The following list of Sudoku Solving Techniques is based on a collection of tips originally published by Simon “Sadman” Armstrong. Simon has graciously granted permission to republish this collection, which I have updated and edited.
– Jim Bumgardner
These techniques are listed in roughly increasing order of complexity - from the simple and obvious, to the advanced and complex. Many published sudokus (including the Easy, Novice and Intermediate puzzles on this website), won't require any technique beyond the first two, but the more advanced techniques are useful against the harder puzzles (Challenging thru Insane).
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.
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.
These first two techniques are all the only strategies needed to solve my Easy, Novice and Intermediate puzzles (the main differences between these levels are the number of extra clues).
With the notable exception of forcing chains, the remaining techniques are all about reducing the number of candidates for cells. The aim being to reduce the candidates to such an extent that the first two techniques can be used. These additional techniques become increasingly necessary for more advanced puzzles on my site, starting with the Challenging level.
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.
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.
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.
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.
This is another method of reducing the candidates when two rows have the same candidate only in the same two columns.
Swordfish is on the same principle as X-wings, but extended to three columns or rows.
This is similar to a short forcing chain with only two links for each candidate.
This is a variation of an XY-wing.
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.
This technique is a combination of naked pairs and coloring.
XY chains allow you to make eliminations by following a chain of cells that have only two candidates each.
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. Read more »