Paste any Sudoku puzzle, load an example, or enter a puzzle by hand and our free online solver will walk you through the solution one logical step at a time, naming the strategy used for every digit it places. Try it on the famous World's Hardest Sudoku by Arto Inkala to see the solver fall back to backtracking when human strategies run out.
The interactive solver above accepts puzzles three ways. Click any cell and tap a number to enter clues by hand, paste a puzzle as 81 digits (use 0 or . for empty cells) into the paste box, or hit one of the example buttons to load a known puzzle. Once you have entered a valid puzzle with at least 17 clues, choose Solve step-by-step to walk through the logic one move at a time, or Solve all to reveal the complete solution.
Every step shows three things: the strategy used (with a link to a tutorial that explains how the technique works), the cell coordinates in R-C notation (e.g. R3C5 means row 3, column 5), and the digit being placed. The current step is highlighted on the grid in teal so you can see exactly where the solver is looking.
If you enter a puzzle that has no solution or has multiple solutions, the solver will tell you. Every valid Sudoku must have exactly one solution.
The step-by-step engine tries human-style strategies in order from easiest to hardest, falling back to brute-force backtracking only when no logical move can be made. Each named strategy links to a full tutorial in our strategy guide.
A cell where only one digit is possible because every other digit already appears in its row, column, or box. The first technique anyone learns and the most common move in easy puzzles.
A digit that can only fit in one cell of a given row, column, or box, even though that cell may have other candidates remaining.
Two or three cells in a unit that share the same two or three candidates, locking those digits into those cells and eliminating them from the rest of the unit.
Two or three digits that can only fit in the same two or three cells of a unit, eliminating other candidates from those specific cells.
When a candidate is restricted to one row or column inside a single box, that digit can be removed from the rest of the row, column, or box.
Pattern-based eliminations across two or three rows (or columns) where a candidate forms a rectangle or 3x3 grid pattern, allowing eliminations along the perpendicular.
Chain-based techniques that follow forcing relationships between cells with two or three candidates to derive contradictions.
When no human strategy applies, the solver finishes the puzzle with brute-force search and labels those steps as Backtracking. This happens on the World's Hardest Sudoku and other extreme puzzles.
In 2012, Finnish mathematician Arto Inkala released a Sudoku he claimed was the most difficult one ever constructed. Most logical solvers stall on it after a handful of moves and have to fall back on guessing. Load the World's hardest preset above to watch our solver chip away with named strategies, then switch to backtracking once it runs out of options.
What makes Inkala's puzzle so hard is that it is rich in forcing chains and other deep techniques that require looking many cells ahead at once. Even expert human solvers typically need an hour or more to finish it without computer assistance. For more on extreme puzzles, see our article on the hardest Sudoku ever made.
At its heart, Sudoku is a constraint satisfaction problem (CSP). The 81 cells are variables, the digits 1-9 are the domain, and the row, column, and box constraints define what counts as a valid assignment. Two algorithmic ideas together make modern Sudoku solvers fast: constraint propagation and backtracking search.
Constraint propagation works by maintaining a candidate list for every empty cell and removing impossible candidates whenever a digit gets placed. The same logical patterns human solvers use - naked singles, hidden singles, naked pairs, pointing pairs, X-Wings - are all rules of constraint propagation. When propagation alone is not enough, the solver picks the cell with the fewest remaining candidates (the Minimum Remaining Values heuristic), tries each candidate, and recurses.
Peter Norvig famously demonstrated that combining propagation with backtracking solves any 9x9 Sudoku in milliseconds, and easy puzzles often need no backtracking at all. Donald Knuth's Dancing Links (DLX) implementation of Algorithm X is one of the fastest known approaches; SAT solvers can also handle Sudoku as a trivial sub-problem.
For programmers, our Sudoku for programmers article goes deeper into the implementation side and offers project ideas.
A solver is most useful when you want to learn a technique you have not yet mastered. Watching the solver name and apply X-Wing, then clicking through to the tutorial, teaches you to spot the same pattern next time. Solvers are also great for verifying that a puzzle you found in a magazine or app is well-formed (exactly one solution).
What a solver cannot give you is the satisfaction of finishing a puzzle yourself, or the cognitive workout of holding multiple candidates in your head while you reason about them. If you find yourself reaching for the solver every time you get stuck, try our stuck on a Sudoku? guide first - it walks through what to look for before giving up.
Yes, completely free with no signup, no ads, and no limits. Solve as many puzzles as you want. The solver runs entirely in your browser - your puzzles are never sent to a server.
Most experts point to the puzzle constructed by Finnish mathematician Arto Inkala in 2012, which appears in the 'World's hardest' preset above. It defeats most pure-logic solvers and requires backtracking to finish. You can read more in our hardest Sudoku ever article.
Copy the puzzle as 81 digits in reading order (left-to-right, top-to-bottom). Use 0 or a period for empty cells. The solver also accepts 9-line grids with whitespace or other separators - it strips everything except digits and dots.
A valid Sudoku has exactly one solution. If yours has more than one, it usually means a clue was mistyped or accidentally omitted. Double-check the original source. Our solver requires uniqueness because the solving strategies it teaches only work on well-formed puzzles.
When the solver runs out of human-style logical moves, it falls back to brute-force search - trying candidates and reversing course on contradictions. We label these steps as Backtracking to be honest that no named technique applies. Extreme puzzles like Arto Inkala's often need this.
Modern solvers combine constraint propagation (the same logical strategies humans use) with backtracking search. Propagation eliminates impossible candidates; when no logical move is left, the solver guesses the cell with the fewest options and recurses. Together these techniques solve any 9x9 puzzle in milliseconds.
Only if you're competing. For learning, a solver that names the strategy it just used is one of the fastest ways to internalize new techniques. Most expert solvers learned X-Wings and Swordfish exactly this way.
This solver is built for the standard 9x9 grid. For 4x4, 6x6, and 16x16 puzzles, see our variants guide - those grids use the same constraint engine but a different UI.
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