The (N-1) alliance cells is given by the formula The number of combinations of the remaining (N-2) digits to fit in This idea could be extended to form any N-wing format, but the logistics are astronomical. If any of the above conditions are met then the Z-digit can be eliminated from the rogue cell. X-X-X, Y-Y-Y impossible! it means that the 4th digit '-'-'-'Īls-xz double linked rule can and does apply to some formations of I appreciate that not all strategies can be applied earlier than the appropriate stage, (eg a naked pair strategy can only be applied when there are only two candidates in each cell), but from what I’ve read the wxyz-wing strategy is applicable in this case. And it is this, I believe, which prevents this strategy being applicable. If F2 is 8 then eliminates the 8 in D1, F3, F4 and F6, (plus others). If F2 is 1 then D1 is 8, so eliminates the 8s in F3 and D4 and D6, (plus others) and If F2 is 9 then F4 and F6 become a naked pair and eliminate the 8 in F3 and D4 and D6, (plus others) If F2, as I believe, is still the hinge cell, then. Working through your example WXYZ-Wing example 4, after the 2 Y wings and the first XYZ wing, (IE before the XY cycle), the position includes the following candidates in these cells:Īccording to your website -“ StrmCkr's more general definition - WXYZ-Wings can be considered as a group of 4 cells and 4 digits, that has exactly one non-restricted common digit.†I believe in the current situation 1, 8, 9 are restricted digits. Your solver suggested an WXYZ wing so I looked up your documentation link for this strategy. I’ve been working through the Daily Telegraph’s Diabolical Soduku 4684 and needed help in the next step. Once again thanks for your website giving me the ability to check my progress on Sudokus and also to provide a hint/solution to one more step. The XYZ-wing is analogous to your original, simple version of WXYZ-wing, and the Y-wing is the additional non-trivial configuration if the definition is expanded analogously to the way WXYZ-wing was expanded. If we defined a strategy as one in which there are three cells, containing a total of three disctinct numbers between them, with one of the three numbers unrestricted, then Y-wing plus XYZ-wing cover the non-trivial cases (those that cannot be analysed using simpler methods). 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. ![]() ![]() 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. More thinking about this one - it's been a while.
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