The 15 sudoku solving techniques
A solving technique is a precise line of reasoning that lets you place a digit or rule out a candidate without ever guessing. Solvissima's fifteen techniques form a ladder: each one builds on the previous and prepares the next. Singles can be read straight off the grid; box-line interactions, then subsets, ask you to pencil in candidates; fish and wings look for wider patterns spread across several zones. That's why it pays to learn them in order: skip a rung and you end up hunting for an X-Wing where a naked pair would have done. This page groups them by family, from the simplest to the most advanced, and shows for each one the levels on the site where you're likely to meet it, from Beginner to Extreme. Open a technique to watch a demonstration on a real puzzle, then practice on puzzles where it is the key.
Singles
A cell or a digit has only one possibility left: the foundation of every solve.
Naked Single
A cell only has one digit left: every other number is already placed somewhere on its row, column, or box. It’s the most direct deduction in sudoku — no need to check any neighboring candidates.
Levels: Beginner
Hidden Single
Within a zone (row, column, or box), a digit has only one cell left where it can go — even if that cell still accepts other digits too. It’s “hidden” among its neighbors: you have to scan the whole zone to spot it.
Box-line interactions
A digit confined to the overlap of a box and a row (or column) clears its other candidates.
Pointing Pair
Inside a box, a digit can only sit on one row (or column). It “points” outward: that digit gets ruled out everywhere else on that row, outside the box. The first elimination technique in the path.
Levels: Hard
Claiming Pair
On a row or column, a digit can only land inside one box. It “claims” that box: every other candidate for that digit inside the box gets eliminated. The mirror image of the pointing pair, same weight.
Levels: Hard
Naked subsets
Cells that share exactly a few digits between them: those digits are reserved for them within the zone.
Naked Pair
Two cells in the same zone share exactly the same two candidates between them. Those two digits are reserved for them: nothing else in the zone can take them, even without knowing which cell gets which.
Levels: Hard
Naked Triple
Three cells in the same zone share only three possible digits between them — not necessarily all three in every cell. Those three digits are reserved for them: any other candidate elsewhere in the zone matching one of them gets eliminated. The naked pair, stretched to three.
Levels: Expert
Naked Quad
Four cells in the same zone share only four possible digits between them. Those four digits are reserved for them. Rare in practice: there are a lot of combinations to explore, and the engine only reaches for it as a last resort before the fish techniques.
Levels: Expert
Hidden subsets
Digits that only fit in a few cells of the zone: those cells are reserved for them.
Hidden Pair
Within a zone, two digits can only go in two cells. Those two cells monopolize those digits, even if they still carry other candidates — which get eliminated. The flip side of the naked pair: you hunt for digits, not cells.
Levels: Hard
Hidden Triple
Within a zone, three digits can only occupy three cells. Every other candidate in those three cells gets eliminated. The hard part is the sheer number of combinations to check — there are a lot more than with a pair.
Levels: Expert
Hidden Quad
Within a zone, four digits can only occupy four cells. Every other candidate in those cells gets eliminated. Very rare in practice: if four digits are grouped like this, the remaining five already form an equivalent naked quintuple.
Levels: Expert
Fish
A digit confined to a few rows and columns vanishes from the rest of those columns.
X-Wing
A digit is only possible on two rows, and on each of those rows only in the same two columns. Whichever way it ends up splitting between them, those two columns already have their occurrence inside the pattern: the digit gets eliminated everywhere else on those columns.
Levels: Expert
Swordfish
The X-Wing stretched to three rows and three columns: a digit can only occupy those three columns across those three rows, whatever the exact split. It gets eliminated everywhere else on those three columns.
Levels: Extreme
Jellyfish
The X-Wing stretched to four rows and four columns. Same logic: the digit gets eliminated on the four columns involved, outside the four-row pattern.
Levels: Extreme
Wings
A pivot and two wings that, whatever the pivot turns out to be, force a shared digit.
XY-Wing
A pivot cell with two candidates {A, B} sees two wings: one holds {A, C}, the other {B, C}. Whichever value the pivot ends up taking, one of the wings takes C. Any cell seen by both wings at once loses its candidate C.
Levels: Extreme
XYZ-Wing
An extension of the XY-Wing: the pivot has three candidates {A, B, C}, and its two wings hold {A, C} and {B, C}. Digit C has to belong to one of the three cells. Any cell seen by all three loses its candidate C.
Levels: Extreme
Tips for making progress
Learn in the order of the ladder. If you read about the Jellyfish first, you will get less out of it than if you have spent a week spotting naked pairs. Each technique sets up the reflex for the next: singles teach you to read a zone, pairs teach you to group, fish teach you to cross rows and columns.
Pencil in candidates as early as the Hard level. Until you note them down, no elimination technique shows itself. The Solvissima board turns pencil marks on in one click, and a hint at a dead end points to the technique that would unlock the cell.
Work on one technique at a time. Load three or four puzzles where it is the key, spot it by eye, then play the rest of the grid as usual. A pattern recognized in practice later jumps out on its own on a daily puzzle, often without conscious effort.
Step back without shame. After an Expert puzzle that held out, a Medium the next day puts your eye back in place. The point is not to finish the hardest possible grid, it is to recognize a new line of reasoning.