Sudoku Trainer

Sudoku Trainer: practise the pattern, not the whole puzzle

A strong Sudoku player does not just know the names of techniques. They can look at a grid full of pencil marks and see why a move is forced. That recognition is the thing this trainer drills, and it is the one thing an ordinary puzzle almost never lets you practise on purpose.

Pick a technique from the menu — there are eighteen, from naked singles up to Almost Locked Sets — and the trainer loads a real Sudoku position with every pencil mark showing. Your job is to click the cells that make the pattern work. Check tells you whether you found it, and Find Pattern shows it with the eliminations marked.

That is a narrower question than the other tools on this site ask, and a more useful one to drill. A puzzle asks “can you finish this grid?” The Sudoku Solver answers “what is the answer?” The Sudoku Helper answers “what should I do next?” A trainer asks the question that actually transfers to your own solving: can you see this pattern when it is sitting in a real board, surrounded by ninety other pencil marks that have nothing to do with it?

Why you will walk past an X-Wing and almost never be forced to use one

That claim can be measured rather than asserted, because we have both halves of the measurement: the eighteen technique detectors behind our Sudoku Helper, and the puzzle banks this site actually serves. We ran every detector over every board state of 1,000 puzzles — 500 from the Evil bank and 500 from the Extreme bank, 28,230 positions in total — recording two different things at each position. Whether a technique was available, and whether it was the simplest technique available, which is the move a player working from easiest to hardest would actually make.

The two numbers are nothing like each other. An X-Wing was available on 29.2% of boards and was the simplest move on 69 positions out of 28,230 — 0.24%. You will walk past one on roughly every third board, and be forced to use one about once in four hundred moves. A Jellyfish was available on 21.4% of boards and was never once the simplest thing to do. Neither was a Unique Rectangle, in 28,230 chances.

This is not an argument for skipping the advanced techniques. When a hard puzzle genuinely stalls, they are what break it, and the table below shows which ones carry that weight. It is an argument about where you can learn them. If you wait for a puzzle to demand an X-Wing before you practise one, you will wait a very long time — and the position that finally demands it will be a hard one you are already stuck in. That gap is the whole reason this page exists.

Across 28,230 board states from 1,000 puzzles in our own Evil and Extreme banks, using the same eighteen detectors the Sudoku Helper runs. On the board is how often the technique was available at all; the move to make is how often it was the simplest one available, and so the move a player working from easiest to hardest would actually play. The two columns do not measure the same thing and the gap between them is the point. The remaining 2.7% of positions are the ones where none of the eighteen fired at all.

Every board here is a real position, and the pattern is really in it

The lessons are not drawn by hand. They are harvested. Our generator produces a puzzle, the eighteen detectors are asked what they can find in it, and whatever they find is written down along with the cells that carry the argument and the detector's own explanation of that instance. There are 180 lessons, ten for each technique, and each one sits on its own board — so changing the technique or the example always changes the grid in front of you.

The pencil marks are not stored at all. A lesson keeps the position and nothing else, as 81 characters, and your browser recomputes the candidates with the same engine the solver and the helper use. That is a constraint rather than a saving: because nothing anywhere records the pencil marks, a board cannot show a candidate that the position rules out. In 169 of the 180 lessons the marks are exactly what the givens imply; in the other 11, some candidates have already been eliminated by earlier logic, and the lesson carries those eliminations so the board matches what a solver would really be looking at.

Seventeen of the eighteen techniques turn up in positions a solver reaches by ordinary logic, most of them in the opening position of a freshly dealt puzzle. The exception is the Unique Rectangle, which cannot appear in an opening position at all: it needs four cells already reduced to the same two candidates, and a grid straight from the generator has not had time to reduce anything. Those ten lessons are positions further into a solve, reached only by logical moves — the trainer never shows you a board that was arrived at by guessing.

How to use the trainer

Pick a technique, then work down its ten examples in order. They are sorted gentlest first: example 1 of any technique is the least crowded board we found it on, and example 10 the busiest.

1. Pick one technique and stay on it. Do not rotate through everything at once. Five or ten examples of the same pattern is what builds recognition.
2. Read the panel. It names the technique, gives the target digit where the technique is about a single digit, and tells you exactly how many cells the pattern has.
3. Scan like a solver, not like a spotter. Take one digit or one house at a time. Trying to see the shape whole is what fails on a busy board.
4. Click every cell the pattern needs. For a fish that is every cell holding the digit in those rows or columns; for a wing it is the pivot and both pincers.
5. Press Check. It accepts the pattern cells and nothing else.
6. Use Find Pattern last. The reveal is worth most when you compare it against a proof you already tried to make.

