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Solving Sudoku efficiently is less about knowing the most advanced technique and more about using the right level of logic at the right time.
Start with direct placements. Add candidates when the grid stops giving you obvious answers. Use eliminations to simplify the candidate state, then immediately look again for easy moves.
A useful principle is:
simple placements → candidate eliminations → new simple placements.
How Sudoku solving works: placements and eliminations
Almost every logical Sudoku technique produces one of two kinds of progress.
A placement proves which digit belongs in a cell. A candidate elimination proves which digit cannot belong in a cell.
Easy puzzles often contain long runs of placements. Harder puzzles may require several eliminations before the next placement appears. That does not mean the elimination was a secondary result: removing a candidate can be the exact step that makes a later Single or subset possible.
This is why a systematic solver does not ask only “which cell can I fill?” The broader question is “what can I prove from the current candidate structure?”
Step 1: Find last missing digits
Begin with rows, columns, and boxes that are almost complete.
If a unit contains eight different solved digits, its final cell must contain the one missing digit from 1–9. This simplest pattern is often called a Full House or last-missing-digit placement.
These moves are worth checking first because they are immediate, reliable, and frequently create new restrictions in neighboring units.
Step 2: Scan the most constrained areas
Look for rows, columns, and boxes that already contain many solved digits, then scan individual digits through the grid.
Suppose you are trying to place 7 in a box. Existing 7s in intersecting rows and columns can block several cells. If one position remains, 7 is forced there.
Scanning is especially valuable early in a puzzle because it works directly from placed digits and often requires few or no written candidates.
Do not scan only one unit type. A constrained box may be unlocked by a row; a constrained row may become obvious after you inspect its boxes.
Step 3: Find Naked and Hidden Singles
Singles are forced placements and should remain near the front of your solving queue throughout the puzzle.
Naked Single
A cell has only one candidate left.
If the candidates for a cell are {6}, the cell must contain 6.
A Naked Single is cell-focused: you determine the contents of one cell by ruling out the other eight digits.
Hidden Single
A digit has only one possible cell within a row, column, or box.
The target cell may still contain several written candidates, which is why the correct digit is “hidden” among other possibilities.
A Hidden Single is unit-focused: you track one digit across a row, column, or box and discover that only one position remains.
Singles should be checked repeatedly because almost any useful elimination can create a new one.
Step 4: Build and maintain accurate candidates
When direct scanning no longer reveals enough information, record the digits that can still legally fit in unsolved cells.
Candidates make relationships visible. They can show that:
- two cells contain the same restricted pair;
- a digit is confined to one row inside a box;
- a digit occupies matching positions across two rows;
- several bivalue cells form an implication pattern;
- a candidate network contains Strong and Weak Links.
Accurate candidate information matters more than the amount of notation you use. Full notation can be useful on difficult puzzles, while selective notes may be enough earlier in a solve.
Whenever you place a digit or prove an elimination, update the affected candidates before trusting a pattern that depends on them.
Step 5: Use intersections and Locked Candidates
A common intermediate source of progress is the intersection between a box and a row or column.
If every candidate for a digit inside a box lies on the same row, that digit must appear somewhere on that row inside the box. The same digit can therefore be removed from other cells in the row outside the box. This is the Pointing form of Locked Candidates.
The reverse direction also works. If all candidates for a digit in one row are confined to a single box, that digit can be removed from the other cells in the box. This is usually called Claiming or Box-Line Reduction.
Locked Candidates are important because they teach a central intermediate habit: progress does not always fill a cell immediately. A candidate elimination can reshape the puzzle enough to reveal the next direct move.
Step 6: Look for pairs, triples, and other subsets
Subsets reserve a small group of digits for the same number of cells inside one unit.
Suppose two unsolved cells in a row contain only {3, 8} and {3, 8}. Those two digits must occupy those two cells in some order. Therefore, 3 and 8 can be removed from every other cell in that row.
