![]() ![]() You can follow any responses to this entry through the RSS 2.0 feed.īoth comments and pings are currently closed.Ģ Responses to “Sudoku Troubleshooter #4 – XYZ-Wing” On Thursday, November 24th, 2011 at 8:49 pm and is filed under Puzzles. For the curious, the following puzzles contain an XYZ-Wing. It’s fairly rare, and only occurs in 8 of my tough puzzles, as compared to XY-Wing, which occurs 10 times more often. ![]() From here, the rest of the puzzle solves pretty easily.Īs I said, this particular configuration, in which D3 contains XYZ, and E1 contains XZ, and A3 contains YZ, enabling us to eliminate Z from a 4th cell which is connected to all three cells, is called an XYZ-Wing. Therefore, since this covers all the possible values for D3, F3 can’t ever be 4. If D3 is 7, then A3 must be 4, and F3 can’t be 4. If D3 is 5, then E1 must be 4, and F3 can’t be 4. Take a look at cell D3, and the effect it has on cell F3. XYZ-Wing is an advanced solving technique which is closely related to the more common XY-Wing, which I’ve covered in a previous column. In the next diagram, I’ve highlighed three cells which form an XYZ-Wing. If you’d like to try it yourself, you’ll find it here: This is a tough puzzle, book 85, puzzle #1. Here’s the puzzle that Michael got stuck on. am I missing something here or do I just need to guess? My question was is this a valid way of solving puzzles for you? As you will see I have gone through this puzzle attached and I can’t see a logical way to solve it. It seems like more recently you have been posting puzzles with no “logical” solution but that requires one to guess or work it out on the scratch pad. I have been going through a bunch of them and I have a question for you. I really enjoy your puzzles and I have advanced to your tough ones now. Good morning and an early happy thanksgiving. If you are stuck on a particular Krazydad puzzle, drop me a note, and I’ll use this space to help you out. The WXYZ-Wing can be replicated as an ALS-XZ move by considering the XZ cell as an ALS and the other three cells as the other ALS, with W as a restricted common.This is part of a series on puzzle solving techniques. This is a Type 1 WXYZ-Wing (marked yellow) which leads to the elimination of 4 from the blue cell. One of the XYZ cells may appear in the same line as WZ, in which case the XYZ cell may also have W as a candidate.The WXYZ and WZ cells belong to the same line.One of the XYZ cells may appear in the same box as WZ, in which case the XYZ cell may also have W as a candidate.Each of the four cells may contain a subset of the candidates as shown, e.g.The WXYZ and WZ cells belong to the same box.The WXYZ and the two XYZ cells form an almost locked set.We can perform the same eliminations for Z on the starred cells so long: Then the ALS-XZ rule can be applied with W being the restricted common, so Z can be eliminated from the starred cells. Put another way, observe that there are two almost locked sets: (a) WXYZ, XZ and YZ and (b) WZ. If the WZ is Z, then obviously Z can also be eliminated from the starred cells.If the WZ is W, then the WXYZ (which becomes XYZ), XZ and YZ cells form a naked subset, and so Z can be eliminated from the starred cells.The idea from the extended form of the WXYZ-Wing comes from the following observation: In all possible options for the pivot cell, Z will be eliminated from the starred cells. Similar to the XYZ-Wing, the pivot has the candidates WXYZ. Seeing the extension of XYZ-Wing to WXYZ-Wing, one can further extend the technique to VWXYZ-Wing, UVWXYZ-Wing and so on. The WXYZ-Wing is an extension of the XYZ-Wing, and is sometimes called XYZW-Wing. ![]()
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