Sudoku Solving Strategies — From Beginner to Expert
Every Sudoku solving technique Logic Wiz teaches — naked singles, hidden pairs, X-wings, forcing chains, and 40+ more. Step-by-step examples and tips.
beginner
- Hidden Single When a digit appears as the only candidate in one cell within a Region, it’s called a Hidden Single. This digit must be placed in that cell.
- Naked Single When a cell has only one candidate it is called a Naked Single. The digit must be placed in that cell.
- Hidden Pair When two cells in a Region contain the same two digits, and those digits don’t appear in any other cell in the Region, this is called a Hidden Pair. The two cells must contain only those digits, and any other candidates in these cells can be eliminated.
- Naked Pair Two cells that see each other and contain only two possible digits are called Naked Pair. These digits can be eliminated from other cells that see both of these cells.
medium
- Hidden Quad When four cells in a Region contain the same four digits (or a subset of them), and those digits don’t appear in any other cell in the Region, this is called a Hidden Quad. The four cells must contain only those digits, and any other candidates in these cells can be eliminated.
- Hidden Triple When three cells in a Region contain the same three digits (or a subset of them), and those digits don’t appear in any other cell in the Region, this is called a Hidden Triple. The three cells must contain only those digits, and any other candidates in these cells can be eliminated.
- Locked Set When a group of cells contains the same digit, and one of them must be that digit, it’s called Locked Set. The digit can be eliminated from any cell that ‘sees’ all the Locked Set cells.
- Magic Triple Magic Triple focuses on three cells that see each other, with three candidates. One of the candidates(X) can only go in two of these cells. X can be eliminated from any other cells that see both of these cells.
- Naked Quad Four cells that see each other and have only four digits are called Naked Quad. These digits can be eliminated from cells that see all the four cells.
- Naked Triple Three cells that see each other and have only three digits are called Naked Triple. These digits can be eliminated from cells that see all the three cells.
- Candidate Restrictions Candidate Restrictions happen when the candidates of a cell limit the possible candidates in other cell(s). For example, in a Non-consecutive puzzle, if a cell’s candidates are only 1 and 3, the cells directly above, below, left, or right cannot contain the digit 2, as it would create consecutive digits.
- Violation Prevention In Violation Prevention, candidates that would violate the rules if placed in a cell are eliminated. For example, in a Non-consecutive, a candidate that would force a neighboring cell to be consecutive is removed. Similarly, in Thermo, a candidate that would break the ascending order of digits on a thermometer is eliminated.
expert
- Chain Violation Guard Chain Violation Guard is an advanced strategy where we eliminate candidates that, if chosen, would lead to a rule violation on the board. The key question to ask is, “What if?"—what would happen to the puzzle if a particular candidate were the solution for a given cell?
- Empty Rectangle The Empty Rectangle strategy is useful when a candidate within a specific box is restricted to a single row and column. It helps locate digit eliminations, regardless of its exact placement of the candidate within the box.
- Forcing Chain The Forcing Chain strategy creates a logical sequence of if-then scenarios, starting from an initial assumption about a candidate in a specific cell. By following the chain of implications, you determine whether the assumption leads to a contradiction or confirms a candidate’s placement.
- Hidden Unique Rectangle The Hidden Unique Rectangle strategy ensures the puzzle has only one solution by eliminating possibilities that would create a Deadly Rectangle, which could result in multiple solutions. When four cells in two boxes, two rows, and two columns share the same two candidates, it creates the risk of a Deadly Rectangle. To avoid this, one of these cells must have a different digit as its solution.
- Jellyfish A Jellyfish pattern occurs when a digit X is a candidate in exactly four rows, and in each row, X appears only in the same four columns. This means X must be placed in those cells, and it can be eliminated from other rows within those columns. Similarly, the strategy also works if rows and columns are swapped in this description. Jellyfish doesn’t have to include the digit in all the 16 cells of the pattern.
- Sashimi X-Wing Sashimi X-Wing is a variation of the X-Wing strategy. It arises when an X-Wing pattern is nearly complete, but one corner has a missing candidate, a shifted candidate, or an extra candidate. Despite this imperfect X-Wing formation, the pattern still enables the elimination of candidates that see all the cells of the malformed corner.
- Simple Coloring Simple Coloring, also known as Simple Chain, is a chaining strategy used on a single digit for eliminations. It’s an advanced technique involving a series of Strong Links connected to form a chain. The minimum requirement to create a chain is two Strong Links that can be connected.
- Swordfish A Swordfish pattern occurs when a digit X is a candidate in exactly three rows, and in each row, X appears only in the same three columns. This means X must be placed in those cells, and it can be eliminated from other rows within those columns. Similarly, the strategy also works if rows and columns are swapped in this description. Swordfish doesn’t have to include the digit in all the 9 cells of the pattern.
- 3D Medusa 3D Medusa is an extension of Simple Coloring, expanding it into a multi-digit chain of Strong Links. Simple Coloring involves creating a chain of Strong Links for a single digit, enabling the elimination of candidates either within or outside the chain. In 3D Medusa, we extend this concept by chaining Strong Links across multiple digits. Bi-value cells, which contain only two candidates, facilitate this chaining. Since these two candidates form a Strong Link (if one is false, the other must be true), they allow us to extend Simple Coloring into a multi-digit chain, enabling more advanced eliminations both on and off the chain.
