Not in the columns you were looking at — in the two rows that cross them.
You never learn which corner takes what. You don't need to.
Finding one
Same board this series has run on throughout, back at its starting position.
The 6 is the digit to follow. Write out where it can still go in the fourth column and the sixth column, and the whole thing falls out.
Read the fourth column for 6s. Six squares are empty, and only two of them can take a 6: the one at the very top and the one at the very bottom. The four in between are carrying 2 3, 5 7 9, 5 9 and 3 5 7 — not a 6 among them.
Now read the sixth column for 6s. Six empty squares again, and again only two can take a 6 — the top one and the bottom one.
Same two rows. The first row and the ninth.
That's the X-wing. Four corners: top of column four, top of column six, bottom of column four, bottom of column six.
What it buys you
Column four's 6 is in row one or row nine. Column six's 6 is in row one or row nine. One of them takes row one and the other takes row nine — there's no arrangement where they both go to the same row, because a row can't hold two 6s.
So row one's 6 lives at column four or column six. And row nine's 6 lives at column four or column six. Every other square in either row has just lost its 6.
Go and see what that actually hits.
Row one first. Its other empty squares are carrying 1 2 4, then 1 4 8 9, then 1 2 4 9, then 2 4 8. Not a 6 anywhere. The X-wing does nothing at all in row one.
Row nine is where it pays. The squares to the left hold 1 2 3, then 1 2 4 5, then 1 2 3 4 5 — no 6s there either. But the seventh square along holds 1, 3, 4 and 6.
That 6 is dead.
One candidate. That's the whole payout.
It's worth being blunt about that rather than dressing it up, because the gap between what X-wing sounds like and what it does is where people lose faith in the technique. You held two columns in your head, compared their candidate lists, spotted a rectangle across seven rows — and struck one digit off one square.
That is a completely normal X-wing. They're not generous. What makes them worth knowing is that they turn up exactly when nothing else will move, and on a board that's genuinely stuck, one candidate is the difference between a puzzle that continues and a puzzle you abandon.
Every other technique in this series pays more per unit of effort. This one pays when the others pay nothing, which is a different kind of useful.
The jargon, deflated
X-wing. Draw lines between the four corners and you get a rectangle with an X through it. That's it — the name describes the picture, not the logic, which is unusual for this subject and mildly unhelpful.
Rows and columns are interchangeable, and this trips everyone up once. The worked example above found the digit confined to two rows within two columns, and eliminated along the rows. Turn it ninety degrees: a digit confined to two columns within two rows eliminates along the columns. Same pattern, same argument, and you have to check for both. If you only ever scan columns you'll find half of them.
The rule for which direction you eliminate in: you eliminate in the lines you did not search. Find it by reading columns, clear it from the rows. Find it by reading rows, clear it from the columns. Getting this backwards produces confident, wrong eliminations, and it's the most common way to break a board with this technique.
One more thing worth knowing. A corner is allowed to carry other candidates — all four of the corners in the example above were holding a 2 as well, and one of them was holding four different digits. The technique only cares where the chosen digit can go. It says nothing about what else those squares might be.
Swordfish: the same shape, three wide
A swordfish is an X-wing with three lines instead of two: one digit whose homes in three different columns all fall within the same three rows, which clears that digit from the rest of those three rows.
The argument is identical, and so is the reason it works. Three columns each need the digit. Between them they use up all three rows, one each. So the rest of those three rows is dead.
The one detail that catches people: each column doesn't need all three rows available. A column with the digit in two of the three still counts. What matters is that the three columns between them touch no rows outside the three — not that any individual column touches all of them. Insisting on three-by-three-full is why most people never find one.
Past that it keeps going — four lines is a jellyfish — and past that it stops being worth your time. The count was never what made the technique work. The rectangle was, and a swordfish is just a rectangle with an extra side.
There's no swordfish worth showing on this board. The grid this series runs on has one pattern that technically qualifies, and it clears nothing at all — a dry one, in the language of pointing pairs. Rather than move to a different grid for one folded section, this is the honest version: you now know the shape, and you'll recognise it when a genuinely hard puzzle hands you one.
