The New Sudoku Players' Forum

[EkMetz53]

Friends,
I did a search on XY-Wings, but the results overwhelmed me. I have yet to find an explanation of XY-Wings that can get through my dense head. I can often find three cells that contain pairs and that contain exactly three candidates, such as 1,7; 1,8; 7,8. But I have no idea which of these is the "stem" and which are the "branches." (Which I have also seen termed "pincers." I've been to a dozen websites that describe these wings, but I can never use the technique in my solving. I mostly use a program called "Simple Sudoku," and I can use all the techniques described up to that point, but I just can't seem to understand xy-wings. I'd greatly appreciate any help.
Ed

[daj95376]

Here's an explanation based on how to find an XY-Wing.

Bivalue cell: A cell with exactly two candidates in it.

Find two bivalue cells that do not see each other and have one candidate value in common; e.g., the cells <13> and <23> below have only the candidate <3> in common. These cells are called the pincer cells.

Now, look in all of the (*) cells that see both of the original cells. If you find a bivalue cell that contains the non-common candidates from the first two cells, then you have an XY-Xing; e.g., the cell with <12> below. This cell is called the pivot/vertex cell.

At this point, you can eliminate the common candidate from the remaining (*) cells.

Code: Select all

 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  . 12* .  |  .  .  .  |  .  . 13  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  . 23  .  |  .  .  .  |  .  . -3* |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


Code: Select all

 +-----------------------------------+
 |  .  .  .  |  .  .  .  | -3* .  .  |
 |  .  .  .  |  .  .  .  | -3* . 13  |
 |  .  .  .  |  .  .  .  | -3* .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  . -3* |
 |  .  .  .  |  .  .  .  | 23  . -3* |
 |  .  .  .  |  .  .  .  |  .  . 12* |
 +-----------------------------------+


Once you learn this approach, you can easily alter the second grid to test for an XYZ-Wing at the same time.

Code: Select all

 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  . 13  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  . -3* |
 |  .  .  .  |  .  .  .  | 23  . -3* |
 |  .  .  .  |  .  .  .  |  .  . 123*|
 +-----------------------------------+


[EkMetz53]

Thanks very much, daj95376, for your excellent reply. I've already had the opportunity to put it to use. I really appreciate it.
Ed