Learn them in this order: naked singles, hidden singles, pointing pairs, naked pairs, hidden pairs, X-wing, XY-wing. That's the whole ladder, and we counted exactly how far it gets you against the 300 puzzles that ship inside our app. The first three finish almost every Easy puzzle — 205 of 207. The first five finish almost every Medium — 56 of 57. And all seven together finish none of the 28 Hard ones.
That last number is the honest one, and no other guide will tell you it. Hard puzzles in this app need something off the end of this ladder — a skyscraper, a W-wing, a remote pair, a locked triple, a BUG+1. Those are real techniques with real names, and they're past where this page stops.
So learn the ladder for what it actually is: the thing that takes you from a beginner to somebody who finishes almost every Easy and Medium board. That's 264 of the 300 puzzles in the app, and stopping there costs you nothing.
| Technique | What it does | Places a number? | When you need it |
|---|---|---|---|
| Naked single | Finds a square with one number left | Yes | Immediately. Every puzzle, every time |
| Hidden single | Finds a number with one square left | Yes | When crossing off squares stops paying |
| Pointing pair | Corners a number onto one line and clears it from the rest | No | When both singles have stalled |
| Naked pair | Two squares own two numbers, so nobody else in the region can have them | No | Medium, mostly — it's the technique Medium turns on |
| Hidden pair | Two numbers own two squares, so those squares drop every other candidate | No | Rare. One puzzle in our whole bundle, an Expert |
| X-wing | One number boxed into a rectangle, cleared from two whole lines | No | Rare. Two puzzles in the bundle, one Hard, one Expert |
| XY-wing | Three linked squares force a number out of everything they both see | No | Rare. One puzzle, an Expert |
Notice the third column, because it's the thing that trips people up. Only the first two techniques put a digit on the board. Everything after them takes possibilities away instead — and if you've been waiting for each move to produce a number, that expectation is what's standing between you and a Hard puzzle. Clearing candidates isn't a consolation prize. It's how a single gets made.
Two notes on the counts, since we're printing them. They're taken from the 300 puzzles bundled inside our app, not from Sudoku at large — a different app's Mediums would land somewhere else. And we count a locked pair as a naked pair, because it is one: two squares, the same two candidates, which happen also to share a line. That's the definition in our naked pairs piece, and it's the single biggest thing standing between a solver and a Medium board.
Everything below assumes you know the rules. If you don't yet, they take two sentences — how to play Sudoku covers them and walks you through a first move, and then this page picks up where it leaves off.
Naked singles
A naked single is a square whose row, column and box between them have already ruled out eight of the nine numbers, leaving exactly one.
It's the only technique you can use on a completely blank-looking grid, and it places a number every time it fires. Find the most hemmed-in square you can — one sitting in a busy row, a busy column and a busy box at once — and count what its three regions have already used up. If eight numbers are gone, the survivor isn't a guess.
Start here. Every other technique on this page exists to manufacture more of these.
Naked singles: the square that can only be one number
Hidden singles
A hidden single is a number with only one home left in a row, column or box — even though the square it lands in may still be carrying several other candidates.
It's the same crossing-off as a naked single, asked in the opposite direction. Instead of picking a square and asking what can go in it, you pick a region and a number and ask where that number can go. A square with four candidates is invisible to the first question and can be the answer to the second, which is why this one turns up moves that feel like they came from nowhere.
The trick for spotting them: hunt the digit the board already has most of. Six 8s placed means six lines cutting across the grid, doing your eliminations for free.
Hidden singles: the number with only one home
Pointing pairs
A pointing pair is a number whose only remaining homes inside one box all sit on the same row or the same column — which means that number is somewhere on that line, so it can be crossed off the rest of the line outside the box.
This is the first technique that places nothing, and the first that acts at a distance: you read one box and cross something off five squares away. If three squares share the line instead of two it's a pointing triple and works identically, because the count was never the point. The shared line is.
The same idea read the other way round is called box-line reduction: when a row's homes for a number all fall inside one box, the number clears from the rest of that box. If you can do one you can already do the other.
Pointing pairs: reading a box like a sentence
Naked pairs
A naked pair is two squares in the same row, column or box holding the same two candidates and nothing else — so between them those two squares use up both numbers, and both numbers can be cleared from every other square in that region.