That is a Naked Pair.
The same principle extends to Naked Triples and Quads. Hidden subsets express the relationship from the opposite direction: a particular group of digits can appear only in the same number of cells, so other candidates can be removed from those cells.
When searching for subsets, focus on a single row, column, or box at a time. Ask whether a small set of cells or digits has become more restricted than the rest of the unit.
Step 7: Search for single-digit patterns and Fish
When one candidate digit appears in a sparse, repeated structure across several rows or columns, switch from thinking about whole cells to thinking about one digit at a time.
This is the territory of patterns such as Skyscraper, Two-String Kite, X-Wing, and Swordfish.
Fish techniques use relationships between candidate positions across rows and columns. An X-Wing, for example, can occur when the same candidate is restricted to the same two columns in two rows. That structure can prove eliminations elsewhere in those columns.
Single-digit patterns may look visually different, but they share a useful recognition cue: one digit has a limited set of positions connected through rows, columns, boxes, or Strong Links.
Step 8: Look for Wings and bivalue patterns
A bivalue cell has exactly two candidates. Groups of bivalue cells can create strong implications because if one candidate is false, the other must be true.
Techniques such as XY-Wing, XYZ-Wing, and W-Wing use those restricted candidate relationships to eliminate a digit from cells that see the relevant endpoints or pincers.
You do not need to test every bivalue cell against every other one. First look for a meaningful shared candidate structure: cells with two candidates, overlapping peers, and a candidate that can be forced regardless of which branch is true.
Step 9: Follow Coloring, Links, and Chains
At higher difficulty, candidates can be connected through Strong Links and Weak Links.
A Strong Link says that, within the relevant relationship, if one candidate is false the other must be true. A Weak Link says that both candidates cannot be true at the same time.
Simple Coloring, X-Chains, XY-Chains, and broader chain techniques use these relationships to propagate implications and prove eliminations.
The key shift is conceptual: instead of recognizing only a compact geometric shape, you begin following a logical network from candidate to candidate.
Step 10: Use expert techniques only when the puzzle requires them
Some difficult Sudoku puzzles go beyond common Fish, Wings, Coloring, and basic Chains.
More specialized solving can involve larger or finned Fish, advanced alternating chains, uniqueness extensions, Almost Locked Sets, forcing methods, and other expert structures.
The existence of those techniques does not mean you should search for them in every hard puzzle. Use the simplest deduction that actually fits the current grid. A complicated technique is not better than a Single; it is simply useful when easier logic no longer produces progress.
After every elimination, start again from the top
This is one of the most useful habits in Sudoku solving.
An advanced elimination is often valuable because it creates something simpler:
- a last missing digit;
- a Naked Single;
- a Hidden Single;
- a new Locked Candidate;
- a smaller subset;
- a more constrained candidate pattern.
Do not keep searching for another advanced pattern just because you successfully used one.
Advanced techniques do not replace simple techniques. They create new opportunities for simple techniques.
Return to the beginning of your solving loop after every meaningful change.
A complete Sudoku solving order
There is no mandatory technique order that fits every puzzle, but this hierarchy is a useful default:
- Last missing digits / Full Houses.
- Scanning and crosshatching.
- Naked Singles.
- Hidden Singles.
- Candidate cleanup.
- Locked Candidates.
- Naked and Hidden Pairs.
- Triples and larger subsets.
- Single-digit patterns and basic Fish.
- Wings and other bivalue patterns.
- Coloring, Links, and Chains.
- Uniqueness and expert techniques when genuinely required.
Treat this as a search hierarchy, not a difficulty law. Solvers differ in what they notice quickly, and different rating systems order techniques differently.
The practical rule is simpler: exhaust clear, low-cost deductions before spending time on deeper structures.
How do you know which Sudoku technique to look for?
Technique recognition becomes easier when you search by structure instead of memorizing a long list of names.