When to reach for it
Last, and rarely.
Work naked and hidden singles until they stall. Then pointing pairs, then naked and hidden pairs. Only when a board has stopped answering to all five is an X-wing worth the search — and on Easy and Medium boards that moment never arrives at all. Of the 300 puzzles bundled in our app, two have an X-wing anywhere in their solve path, and neither is Easy or Medium. This is a technique you will meet on an Expert board or not at all.
When you do search, do it the cheap way round. Pick a digit that's well advanced on the board, because a digit with six or seven already placed is the one whose remaining homes have been squeezed down to two per line. Then read each column and note which have exactly two homes for it. If two of those columns share the same pair of rows, that's your X-wing. Digits with five or six homes per column are wasted effort.
And be straight with yourself about the payoff before you spend the time. Look at what's sitting in the two crossing rows first. If nothing out there is carrying your digit, the X-wing is real and worth nothing, and you're better off going back to the singles.
Which brings up the honest caveat this series has made twice before and will make once more: this board doesn't need an X-wing. It's an easy grid and singles alone will finish it. The one above is genuine — that 6 really is confined and it really does kill the 6 in the bottom row — but you're seeing the technique on a board that would forgive you for missing it.
Now find one yourself
Not a second X-wing. There isn't another one on this board worth your time, and sending you to look for something that isn't there is a waste of ten minutes.
Instead, go back and check the one you've just been handed, because the checking is the skill.
Four 6s already sitting on the board do all the work above. They're what squeeze the sixth digit out of every square in columns four and six except the top and the bottom. Find them.
There are five 6s on the grid. One of them is doing nothing for this pattern. Work out which four matter and why, and you'll have learnt more about how X-wings are made than a second worked example would teach you.
The four that matter — open when you've had a go
Rows count from the top, columns from the left. Columns four and six each have six empty squares. Four of those six rows get ruled out, and it's one 6 per row:
| The 6 at | Rules out | Because |
|---|---|---|
| row 3, column 8 | row 3 | that row already has its 6 |
| row 4, column 5 | row 4 | same |
| row 6, column 9 | row 6 | same |
| row 7, column 2 | row 7 | same |
Four rows gone from both columns at once — and that's the part worth noticing. These four 6s are horizontal. Each one lies across a row, and a row cuts through column four and column six equally. That's precisely why the two columns end up with the same two survivors rather than two different pairs, and it's the structural reason X-wings exist at all.
Rows 1 and 9 survive in both columns. Four corners.
The fifth 6, at row 2 column 1, is the one doing nothing. It rules out row 2 — but row 2's squares in columns four and six are a given 1 and a given 5, already filled. It was never in the running.
The lesson to take. When you're hunting an X-wing, don't scan for rectangles. Scan for a digit with a lot of lines already placed, because every one of those lines is an elimination you get for free across the whole board. Five 6s on the grid is what made this pattern possible. A digit with two placed would have squeezed nothing.
Where you are now
Six techniques:
- Naked single — this square has one number left. Places.
- Hidden single — this number has one square left in a region. Places.
- Pointing pair — this number's homes in a box share a line; it clears from the rest of the line. Clears.
- Naked pair — two squares hold the same two numbers; both clear from the rest of the region. Clears.
- Hidden pair — two numbers hold the same two squares; everything else clears out of them. Clears.
- X-wing — one number, two lines, two crossing lines; it clears from the crossings. Clears, and from a long way off.
The first five all work inside a region. This one is the first that doesn't, and that's the real content of the sixth rung — not the rectangle, but the willingness to compare two parts of the board that have nothing to do with each other.
There's one more rung on this ladder, and it takes that idea further. Three squares are linked in a chain — a pivot and two wings — and whichever way the pivot falls, one of the two wings ends up holding the same digit. So that digit clears from any square that sees both wings.
Earlier in this series: naked singles, hidden singles, pointing pairs, naked pairs and hidden pairs. The whole ladder is laid out in Sudoku techniques, in the order worth learning them.