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x-wings, xy-wings

 
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mrmorrighan



Joined: 24 Jun 2006
Posts: 5
Location: Houston, Texas

PostPosted: Sun Jun 25, 2006 12:56 am    Post subject: x-wings, xy-wings Reply with quote

I've gotten good at using all the techniques up to a certain point when a few certain numbers can go in several locations. I can use hint, but never understand the reason. I'm unfamiliar with the x-wing technique.

As I've looked at the writings on x-wings, I want to see if I understand it:

The boxes have to have the same two or three possibilities, and four boxes must be lined up to create a rectangle. then if one of the numbrer options appears along the line (column or row) that connects the squares, it is eliminated, which may offer the one correct answer for that cell.

I that it? Either i don't have it right, or I just don't understand the logic yet.

Also, how is x-wing different from XY-wing. I also found a lot of posts on that, but it seems to be a different thing entirely. Can someone please clear these wing things up for me?????
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Jun 25, 2006 3:08 pm    Post subject: Reply with quote

Maggie Rose,

This grid contains an x-wing on 6's. Look at rows 2 and 7. Each row contains only two cells that can possibly be a 6. In both rows the cells that can be a 6 are in the same two columns (columns 1 & 4). This is the x-wing. Any other cells in those two columns that contain a 6 can be deleted, which in this case is r4c1 (and r8c4, as noted by Marty).

Code:
 
 *-----------------------------------------------------------*
 | 9     27    28    | 278   1     5     | 4     6     3     |
 | 267X  4     1     | 267X  27    3     | 8     9     5     |
 | 3     5     68    | 9     4     68    | 1     7     2     |
 |-------------------+-------------------+-------------------|
 | (26)  268   3     | 5     278   278   | 9     1     4     |
 | 4     1     7     | 3     6     9     | 5     2     8     |
 | 5     28    9     | 4     28    1     | 6     3     7     |
 |-------------------+-------------------+-------------------|
 | 267X  9     5     | 267X  3     4     | 27    8     1     |
 | 1     267   26    |(2678) 5     2678  | 3     4     9     |
 | 8     3     4     | 1     9     27    | 27    5     6     |
 *-----------------------------------------------------------*


An x-wing focuses only on a single digit, so it doesn't matter what other numbers share the cells. The rule for an x-wing is 1 number, 2 possibilities for that number, 2 rows and 2 columns.

An xy-wing is entirely different that an x-wing. When I find an example I'll post it, unless someone beats me to it.


Last edited by TKiel on Wed Jul 19, 2006 8:03 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Sun Jun 25, 2006 3:58 pm    Post subject: Reply with quote

Quote:
An xy-wing is entirely different that an x-wing. When I find an example I'll post it, unless someone beats me to it.


Hey Tracy, get the lead out, someone beat you to it. Laughing

Maggie, there is a load of help on the web for solving Sudokus. I learned a lot by using a search engine looking for techniques, advanced techniques, or specific techniques. A search for "sudoku xy-wing" yielded lots of hits, and I think this one explains it pretty well. If there are further questions, there are lots of helpful people here who have helped me, like Tracy, above.

http://www.brainbashers.com/sudokuxywing.asp
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun Jun 25, 2006 4:10 pm    Post subject: Reply with quote

Maggie Rose,

This puzzle contains an xy-wing. The cell with the brackets (r7c5) is referred to as the 'stem' cell. The cells with the curly brackets (r1c5 & r8c6) are referred to as the 'wing' cells. All three cells in an xy-wing must contain only 2 digits. The stem cell must share a group (either row, column or box) with each of the wing cells. In this case the stem cell shares a column with r1c5 and a box with r8c6. The stem must also share a digit with each of the wing cells. In this case the stem shares a 2 with wing r1c5 and an 8 with wing r8c6. The 'leftover' digit in each wing cell (the one not shared with the stem cell) must be the same. In this case both wing cells contain a 5.

Any cell that 'sees' (shares a group with) both of the wings cells cannot be a 5 and the 5 can be excluded from that cell. In this case both r1c6 and r9c5 (marked with a X) can have 5 excluded.

Code:
 
 *-----------------------------------------------------------*
 | 457   27    6     | 2345  {25}  2345X | 1     9     8     |
 | 59    1     29    | 258   2589  7     | 3     6     4     |
 | 49    8     3     | 14    6     149   | 2     5     7     |
 |-------------------+-------------------+-------------------|
 | 2     9     7     | 18    4     18    | 6     3     5     |
 | 3     5     4     | 9     7     6     | 8     2     1     |
 | 1     6     8     | 25    3     25    | 4     7     9     |
 |-------------------+-------------------+-------------------|
 | 78    4     5     | 2378  [28]  238   | 9     1     6     |
 | 789   27    29    | 6     1     {58}  | 57    4     3     |
 | 6     3     1     | 457   59X   459   | 57    8     2     |
 *-----------------------------------------------------------*


The logic behind it goes something like this: If, for example, r9c5 were 5 then r8c6 would have to be 8, r1c5 would have to be 2 and that would leave r7c5 (the 'stem' cell) with no possible value. So r9c5 can't be 5.
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Ian



Joined: 24 May 2006
Posts: 6
Location: Canberra Australia

PostPosted: Sun Jun 25, 2006 10:39 pm    Post subject: Reply with quote

There is another x-wing on 6 at R38, C36. With the other x-wing aleady identified the puzzle can be solved.
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mrmorrighan



Joined: 24 Jun 2006
Posts: 5
Location: Houston, Texas

PostPosted: Sun Jun 25, 2006 11:52 pm    Post subject: Reply with quote

Tracy, Your explanation was perfect! Thank you so much for your time. I now completely understand x-wings, and I'm getting the idea behind xy-wings. Now maybe I can do those really hard ones without a "hint". You're wonderful!! :)

And thanks, Marty, for the other search info. I'd done some searching, but evidently not enough.
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MartinDick



Joined: 18 Jul 2006
Posts: 3

PostPosted: Wed Jul 19, 2006 4:17 am    Post subject: x-wing Reply with quote

Tracy’s explanation to Maggie Rose is perfect for me.

Now, what confuses me, is when Ian says, “There is another x-wing on 6 at R38, C36.” In row 8 there are four possible sixes, and I thought the row had to be limited to only two possibilities.

This whole discussion is very helpful to me, and I am deeply grateful for your time, patience and expertise.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Jul 19, 2006 11:05 am    Post subject: Reply with quote

An x-wing can be either in rows, which means the rows only have two cells and the exclusions take place in the columns, which can have any number of cells with that value. Or, as in the one pointed out by Ian, they can be in columns, with the exclusions taking place in the rows, which can have any number of cells with that value.
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MartinDick



Joined: 18 Jul 2006
Posts: 3

PostPosted: Wed Jul 19, 2006 12:54 pm    Post subject: Of course Reply with quote

Of course; thank you.
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Wed Jul 19, 2006 3:47 pm    Post subject: Reply with quote

Quote:
This is the x-wing. Any other cells in those two columns that contain a 6 can be deleted, which in this case is only r4c1.


By the way, Tracy, unless there's a typo, there's also a "6" which can be deleted from r8c4 (not that it does much good). Smile
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