Ask what kind of information the grid is giving you:
- one unit has only one digit missing → complete the unit;
- one cell has one candidate → Naked Single;
- one digit has one position in a unit → Hidden Single;
- one digit is confined to a box/line intersection → Locked Candidates;
- a few cells share a small candidate set → subsets;
- one digit forms repeated sparse positions across rows or columns → Fish or single-digit patterns;
- several cells have two candidates and share useful values → Wings or XY-style chains;
- candidates form Strong/Weak implication relationships → Coloring or Chains;
- the grid contains a pattern that would otherwise permit multiple completions → uniqueness techniques.
The more you practice, the less this feels like checking a list and the more it feels like reading the candidate structure of the puzzle.
How to solve a hard Sudoku
Hard Sudoku uses the same rules and the same overall process as an easy puzzle. The difference is that the next deduction may be several logical steps away from an immediate placement.
For a hard puzzle:
- make candidate notation trustworthy;
- re-check Singles and Locked Candidates before assuming the grid is advanced;
- search one candidate digit at a time for Fish or single-digit structures;
- inspect bivalue cells for Wings and chains;
- use advanced methods to create an elimination;
- immediately return to simpler logic after that elimination.
Trying harder technique names at random is usually less effective than identifying what kind of candidate structure is actually present.
What should you do when no technique seems to work?
Being stuck is often a recognition problem before it is a logic problem.
Before assuming you need a technique you have never learned, check for:
- an outdated or missing candidate;
- a Hidden Single obscured by dense notes;
- a Locked Candidate you did not revisit after a placement;
- a subset in a different unit;
- a useful digit whose candidate positions have become sparse;
- a recent elimination that created a simpler move elsewhere.
If the puzzle is intentionally above your current solving level, a logical hint can be more useful than guessing because it tells you what structure you failed to recognize.
Should you guess when stuck?
For human-style logical Sudoku, guessing should not be the default response to being stuck.
A speculative digit may eventually lead to a contradiction, but following that branch is a different solving approach from proving the next move directly from the current grid.
A difficult puzzle may require a technique you do not know yet, or a familiar pattern that you have not spotted. If you are learning, prefer a hint or explanation that identifies the logical next step.
Computer solvers may use search or backtracking for validation, generation, or exhaustive solving. That does not make guessing necessary for the human-oriented logical path of a well-designed puzzle.
There is a separate Guide dedicated to guessing, trial and error, and logical solving.
FAQ
What is the fastest way to solve Sudoku?
For most players, speed improves by recognizing common deductions quickly, scanning systematically, and avoiding unnecessary candidate work. When learning, prioritize correct recognition before raw speed.
Can every Sudoku be solved with the same techniques?
No. Different puzzles require different levels of logical deduction. Easy puzzles may resolve with scanning and Singles, while harder puzzles can require advanced candidate patterns or chains.
Should I always start with Singles?
Start with the simplest available deductions. A last missing digit or direct scan may be even more immediate, but Singles should remain one of the first things you re-check after every change.
Why do advanced techniques remove candidates instead of placing digits?
Because many difficult positions do not immediately prove a cell's final value. Instead, they prove that one or more candidates are impossible. Those eliminations simplify the grid until a placement becomes forced.
Is there one best Sudoku solving algorithm for people?
No fixed human sequence finds every next move efficiently. A hierarchy from simple deductions to increasingly complex candidate structures is useful, but recognition skill and puzzle design affect which technique becomes natural to search for next.
Can you solve Sudoku without pencil marks?
Many easy puzzles can be solved with scanning and mental elimination. As candidate relationships become denser, written or digital notes make intermediate and advanced logic much easier to track accurately.
What to learn next
If you still solve mostly without notes, study Scanning and Sudoku Candidates first. Then learn Naked Singles, Hidden Singles, and Locked Candidates. Once those are comfortable, use Sudoku Strategies to organize how you search for intermediate and advanced patterns.