How To Solve Sudoku
Introduction
There are many strategies employed to solve Sudoku puzzles ranging from simple (Naked Candidates) to complex chains (X-Wing, graph colouring etc). A few of the more common techniques are introduced below.
Naked Candidates
The search for naked candidates is usually the first strategy used to solve a Sudoku. Easier puzzles tend to have more naked candidates than harder puzzles.
The simplest example of this is the naked single. When all candidate numbers but one exist in the same row, column and 3x3 box; the remaining digit is the only choice. I.e. only one possible number exists for a given cell.
Naked pairs follow similar logic. A naked pair is a set of two candidate digits in two cells that are common to at least one row/column/box. This means that you can remove the candidate pair from the other cells in their shared row/column/box.
Naked triplets and quads are an extension to this technique, although keeping track of candidates can be difficult.
Hidden Candidates
A hidden single exists when there is only one cell left in a row/column/box that allows a certain digit.
If two cells in a group contain a pair of candidates (hidden amongst other candidates) that are not found in any other cells in that group, then other candidates in those two cells can be excluded safely.
Intersections
If any one number occurs twice or three times in just one unit (any row, column or box) then we can remove that number from the intersection of another unit.
X-Wing
This strategy is looking at single numbers in rows and columns. When there are only two possible cells for a value in each of two different rows, and these candidates lie also in the same columns, then all other candidates for this value in the columns can be eliminated.