The following algorithm for simplifying (and very often completely solving) Sudoku puzzles:
- Label each cell with the set of all possible values it could take.
- Pick a row/column/block and for a value of $K\in[1, 9)$, look for "$K$-partnerships" -- $K$-tuples of cells that satisfy "the union of labels of each cell in the tuple has cardinality $K$". Call the "union of labels of each cell in a partnership" the "banned set" of the partnership.
- For each such partnership, for all cells in that row/column/block not in the partnership remove any element in its label that are in the banned set of the partnership.
- Repeat Steps 2-3 for all values of $K$ and all rows, columns and blocks.
(i.e. "if you have three cells labeled as (4, 5), (4, 7), (4, 5, 7), no other cell in that row can be 4, 5 or 7")
... has always seemed obvious to me, but I'm now informed from some sources that it has a name called "Crook's algorithm":
The latter (by Crook) attributes the algorithm to texts written in 2005 and 2006. Are these really the earliest references? I'm pretty sure this must have been well-known for decades, but I'm not sure what to search for to find older references.