- Two-String Kite The Two-String Kite involves two strong links on the same candidate (a), starting from different regions but converging in a shared region (row, column, or box). Digit a can be eliminated from any cell that sees both far ends of the links.
- Unique Rectangle The Unique Rectangle strategy ensures the puzzle has only one solution by eliminating candidates that would create a Deadly Rectangle, which could result in multiple solutions. When four cells in two boxes, two rows, and two columns share the same two candidates, it creates the risk of a Deadly Rectangle. To avoid this, one of these cells must have a different digit as its solution.
- W-Wing The W-Wing strategy involves two cells and a Strong Link:
- WXYZ Wing A four-cell pattern where the combined candidates of the cells contain exactly four digits. One of these digits can be eliminated from other cells that see all the cells that contain the digit.
- X-Cycles X-Cycle is a tough and powerful solving strategy that uses chaining on a single digit to eliminate candidates. It is a closed chain (Cycle) where each node in the chain is used exactly once. The cycle alternates between Strong Links and Weak Links, allowing for smart decisions that would be impossible due to the weak links. A Strong Link can count as a weak link for alternation purposes. While an X-Cycle can include only Strong Links, strategies like Simple Coloring can handle cases with fewer than two weak links.
- X-Wing The X-Wing strategy involves finding two rows (or columns) where a candidate appears in exactly two cells, and these cells align in the same columns (or rows). If this pattern is found, the candidate can be eliminated from other cells in those columns (or rows). The strategy can be extended to additional type of Regions like Diagonal.
- XY-Chain The XY-Chain strategy links cells with pairs of candidates (bivalue cells) using strong links, assigning a different color to each candidate. The chain starts and ends with the same candidate (X) but in two different colors. Any candidate X that can see both ends of the chain can be eliminated.
- XY-Wing The XY-Wing strategy involves three cells with 2 candidates each, forming a pattern where one cell (the pivot) shares a candidate with two others (the wings). If the pivot has candidates X and Y, and the wings have pairs XZ and YZ, the candidate Z can be eliminated from any cell that sees both wings.
- XYZ-Wing The XYZ-Wing strategy involves three cells where:
variant
- Arrow The Arrow variant offers a range of strategies, each with varying levels of complexity.
- Ascending Sequences In Ascending Sequences, each row must contain as many ascending digit sequences as the number indicated to its left, while each column must contain as many ascending digit sequences as the number above it. An Ascending Sequence refers to a series of cells with digits that increase from left to right in a row, or from top to bottom in a column.
- Between Lines Digits on a Between Line must be strictly between the digits in the circles at the ends of the line. This means the digits must be smaller than the larger digit in the circles and larger than the smaller digit in the circles.
- Index Lookup In Index Lookup, marked cells act as GPS pointers - the digit inside tells you exactly where to find that cell’s own row or column number. A cell may have Horizontal arrows, Vertical arrows, or both.
- Killer In the Killer Variant, we examine which digits can fit in each cage and make decisions based on various board rules and restrictions. There are multiple Killer strategies with varying levels of difficulty.
- Lockout Lines Digits along a Lockout line must be strictly outside the range of the digits in the squares at the ends of the line. The difference between the digits in the squares at the ends of the line must be at least 4.
- Quadruple Boards with the Quadruple variant have circles at some junctions of the puzzle. Each circle contains 1 to 4 digits, and these digits must appear in the four surrounding cells. Several strategies can assist when solving puzzles that include the Quadruple variant.
- Renban Lines Digits on a Renban line must be distinct consecutive digits, arranged in any order. There are multiple Renban strategies with varying degrees of difficulty.
- Running Cells In Running Cells, the number of consecutive cells in a row or column must match the number indicated to the left of the row or above the column.
- Sandwich The Sandwich variant has multiple strategies with varying degrees of difficulty.
- Skyscraper Skyscraper involves examining a column or row from the perspective of the skyscraper clue outside the grid and making eliminations and decisions based on several parameters: the clue outside the grid, digits in the row or column, candidates in cells, digit placement to achieve the Skyscraper, and the board variants.
- Slingshot In Slingshot, arrows on the board point from a cell with digit X (Origin Cell) towards the same digit X (Target Cell), where the digit in the arrow cell (Y) (Distance Cell) indicates how many cells the digit X is away from the arrow, excluding the cell with the arrow itself.
- X-Sum Boards with the X-Sum variant feature numbers positioned above and below the columns, as well as to the left and right of the rows. These numbers indicate the sum of the first X cells from that viewpoint, where X corresponds to the value of the first cell in that direction. For example, if the number above column 2 is 33, the first X cells in column 2 must sum up to 33, and the value of X is the solution for cell A2.
- Zipper Lines On a Zipper Line, the sum of the digits at equal distances from the center equals the digit in the center of the line. The Zipper Line offers various solving strategies across different difficulty levels.
No strategies match your search.