Sudoku
Sudoku is a number-placement logic puzzle. Fill a 9x9 grid so each row, column and 3x3 box contains digits 1-9.
Key features
- Classic 9x9 Sudoku puzzle grid
- Multiple difficulty levels from easy to expert
- Note/pencil mark system for candidates
- Undo, hint and validation features
Guide
Sudoku is a logic-based number placement puzzle that traces its modern form to a 1979 puzzle published in Dell Pencil Puzzles and Word Games magazine under the name Number Place. The puzzle was designed by Howard Garns, a retired architect from Indiana. In 1984, the Japanese publisher Nikoli introduced the puzzle to Japan under the name Sudoku, a contraction of the Japanese phrase suuji wa dokushin ni kagiru, meaning the digits must remain single. Nikoli refined the format by requiring that the given numbers form a symmetric pattern and that each puzzle have exactly one solution. The puzzle remained primarily a Japanese phenomenon until 2004, when Wayne Gould, a retired judge from New Zealand, convinced The Times of London to publish daily Sudoku puzzles. The resulting craze swept the world within months. A standard Sudoku puzzle consists of a 9x9 grid divided into nine 3x3 sub-grids called boxes (also called blocks or regions). Some cells are pre-filled with digits from 1 to 9. These given digits (called clues or givens) provide the starting information needed to solve the puzzle. Your task is to fill every empty cell with a digit from 1 to 9 such that every row contains each digit exactly once, every column contains each digit exactly once, and every 3x3 box contains each digit exactly once. A well-constructed Sudoku puzzle has exactly one valid solution. The number of clues in a puzzle largely determines its difficulty, though the arrangement of clues matters as much as their quantity. The minimum number of clues for a Sudoku puzzle with a unique solution is 17, proven mathematically in 2012 by Gary McGuire and colleagues. Easy puzzles typically have 36 to 45 clues. Medium puzzles have 27 to 35. Hard puzzles have 22 to 26. Expert-level puzzles may have as few as 17 to 21 clues. However, a puzzle with 25 clues can be easier than one with 22 clues depending on which cells are filled and what solving techniques are required. Naked singles are the most basic solving technique. A naked single occurs when a cell has only one possible value because all other digits (1 through 9) already appear in that cell's row, column, or box. Scan each empty cell and note which digits are already present in its row, column, and box. If eight of the nine digits are accounted for, the remaining digit goes in that cell. Easy puzzles can be solved entirely using naked singles. Hidden singles are the next technique. A hidden single occurs when a digit can only go in one cell within a row, column, or box, even though that cell might have multiple candidates. For example, if within box 5, the digit 7 can only be placed in one specific cell (all other empty cells in the box see a 7 in their row or column), then 7 goes in that cell. Scanning for hidden singles across all rows, columns, and boxes is the primary technique for solving easy and medium puzzles. Pencil marks (also called candidates or notes) are small numbers written in cells to track which digits are still possible for that cell. In browser Sudoku, there is usually a notes mode activated by toggling a button or pressing a key. Maintaining accurate pencil marks is essential for harder puzzles. Update pencil marks after every digit placement by removing the placed digit from all cells in the same row, column, and box. Clean pencil marks make advanced techniques visible. Naked pairs occur when two cells in the same row, column, or box have exactly the same two candidates and no others. For example, if two cells in row 3 both have candidates {4, 7} and only those two, then 4 and 7 must go in those two cells (in some order). This means you can eliminate 4 and 7 from all other cells in that row. Naked triples and naked quads extend this logic to three or four cells with three or four shared candidates. The cells do not need to contain all three (or four) candidates individually, as long as the union of their candidate sets has exactly three (or four) digits. Hidden pairs work inversely. If two digits appear as candidates in only two cells within a row, column, or box, those two cells must contain those two digits. All other candidates can be removed from those two cells. Hidden triples and hidden quads follow the same pattern. Finding hidden subsets requires careful scanning of candidate distributions, which is why accurate pencil marks are critical. Pointing pairs (also called locked candidates type 1) occur when a candidate within a box is confined to a single row or column. Since the digit must appear in that box and can only be in that row (or column), it cannot appear in that row (or column) outside the box. You can eliminate that candidate from cells in the same row or column that are outside the box. The reverse case, locked candidates type 2 (claiming), occurs when a candidate within a row or column is confined to a single box, allowing elimination within that box outside the row or column. X-Wing is a fish-based technique applicable to rows and columns. If a candidate appears in exactly two cells in each of two rows, and those cells share the same two columns, the candidate can be eliminated from all other cells in those two columns. The pattern forms an X shape when you connect the four cells diagonally. Swordfish extends this to three rows and three columns. Jellyfish extends to four. These techniques eliminate candidates that would otherwise remain stubbornly persistent. XY-Wing (also called Y-Wing) is a chain-based technique involving three cells. A pivot cell with two candidates sees (shares a row, column, or box with) two wing cells that each share one candidate with the pivot. The wing cells share a candidate with each other that is not in the pivot. Any cell that sees both wing cells can have that shared candidate eliminated. XY-Wings solve many medium-hard puzzles that resist simpler techniques. Coloring (also