Sudoku techniques: from Hidden Single to X-Wing
Once the easy digits are placed and nothing moves anyway, solving techniques help you on. They are not magic but clear rules with which you rule out candidates until a cell becomes unambiguous again. Here you will find the most important techniques, from the simple single to the elegant X-Wing, with short examples.
The foundation: candidates
Almost every technique builds on candidates: the small notes in a cell that record which digits are still allowed there. At the start every empty cell carries all digits that do not yet appear in its row, its column or its block. Each digit you place then removes candidates from the affected units. The techniques on this page tell you when you may cross off additional candidates, and when doing so makes a cell unambiguous. Whoever works cleanly with candidates solves even hard and extreme puzzles reliably, without guessing.
Techniques for getting started
The following two techniques occur in almost every puzzle and are quickly internalised. Whoever masters them confidently solves easy and medium Sudokus mostly without any further method. They are the foundation on which everything else builds.
Naked Single: the naked single
The simplest case. If after crossing off only a single candidate remains in a cell, then that digit belongs there. It is "naked" because no alternative stands beside it any more. Example: A cell had the candidates 2, 5 and 8. In its column a 5 is placed, in its block an 8. Only the 2 remains, so you enter it. Naked Singles constantly arise as a consequence of other moves. It pays to check briefly after every placed value whether only one candidate remains anywhere.
Hidden Single: the hidden single
A Hidden Single is a digit that within a unit, that is a row, column or block, is possible in only a single cell, even if that cell also carries other candidates alongside. Example: Consider a block. The 6 is ruled out in eight of its nine cells because a 6 already stands in the associated rows and columns. If only one cell remains into which the 6 fits at all, then it belongs there, even if that cell still lists 1 and 4 as candidates. Hidden Singles are one of the most common ways forward on all difficulty levels.
Techniques for advanced players
When singles alone no longer help, pairs and locked candidates come into play. These techniques do not close a cell directly but cross off candidates, so that singles surface again afterwards. On the Hard and partly Extreme tiers they are the decisive tool.
Naked Pair: the naked pair
A Naked Pair is two cells in the same unit that hold exactly the same two candidates. Example: In a row two cells hold only 4 and 7. However it turns out: one cell becomes 4 and the other 7, or the other way round. In every case 4 and 7 occupy exactly these two cells. So 4 and 7 may be crossed off all remaining cells of the same row. The same idea exists as a triple with three cells and three candidates. Naked Pairs often bring the decisive cut that then exposes several Naked or Hidden Singles.
Hidden Pair: the hidden pair
The counterpart to the naked pair. A Hidden Pair occurs when two candidates within a unit appear only in the same two cells, even if those cells carry further candidates alongside. Example: In a block the digits 2 and 9 are possible only in two cells; in both a 5 and 6 also stand. Because 2 and 9 must necessarily occupy these two cells, you can cross off all other candidates there: 5 and 6 fall away, leaving only the pair 2 and 9 in both cells. Hidden Pairs are a little harder to spot than naked pairs, but in return they often clear up spots that would otherwise be blocked.
Locked Candidates and Pointing Pair
Sometimes a digit within a block is confined to a single row or column. Then it is "locked" and points into that line. Example (Pointing Pair): In a block the 3 appears in only two cells, both lying in the same row. The block's 3 must therefore land in that row, so you can remove the 3 from all other cells of that row outside the block. Conversely: if a digit in a row is possible only within a single block, it can be crossed off the remaining cells of that block. Both variants are grouped together as Locked Candidates.
Techniques for Extreme
Right at the top, on the Extreme tier, local considerations are sometimes no longer enough. Then a pattern helps that works across several rows and columns at once. The X-Wing is the classic entry into these advanced patterns.
X-Wing: the rectangle
The X-Wing is the first of the "advanced" techniques and works across two units. Example: Take the digit 5. In row 2 the 5 is possible only in columns C and G, in row 6 likewise only in columns C and G, nowhere else in these rows. These four cells form a rectangle. Whichever of the two diagonals the 5 finally occupies: in columns C and G the 5 is thereby ruled out for all other rows and can be crossed off there. Rows and columns are interchangeable here; the X-Wing works just the same when two columns allow the digit only in the same two rows.
In what order should you proceed?
As a rule of thumb you go from the simple to the elaborate. First place all Naked and Hidden Singles until nothing moves directly any more. Then look for Naked Pairs and Locked Candidates and cross off the candidates made impossible by them; usually new singles fall out again afterwards. Only when that too stalls is it worth a look at patterns like the X-Wing. This interplay of crossing off and placing carries you through nearly every puzzle without ever having to guess; in a well-set Sudoku pure logic always leads to the one unique solution.
Try the techniques right away →Explained individually, with an interactive example
The most important techniques have their own pages with an example grid you click through step by step until the elimination becomes visible:
Why you never have to guess
A cleanly set Sudoku always has exactly one solution, and that solution can be found by logic alone. Guessing is therefore never needed, and usually even harmful, because a wrongly guessed value drags follow-up mistakes behind it that you later have to trace back laboriously. When you get stuck, it is almost always because a technique has not yet been applied or a candidate has been overlooked. Then go through the units calmly once more: where is a digit confined to few cells? Where do two cells form a pair? Especially on the Hard and Extreme tiers, exactly this patience is the difference between getting stuck and solving.
Techniques are learned best by applying them. At Sudoku Sagax you can ask for a hint when needed if you simply cannot crack a situation; over time you then recognise the patterns yourself and need the help less and less. Feel free to start on Easy to master the simple techniques confidently, and work your way up tier by tier.
Frequently asked questions about techniques
What is a Hidden Single?
A Hidden Single is a digit that within a row, column or block is possible in only a single cell, even if that cell still carries other candidates. Because the digit fits nowhere else in that unit, it belongs unambiguously in that cell.
How does a Naked Pair work?
A Naked Pair is two cells in the same unit that hold exactly the same two candidates, say 4 and 7. These two digits necessarily occupy exactly those two cells. Therefore 4 and 7 can be crossed off all other cells of the same row, column or block.
What is an X-Wing in Sudoku?
An X-Wing concerns a digit that in two rows is possible only in the same two columns. These four cells form a rectangle. Whichever diagonal the digit occupies, it is thereby ruled out in those two columns for all remaining rows and can be crossed off there. Rows and columns are interchangeable.