## How to Solve Sudokus - an Index of Sudoku Solving Techniques

These are some of the techniques that can be used to solve Sudoku puzzles. They're listed in roughly increasing order of complexity - from the simple and obvious, to the advanced and complex. Many published sudokus won't require any technique beyond hidden subsets, but the more advanced techniques are often useful against the very hardest puzzles.

There are only three techniques that allow for entering a solution numbers — these are naked single, hidden single, and forcing chains. All the other techniques are about eliminating candidates, the aim being to reduce the number of candidates to such an extent that the first two techniques can be used.

The brief descriptions below link to pages with detailed explanations and example Sudokus that can be solved using each technique.

See the glossary for an explanation of the terms used in the explanations.

- Naked Single (Singleton, Sole Candidate)
It is often the case that a cell can only possibly take a single value, when the contents of the other cells in the same row, column and block are considered. More …

- Hidden Single (Unique Candidate)
If a cell is the only one in a row, column or block that can take a particular value, then it must have that value. More …

- Block and Column / Row Interactions (Pointing Pair)
Sometimes, when you examine a block, you can determine that a certain number must be in a specific row or column, even though you cannot determine exactly which cell in that row or column. More …

- Block / Block Interactions
If a number appears as candidates for two cells in two different blocks, but both cells are in the same column or row, it is possible to remove that number as a candidate for other cells in that column or row. More …

- Naked Pair, Triplet, Quad (Locked Set, Naked Subset, Disjoint Subset)
If two cells in the same row, column or block have only the same two candidates, then those candidates can be removed from other cells in that row, column or block. This technique can also be extended to cover more than two cells. More …

- Hidden Pair, Triplet, and Quad (Hidden Subset, Unique Subset)
This technique is very similar to naked subsets, but instead of affecting other cells with the same row, column or block, candidates are eliminated from the cells that hold the hidden subset. More …

- X-Wing
This is another method of reducing the candidates when two rows have the same candidate only in the same two columns. More …

- Swordfish
Swordfish is on the same principle as X-wings, but extended to three columns or rows. More …

- XY-Wing
This is similar to a short forcing chain with only two links for each candidate. This a very common pattern in the harder puzzles. More …

- XYZ-Wing
This is a variation of an XY-wing but includes an additional cell. More …

- Colouring
Colouring considers cells where a particular candidate occurs for only two cells in a unit. More …

- Remote Pairs
This technique is a combination of naked pairs and colouring. More …

- XY-Chain
XY chains allow you to make eliminations by following a chain of cells that have only two candidates each. More …

- Forcing Chains
Forcing chains is a technique that allows you to deduce with certainty the content of a cell from considering the implications resulting from the placement of each of another cell's candidates. More …

- Trial and Error
There are some that would argue trial and error is not a logical technique, and is no better than guessing. When further moves seem impossible, trial and error may be the only way forward. More …

### Less Common Techniques

- Turbot fish: This is somewhere between X-wings and swordfish, and is also related to colouring.
- Jellyfish and Squirmbag: tongue-in-cheek names for extensions of the X-wing and swordfish techniques to an even greater number of cells.
- Tabling: this is an exhaustive search using "structured trial-and-error". Only possible using a computer solver.
- Uniqueness: Assumes that the puzzle is well-formed and so has only one solution, then makes deductions along the lines of "this cell cannot be X, or else the puzzle would have multiple solutions."

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This is a wonderful program - the best I can find relating to sudoku ... Dare I say there is a bit of programming genius there. Michael Wightman, UK |

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