Check is strict, and that is deliberate. It accepts your answer only when you have selected every pattern cell and no others. If your selection is a subset of the pattern it tells you how many of the cells you have — “3 of 4 pattern cells selected” — so a partial answer is useful feedback. The moment you include a cell that is not part of the pattern it stops counting and tells you to clear the extras instead, because “you are two thirds right” is misleading when one of your cells is wrong.

Hint gives ground in three stages. The first press names one cell of the pattern and marks it on the board. The second names the target digit, or, for the patterns that are not about a single digit, tells you to compare candidate sets in the house or link you are looking at. A third press reveals the whole pattern — so Hint is a slope, not a ladder, and if you only want a nudge, stop at two. Reset clears your selection and the hints and puts the board back as it was; Previous and Next move through the ten examples and wrap around at either end.

What counts as “the pattern”

The rule is the same for every technique: click every cell the argument needs, and nothing else. That is usually more than the cells people picture. An XY-Wing is not two pincers, it is a pivot and two pincers. An ALS-XZ is not one almost-locked set, it is both of them. A Simple Colouring chain is both colours, including the colour that turns out to be false — that colour is where the contradiction lives, so leaving it out would be leaving out the proof.

Ranges are measured across the 180 lessons in the bank, not estimated. The panel always tells you the exact number for the example in front of you.

Beginner techniques to train first

The best training starts with singles, because they are 83% of the moves you will ever make. A naked single is a cell with one candidate left. A hidden single is a digit with one possible cell left in a row, column or box. They sound too simple to drill, and the hidden ones are the easiest in the game to walk straight past: our measurement found a hidden single available on 75.3% of all board states, more often than any technique except Almost Locked Sets.

After singles, train the locked candidates. Pointing pairs happen when a digit inside one box is confined to a single row or column, so it can be cleared from the rest of that line. Box/line reduction is the same idea running the other way: a line confines a digit to one box, so it goes from the rest of the box. The pointing pair is the third most-needed move in the whole list, behind only the two singles and ahead of every advanced technique; box/line reduction is sixth.

Then pairs and triples. Naked pairs and hidden pairs are usually the first techniques that feel like real candidate logic rather than scanning. Naked triples and hidden triples extend it, and they need a calmer eye, because the three cells rarely sit together and the three digits rarely all appear in all three cells.

X-Wing practice: search by row, then search again by column

X-Wing is the most searched-for Sudoku technique and the first fish most players meet. The rule is one sentence: if a digit appears in exactly two cells in each of two rows, and those cells share the same two columns, then the digit is gone from the rest of those two columns. Reading that takes fifteen seconds. Seeing it in the board above takes considerably longer, and that difference is the entire skill.

Do not start by looking for rectangles. Start with one digit and ask a counting question: where can 4 still go in this row? Work down the rows noting the ones with exactly two places. When two of those rows name the same pair of columns, you have an X-Wing. It feels slow, and it is far more reliable than waiting for a shape to jump out at you.

Then run the search again with rows and columns swapped, because the pattern works identically in both directions and most guides only draw one of them. The revealed board above is the column form: columns 1 and 3 each confine the 4 to rows 2 and 6, so the eliminations land along the rows instead of down the columns. Four of the ten X-Wing examples in the trainer are this way round — not by design, but because that is how often the harvest found them — so if you only ever search by row, you will miss a good share of them in your own puzzles too.

Fish: X-Wing, Swordfish and Jellyfish

The fish are one family with one idea. An X-Wing is a 2-fish, a Swordfish a 3-fish, a Jellyfish a 4-fish. The scale changes and the question does not: for one digit, are N rows restricted to the same N columns, or N columns to the same N rows? If so, that digit is spoken for inside the intersection, and every copy of it elsewhere in those lines is impossible.

Fish practice teaches discipline more than it teaches fish. You cannot find a Swordfish by looking at the board; you find it by picking a digit, listing which rows hold it in two or three places, and then checking whether three of those rows share only three columns. If that sounds mechanical, good — advanced Sudoku gets easier when the scan is methodical instead of inspired.