You can't see this one without pencil marks; it's invisible on a bare grid. The logic doesn't care which way round the two numbers fall, only that they've nowhere else in the pair to go.
It scales. Three squares sharing three candidates is a naked triple, four sharing four is a naked quad, and the same clearing follows. The detail most guides skip: a square in a triple doesn't need to carry all three candidates. Two of the three is enough, so long as the three squares between them use no other numbers.
Naked pairs: two squares that own two numbers
Hidden pairs
A hidden pair is two numbers whose only homes in a region are the same two squares — so those two squares must hold those two numbers, and every other candidate written in them can be rubbed out.
It's the mirror of a naked pair, exactly as a hidden single mirrors a naked one. You spot a naked pair by looking for squares that have got small; you spot a hidden pair by looking for numbers that have run out of room, and the two squares it lands on can be carrying five candidates each and still qualify.
Hidden pairs clear rather than place, but they often clear enough to leave a naked single sitting in plain sight.
Hidden pairs: two numbers that own two squares
X-wing
An X-wing is one number confined to the same two columns in each of two different rows — which means that number takes one column in one row and the other column in the other, so it can be cleared from the rest of both columns.
Rows and columns swap freely: the same pattern works with two columns each confining the number to the same two rows. Draw lines between the four corners and you've got the X the name comes from.
The same shape at count three is a swordfish — three rows, three columns, one number, same conclusion. The count isn't what makes it work. The rectangle is.
X-wing: one digit, two rows, two columns
XY-wing
An XY-wing is three squares with two candidates each — one holding X and Y, one holding X and Z, one holding Y and Z, with the first sharing a region with each of the other two — which forces Z into one of those other two squares, so Z clears from any square that sees them both.
This is the first technique that chains squares together rather than reading a single region, and it's where solving starts to feel like proof rather than bookkeeping. Whatever that first square turns out to be, one of the other two ends up holding Z. You never find out which, and you don't need to.
How far do I actually need to go?
Here is the whole ladder measured against our own 300 puzzles. Each row means "solvable using nothing above this rung."
| Knowing… | Easy (207) | Medium (57) | Hard (28) |
|---|---|---|---|
| Both singles only | 205 | 5 | 0 |
| The first three | 205 | 16 | 0 |
| The first five | 205 | 56 | 0 |
| All seven | 205 | 56 | 0 |
Three things fall out of that, and none of them is what the long guides imply.
Easy is finished after two techniques. The singles alone take 205 of 207. Pointing pairs and everything above buy you two puzzles on the entire Easy band. If Easy is where you play, you were done four rungs ago.
Medium is where the ladder earns its keep. Two techniques get you 5 of 57; five get you 56. That jump — from a twelfth of the band to almost all of it — is the strongest argument for learning rungs three through five, and it lands almost entirely on naked pairs.
Hard is past the end of this page. Not "harder work with the same tools" — a different set of tools. Every one of the 28 Hard puzzles in the bundle needs something this ladder doesn't cover, and the names are skyscraper, W-wing, remote pair, naked triple, locked triple, BUG+1 and swordfish. We haven't written those up. If you're clearing Mediums comfortably and Hard feels like a wall, that's because it is one, and it isn't your fault.
So the honest read of this page is narrower than its own title suggests: the seven rungs here are what takes you through Easy and Medium. They are not what takes you through Hard. Easy and Medium are 264 of the 300 puzzles in the app, so for the large majority of what you'll actually be handed, this list is the whole job.
And if you're stuck right now, a missing technique is the last thing to suspect rather than the first. Check the cheap causes before the expensive one: candidates never written down, or the same question asked twenty times running. Both are free to rule out, and being stuck is five different problems of which only one is solved by learning something new.
There's no rung past this list that an ordinary player is missing out on. Colouring, forcing chains and the rest are real techniques, but they belong to puzzles built specifically to require them — which is not the kind you meet by opening an app and playing.
Where the boards come from
The techniques with an article linked above are worked through on a real grid rather than described in the abstract, because the gap between reading a definition and recognising the pattern on a board is most of the difficulty. The rest are being written.
After that you need volume. The only way to get quick at spotting a hidden single is to meet a few hundred of them. Our Sudoku app is an endless feed of graded puzzles that finds your level, and 300 of them ship inside the download, so it keeps working with the network off. No account, no ads, and no hint button — because a technique you were handed isn't one you'll have next time.