called simple coloring or singles chains) applies to a single candidate across the grid. When a candidate appears in exactly two cells in a unit (row, column, or box), those two cells form a conjugate pair: if one is true, the other is false. By chaining conjugate pairs, you assign alternating colors (true/false) to cells. If two cells with the same color see each other, that color is false. If a cell outside the chain sees cells of both colors, the candidate can be eliminated from that cell. Forcing chains and forcing nets are advanced techniques that assume a value in one cell and trace the implications. If assuming a cell contains digit X leads to a contradiction (a cell with no candidates or a unit with no place for a digit), then the cell does not contain X. If both possible values for a cell lead to the same conclusion elsewhere (for example, both paths eliminate digit Y from cell Z), then that conclusion is valid regardless of which assumption is correct. These techniques can solve almost any Sudoku but are mentally taxing. Backtracking is the brute-force approach where you guess a value for an empty cell, continue solving, and backtrack (undo the guess) if a contradiction is reached. While guaranteed to find the solution, backtracking is not a logical solving technique and is considered a last resort by purists. Browser Sudoku solvers use backtracking as a fallback when logic techniques are insufficient. For human players, resorting to guessing usually indicates a missed technique rather than a genuinely unsolvable-without-guessing position. Browser Sudoku implementations provide features that paper puzzles cannot. Automatic candidate tracking updates pencil marks in real time as you place digits. Error highlighting marks cells where your placed digit conflicts with the rules. A hint system can reveal the next logical step, sometimes specifying which technique applies. Undo and redo let you experiment without consequences. Timer display tracks solving time for competitive comparison. These features make browser Sudoku an excellent learning tool because they reduce bookkeeping overhead and let you focus on pattern recognition. Keyboard controls in browser Sudoku typically work as follows: click a cell to select it, then type a digit (1 through 9) to place it. Delete or Backspace clears a cell. Arrow keys move the selection between cells. A notes toggle key (often N or a button click) switches between placing digits and entering pencil marks. Some implementations support entering pencil marks by holding Shift while typing a digit. Learning the keyboard shortcuts avoids constant mouse switching and significantly speeds up solving. Difficulty settings in browser Sudoku affect both the number of clues and which solving techniques are required. Easy mode generates puzzles solvable with naked and hidden singles only. Medium mode introduces naked pairs, hidden pairs, and locked candidates. Hard mode requires X-Wings, XY-Wings, and other advanced techniques. Expert mode may require chains and forcing logic. Understanding which difficulty levels require which techniques helps you target your learning. If you can solve medium puzzles comfortably, study naked pairs and pointing pairs to prepare for hard mode. Solving speed improves with systematic scanning. Start by scanning for naked singles in cells with the most filled neighbors. Then scan each row, column, and box for hidden singles. Work through the entire grid before moving to pair-based techniques. After placing each digit, re-scan the affected row, column, and box for new singles created by the placement. This cascading approach clears easy cells first and simplifies the remaining puzzle before advanced techniques are needed. A common beginner mistake is fixating on a single region rather than scanning the entire grid. Sudoku is a global constraint puzzle. Information from row 1 affects row 9 through shared columns and boxes. After placing a digit, look not just at the immediate row and column but also at the 3x3 boxes that intersect them. Another mistake is placing a digit without full verification, leading to errors that propagate and eventually create contradictions many cells later. Always verify that your placement does not conflict with any row, column, or box constraint. For advanced players aiming to solve hard puzzles quickly, the key skills are fast pattern recognition and efficient scanning order. Expert solvers often spot naked pairs and pointing pairs as part of their initial scan rather than treating them as separate passes. They maintain a mental model of candidate distributions across the grid and update it incrementally with each placement. Training this mental model requires deliberate practice: solve puzzles at a difficulty where you need to stretch but do not get stuck for long. Gradually increase difficulty as each level becomes comfortable. The mathematics behind Sudoku are rich. There are 6,670,903,752,021,072,936,960 valid completed Sudoku grids (before accounting for symmetries). After removing symmetrical equivalents (rotations, reflections, relabeling), there are 5,472,730,538 essentially different grids. The search space is vast but the constraint propagation from each placed digit narrows possibilities rapidly. This is why logical techniques work: each placement triggers a chain of eliminations that progressively simplifies the puzzle. Variant Sudoku types add extra constraints beyond the standard rules. Diagonal Sudoku requires each main diagonal to also contain all digits 1 through 9. Killer Sudoku replaces some givens with cages that specify the sum of their cells. Hyper Sudoku adds four extra overlapping boxes. Samurai Sudoku connects five overlapping standard grids. These variants are available in some browser implementations and provide fresh challenges once standard Sudoku becomes too routine.
Frequently asked questions
How do you play Sudoku?
Fill empty cells with numbers 1-9 so that each row, column and 3x3 box contains each digit exactly once.
What difficulty levels are available?
Easy, Medium, Hard and Expert - each with different numbers of pre-filled cells.
