View source for Sue de Coq

The '''Sue de Coq''' [[solving technique]] uses two intersecting sets '''A''' and '''B''', where '''A''' is a set of N [[cell]]s with N [[candidate]]s in a [[line]], '''B''' is a set of N cells with N candidates in a [[box]], and the sets '''A - B''' and '''B - A''' have no common candidates. Candidates can be [[eliminate]]d from the cells in the line that are not in '''A''', and the cells in the box that are not in '''B'''.

This technique was introduced by a member using the alias ''Sue de Coq'' in the Sudoku Players' forum, who named it '''Two-Sector Disjoint Subsets''', but a remark that this was a true '''Sue de Coq''' gave the technique its present name.

This technique can be extended into '''Three-Sector Disjoint Subsets''', but this extension is very rarely seen.

== Example ==

The following image shows an example of the '''Sue de Coq''' technique:

[[image:sue de coq.png]]

Consider the intersection of row 3 and box 3. It has candidates 1,2,5,8,9. It cannot contain both 2 and 9 as this would conflict with '''r3c2'''. It cannot contain both 5 and 8 as this would conflict with '''r1c7'''. The intersection must contain 1 + (2 or 9) + (5 or 8). This allows us to eliminate candidates for digit 1 from row 3 and box 3, candidates for digit 2 and 9 from the remainder of row 3 and candidates for digits 5 and 8 from the remainder of box 3 (if there were any). These eliminations are shown in red.

Sue de Coq is both an elegant and effective technique, often causing several eliminations. Despite this, the technique is not often used.

== Note ==

'''Sue de Coq''' is a special case of '''[[Subset Counting]]'''.

== External Links ==
* [http://www.sudoku.com/forums/viewtopic.php?t=2033 Two-Sector Disjoint Subsets] (''Sudoku Players' forum'')
* [http://homepages.cwi.nl/~aeb/games/sudoku/solving12.html Subsets] (''Solving sudokus'' by ''Andries E. Brouwer'')

== See Also ==
* [[Almost Locked Set]]
* [[Subset Counting]]
* [[Aligned Pair Exclusion]]

[[Category:Solving Techniques]]