Thanks Andrew for starting this thread.
Generalised X-Wing Here is another example that comes from vanilla sudoku, but this time works because of an extra constaint, the diagonals (1-9 cannot repeat on the diagonals) from a sudoku X. It works the same way as normal X-Wing, but involves one diagonal. This comes from my walk-through for Cage-Pairs 6 Overlap X
hereNote: the 9s are highlighted in blue.
Quote:
17. Generalized X-wing on 9 in n9 and D/ -> 9 must be in r29c8, locked for c8; and in r8c29, locked for r8
ie, 9 is only in two places in n9 and only two places in D/ and each of these sees one 9 in nonet 9 or diagonal / -> 9 locked for all common peers.
Afmob's walk-through for A130
here (step 4a) introduced me to the term "generalised X-Wing" for this move involving the diagonal.
Some thoughts on Andrew's Grouped X-Wing exampleAndrew post gives the really nice example of a killer version of X-Wing for A188V2. He calls it "Grouped X-Wing". Just to note that Afmob calls it "Caged X-Wing" in his walk-through
here. I quite like Afmob's usage and will use it when two cages make the move work. I'll use "Grouped X-wing" for situations that lock a candidate(s) in two rows or columns using more than just two cages.
Another observation is that Caged X-Wing are only needed to make eliminations when the two cages require the same digit
and share two rows or columns
and both cross a nonet boundary. If they don't cross a nonet boundary then the simpler way is using locked candidates for 3 different nonets. Don't worry if that doesn't make much sense. It's just By The Way (BTW) really.
BTW2.
SudokuSolver finds "X-Wing", "Generalized X-Wing" and "Caged X-wing" in the "X-cycle simple" routine.
BTW3. Caged X-Wing is a type of killer sub-set. Larger killer subsets involving more than two cages in 2 rows or columns are possible. They are really fun to find.
Cheers
Ed