Comments  Talk
... by: Jon
Great explanation of the YWing. Even a novice dummy like me could grasp it. But,,,, possibly by accident,,,, when I printed it,,,,,, from the start,,,, I only needed one ywing to solve it,,, not 5... Once I went through all the "easier" steps,, I got to the ywing you show in Example 1 and went on to solve it with no other ywings... Did I get lucky and make a mistake along the way??
Andrew Stuart writes: I may have to replace that example, the solve only finds two now. I think that is due to changes in how the solver has evolved over time. And there are many minor variations on the solving path you can take, so yes, your solution might only get the one, depending on what you did and how much intuition you used.
... by: ralph maier
@ DANO As for your ex if you think in terms ABC it is obvious that the 6 will be the C cell not 9 so you can eliminate the 6S that see the 2 cells containing the 6s
... by: dano
I came across a pattern that is similar to what you list. The alignment of the pattern was
68  89 aligned in a row (h1  h7) 89  69 aligned in the same box (h7  I8)
If this is a ywing then the complementary pair are the 9's. Is this a valid y wing and if so can you eliminate all the other 9's from the box that contains the 8969 complementary pair?
... by: S. Lee
While testing my own solving algorithm with your fascinating 5fold Ywing example, I was surprised since my solver just required 2fold exploitation of Ywing strategy as follows:
Step #23 : YWing (< This coincides with your first Ywing step) {3,8}[A2] hinges {4,8}[B3] and {3,4}[J2] > 4 taken from H3
Step #24 : YWing {3,8}[H3] hinges {4,8}[H7] and {3,4}[J2] > 4 taken from J7 > 4 taken from J8
This is the only step that the puzzle required except for Naked Single, Hidden Single and Intersection Lock (=Pointing Pair + Box/Line Reduction).
It is an interesting phenomenon for me that the total number of advanced strategies is largely affected by the way how we realize the strategy into algorithm.
Andrew Stuart writes: You're correct, a different search order will find different instances of the same strategy and potentially a more optimal solve path. Currently the solver only returns the first instance it finds and it's been a big ambition of mine to allow the user to dismiss one and use the next but it would greatly complicate the UI. What we're both after is a fully branching solver that explores all eliminations. That's not to hard offline with lots of memory and time and something I want to explore as well
... by: Mike Kerstetter
I understand the Ywing concept thanks to your excellent explanation. My problem is seeing/finding them in the puzzle. The don't "stand out" for me. Are there any insights you can offer that might help me recognize that a Ywing might be lurking around and how to track it down?
... by: SpearheadJams
I am impressed by the work that you have done on this site. Much respect to you and your team. At the end of the day perfection is simple/elegant...
... by: Dino Hsu
Hi Andrew and all,
There's a small mistake about Ywing in the logic of proof:
I'd like to use the YWing Fig. 1 to explain this. I will use coordinates for the cells: Cell B2 with AB (bivalue), the pivot, which connects (sees) B5 and E2 Cell B5 with BC (bivalue) Cell E2 with AC (bivalue) Cell E5, the target cell to eliminate C, if any, which "sees" both B5 and E2
The definition of "see" is "two cells within the same element (row, column, box)" (the two cells see each other)
The statement "So whatever happens, C is certain in one of those two cells marked C.", which implies C in one of the two cells, actually C can also be in both cells.
Note that: the two B's in cells B2 & B5 are not a "locked pair", in other words, there could be other B's in row B. Similarly, the two A's in cells B2 & E2 are not a "locked pair" either, there could be other A's in column 2. As a result, (B5, E2) could be (C, nonC), (nonC), or (C, C), and in all scenarios, C should be eliminated from cell E5.
I find this mistake (saying the above A, B should be "locked pairs") in the book "Extreme Sudoku for Dummies" by Andrew Heron & Andrew Stuart, so I check here, I hope this helps the discussion to go clear.
Thanks for your attention.
Andrew Stuart writes: It is true that there may be other As, Bs and Cs in any of the rows, columns and boxes to which the marked A, B and C belong. But that is not relevant to the argument  hence the first basic diagram does not need to include them. The reason we don't care about other As or Bs elsewhere is that we are only turning a candidate ON (in B2), ie an argument based on "if a cell contains A then ALL other cells it can see must have A removed". We apply this twice to the pivot cell containing A and B. If B2 contains A then E2 does not contain A  and being a bivalue cell, it will be C If B2 contains B then B5 does not contain B  and being a bivalue cell, it will be C The YWing strategy tells us nothing about the ultimate solution of B2, B5 or E2 (it is not designed to)  and yes it is possible for C to be in both B5 and E2  which just goes to reinforce the idea that E5 can't be C!
... by: Hans
Hallo Andrew,
Thanks for excellent explaining  although I got an other question.
ywing explanations, figure 5, left side: between green marked cells 18 and 15 there is the cell 12578 which contains also an 8. Why is this 8 not deleted?
Andrew Stuart writes: Because that cell can't be "seen" by all the green ringed cells., only by two of them.
... by: senselocke
Thank you so much for the writeup, and the site as a whole.
Doing the stepbystep solving, with explicit reasons and links to the techniques, is exactly what I needed to be a better puzzler. Thank you so much!
... by: nihal
really good example. fantastic site.
... by: Helen
Am I correct in assuming that finding a ywing does not mean that the three cells forming the ywing necessarily have to have those three numbers in the solution. It is only an eliminating strategy/
... by: Reggie
With the techniques in your "Logic of Sudoku" book, I am only able to solve up to level 5 in Dr. Arto Inkala AI Escargot book. Level 6 to 10 make me feel like I know nothing about sudoku
Do you have another more advanced book? Where in the world can I learn strategies that will let me crack those Arto Inkala puzzles?
... by: Vidyasagar
I have not seen such lucid explanation of XY wing as you have done. The reasoing given by you makes one understand this difficult concept. thanks
... by: Ed Wieder
The YWing explaination is very good. It can be improved on by being consistent in numbering examples and figures. It might also be mentioned that the YWing can only be used when one of the canidates is not in the same 3X3 box where the other two are located.
Andrew Stuart writes: Good point.
... by: Jody
The image of the pincer really brought the Ywing concept into focus.
... by: William Balzar
Just learned the "YWing" from your site.... WOW how elegant!!! I am like blown away. I will soon order that book. The best part of all of this is that there is still more to learn!!!! Like in that "Wayne's World" Movie: I am not worthy!!!
Bill (NOT over the hill and just 5 months from 65)
THANKS
... by: John
Nice work! I now can understand the Ywing concept. Thanks for taking the time to teach those of us with lesser skills.
... by: John Myfrianthousis
Brilliant! I am a mediumadvanced player who often falls after a specific point. I believe now = especially with ywing one I will recognize this formation
... by: ChandaMija
I call this a Crooked LWing. But I now get this. Thank you!
... by: Malikov
Easy to understand concept.

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