There are other techniques which involve logic, not a pattern: Loops, chains, and coloring. These are based on the notions of "Strong Links" and "Weak Links". ("Chaining Techniques")

1. Strong Link: If only two cells in the same house (row, column, or box) contain a particular candidate, these cells are a (conjugate) strong link. In the solution, one of the cells will be that candidate.

2. Weak Link: If any two cells in the same house contain a a candidate, they are a weak link. In the solution, one or both cells will not be that candidate.

The simplest example of the use of strong links is perhaps an X-wing, which is two strong links that "line up" on both ends.

Weak links are useful only in conjunction with strong links. The simplest examples are perhaps the skyscraper and the turbot fish.

Let me propose that we can overlay the two classes of techniques, to make "new" techniques. If we are to do so, we need to expand our definitions of "links".

To start:

3. (XY-wing): One (not both) of two cells not in the same house will be a particular candidate in the solution.

4. (W-wing): One (or both) of two cells not in the same house will be a particular candidate in the solution.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2008

5. (Diagonal UR): Two cells are not in the same house. One is <X>, and/or the other is <Y>.

- Code: Select all
`*-------------------------*`

| . . . | . . . | . . . |

| . . . |12 . 125| . . . |

| . . . | . . . | . . . |

|-------+---------+-------|

| . . . | . . . | . . . |

| . . . | . . . | . . . |

| . . . | . . . | . . . |

|-------+---------+-------|

| . . . | . . . | . . . |

| . . . |126 . 12 | . . . |

| . . . | . . . | . . . |

*-------------------------*

(Thanks to daj and Ruud.)

My question is, how do we take the results of one deduction (a "link" across two cells not in the same house) and use it in another (chaining) deduction?

I made an attempt at this in my post, "W-wing meets coloring".

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2028

Best wishes,

Keith

(edited for formatting)