It also occurs to me that this method is very much analogous to Y-wing and XYZ-wing. In any configuration with zero, one, two, or six links between pairs of cells, we get the exact same inference as in WXYZ-wing, and possibly more, using simpler methods. These configurations are all possible logical arrangements with three, four, or five links between pairs of cells. The "diamond": links are AB, BC, CD, DA, and AC. No links between any other pairs of cells.
The "augmented triangle": links are AB, BC, CA, and AD. The "loop": links are AB, BC, CD, and DA. So I am thinking the only configurations that are not trivial (that is, where we can't get the same inference by different methods) are shown below. It could even apply to four completely independent cells (that is, no cell linked to any other cell), but it would be somewhat trvial in this case, because at least one cell would have only the unrestricted value, and we could get the same inference using simpler methods. The definition does not specify how the cells are linked to each other. I've spent a fair amount of time thinking about this one. I'll think now about how these are special cases of ALS. I mention this, because some web sites I see seem to assume that the WXYZ-wing has a group of three cells that share a unit, and this is not the case in the chain or the loop. So the chain, the loop, the augmented triangle, and the diamond are all relevant.
Xyz wing sudoku strategy software#
In any event, I found all four of these possibilities occur and result in eliminations, and disabling any one of them in my software results in some puzzles not fully solved. So the software I wrote doesn't search for this one, it only searches for the chain, the loop, the augmented triangle, and the diamond. Referencing my earlier post, the "star" configuration may exist, but it is either degenerate (any eliminations can be found by the basic strategies listed above, the Y-wing, and the XYZ-wing), or there are no eliminations at all (in the non-degenerate case, it is impossible for a target cell to be linked to all instances of the common digit).
In my database of 244 "advanced" puzzles (those which require something more than naked/hidden singles/pairs/triples/quads, pointing pairs/triples, or box/line reduction), the addition of the various wing strategies gets me 13 fully solved, and 231 only partially solved. Right angles give you a lot of information regarding the empty columns and rows in the cell they’re in, which can help you cancel out incorrect candidates in the adjacent cells.More thinking about this one - it's been a while.
This pattern can help you isolate rows and columns to solve entire rows or columns of the puzzle. Skyscrapers (two rows or columns of a given candidate that are unequal in length).Revisit these regularly to make sure you don’t provide a false solution. Corner patterns help eliminate a ton of potential candidates in the rows and columns connected to it. Corners (a collection of 4 solved squares in any of the 4 corners).X Research source A few common patterns include: There are a bunch of different patterns out there, but if you can spot one, they’ll typically help you solve some element of the puzzle that you’re struggling with. Patterns refer to configurations of solved squares that help players regularly solve a sequence of candidates. There are a handful of patterns most players look for at this point.
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