Be honest with yourself about the payoff, though. Our measurement found a Swordfish was the simplest available move 11 times in 28,230 positions, and a Jellyfish not once. Train them because they sharpen your candidate control and because a Jellyfish makes an X-Wing look small, not because a puzzle is going to demand one.

Wings, and the one that is worth more than X-Wing

Wings train a different muscle from fish. Instead of tracking one digit across lines, you study small groups of cells with two or three candidates each and ask what one cell being true would force somewhere else. An XY-Wing has a pivot holding two candidates and two pincers that each share one of them; if both pincers carry the same extra digit, that digit dies in every cell that sees both pincers.

An XYZ-Wing is the same shape with a three-candidate pivot, which makes the elimination narrower because the target must see all three cells. A W-Wing is two cells holding the identical pair, joined by a strong link on one of the two digits.

The W-Wing is the find worth taking from that table. It was the simplest available move on 2.02% of positions — roughly eight times as often as an X-Wing, and more often than the fish, the Skyscraper, Simple Colouring and the Unique Rectangle put together. It is also the one that tends to appear last in strategy guides, if at all. If you are going to learn exactly one pattern beyond pairs and locked candidates, the numbers say make it this one.

Uniqueness, chains, and where the eighteen run out

The last group leans on links and on uniqueness. A Skyscraper is two strong links on one digit sharing a line. Simple Colouring follows a chain of strong links, tints it in two alternating colours and looks for a colour that contradicts itself. A Unique Rectangle argues from the fact that a proper puzzle has exactly one answer, so a configuration that would allow two cannot be there.

These get much easier once you stop treating the names as magic. A Skyscraper is a pair of linked possibilities. Colouring is bookkeeping for consequences. A Unique Rectangle is a shape that would make the puzzle ambiguous, so something in it must be false.

And there is an honest boundary here, which we can state exactly. Of 500 puzzles from our Evil bank, the eighteen techniques finished 46.2%. Of 500 from the Extreme bank, they finished one. Every one of those puzzles has exactly one answer — we checked — so what runs out is not the puzzle but the technique list: on 2.7% of all positions none of the eighteen fired at all. Past that point a solver needs forcing chains, X-cycles and the longer chain techniques, which this trainer does not yet cover. If you finish all eighteen here and still stall on Extreme, you have not done anything wrong. You have reached the edge of what these eighteen can do.

Common mistakes when learning techniques

Learning the name instead of the proof. If you press Find Pattern and move on, you will remember a colour layout and not an argument. Before you reveal, say the reason out loud: “these two columns put the 4 in only these two rows.” If you can say it, you have learned it.

Practising on pencil marks you got wrong. Every advanced technique depends on the candidate grid being exactly right. One candidate missing or one impossible candidate left behind, and an X-Wing or a hidden pair can appear to exist when it does not. The boards here cannot have that problem, because the candidates are computed from the position rather than typed in — but your own grid at home can, and when a technique “works” and the puzzle then contradicts itself, a stale pencil mark is almost always why.

Reaching for the advanced pattern first. This is the one the data is loudest about. On a real board there are, on average, seven techniques available and the right move is nearly always the dullest of them. Work singles, then locked candidates, then pairs, and only go hunting for a fish when the simple moves have genuinely stopped. The point of training an X-Wing is not to use one; it is to have it ready on the rare board that needs it.

A training plan based on what you will actually need

Spend your practice in proportion to what the board asks for, not in proportion to how impressive a technique sounds. One session on naked and hidden singles — yes, really; they are five sixths of every solve and hidden singles are the most-missed move in the game. One on pointing pairs and box/line reduction. One on naked and hidden pairs, then triples.

Then, when you move to the advanced set, take them in the order the measurement suggests rather than the order the internet suggests: W-Wing first, then XY-Wing, then Almost Locked Sets and X-Wing, and treat Swordfish, Jellyfish, Skyscraper and Unique Rectangle as sharpening rather than as tools you are waiting to need.

A workable weekly routine: pick one technique, solve all ten examples, read the linked guide for any you missed, then open a real puzzle and try to notice the same structure unprompted. When you stall in a live puzzle, the Sudoku Helper will tell you the simplest move available and why, which is the closest thing to marking your own scan. If you only need to check a finished grid, use the Sudoku Solver. And if hard Sudoku is where you want this to pay off, that is the bank to take it back to.

The goal is not to memorise 180 boards. It is to make each pattern ordinary enough that checking for it costs you nothing — at which point the hard puzzles stop feeling hard and start feeling long, which is a much better problem to have.