![]() ![]() This means that any cell that is seen by both r3c3 and r8c5 cannot contain the digit 5, so we eliminate 5 from r3c5. Thus, this is a Double Implication Chain and we showed that either r3c3=5 or r8c5=5. Similarly, by reversing the direction, if r8c55, then r3c3=5. Now, if r3c35, then we have r3c3=1, which implies r7c3=1 and so r8c5=5. ![]() What does this XY-chain mean? Note that both ends of the chain involves the digit 5 as a candidate. The following example shows a XY-chain resulting in an elimination. The shortest XY-Chain is an XY-Wing with only 3 cells.Ī XY-Chain is both a Double Implication Chain and a Alternating Inference Chain. 1.This may seem obvious to you, but some folks don’t do this It’s possible for adept players to solve easier sudokus with pen, but for harder puzzles it’s. I have been teaching my 4 year old grand daughter the basics of Sudoku as I believe you can not get a better tool for forward thinking.A XY-Chain is a chain of cells which each contain only 2 candidates.īecause the chain is entirely made up by bivalue cells, the link between the 2 candidates in each cell cause strong inference, which allows us to use weak inference between the cells. Thank you for posting this particular puzzle – I usually think the “tough” ones are not THAT difficult to solve but got stuck in the same place and enjoyed looking at the solution/strategy that you provided! I have been trying some of the techniques and think I’m doing really well until I get to the end of the puzzle and realize I’ve made a mistake – this is since I’ve been trying to incorporate the X-wing, Y-wing and XY-wing strategies to solve the puzzles. 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. Each pincer has one of the other numbers from the pivot. The pincers have one number in common with each other, and it is a number that appears in the pivot. If you are stuck on a particular Krazydad puzzle, drop me a note, and I’ll use this space to help you out. The XYZ-Wing strategy requires there to be three candidates in the pivot square, instead of two like in Y-Wing. This is part of a series on puzzle solving techniques. ![]()
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