## X-Wing Confusion

Advanced methods and approaches for solving Sudoku puzzles

### X-Wing Confusion

Using the Simple Sudoku (SS) program I tried solving the following puzzle:

--4 32- 9--
9-- --- -2-
-17 -49 6--

--- --- 51-
--- 968 ---
-42 --- ---

--1 59- 34-
-8- --- --9
--9 -84 1--

I reached the following stage where the SS program (hint button) shows an X-Wing pattern exists enabling a candidate to be eliminated from cell r6c5. Cells r4c3, r4c5 and r6c1 have been highlighted, presumably to show where the X-Wing is but which I cannot relate to the required X-Wing pattern for two rows containing two cells (and only two cells) with the specific candidate in each row and these candidates must share the same two columns forming a rectangular X-Wing:

[5][6][4] [3][2][17] [9][8][17]
[9][3][8] [167][157][1567] [47][2][147]
[2][1][7] [8][4][9] [6][35][35]

[8][9][36] [4][37][2] [5][1][367]
[1][57][35] [9][6][8] [24][37][24]
[67][4][2] [17][1357][1357] [8][9][367]

[67][2][1] [5][9][67] [3][4][8]
[4][8][56] [1267][137][1367] [27][567][9]
[3][57][9] [267][8][4] [1][567][257]

I would appreciate help as to which are the four "corner" cells which form this X-Wing pattern assuming there is such a pattern reached in this puzzle.

Bonsai Cec
Cec

Posts: 1039
Joined: 16 June 2005

Can't see the one at the co-ordinates you gave. But you've got an x-wing with the number 5 with corners r2c5, r2c6, r6c5, r6c6, allowing you to eliminate 5 from r2c9.

There's also a "generalised" xwing with 6s, corners r4c3, r4c9, r6c1 and r6c9, and a swordfish with 2s. These may not be required for solving the puzzle, I haven't run it through to the end yet. Also a naked single 2 in r1c5.

[Edit: on further inspections, none of these xwings or swordfish are in fact necessary. They can be solved instead by using locked candidates (and the use of the naked 2 in the top row). After that, my computer can't find any more xwings, so I can't shed any light on what your solver was getting at!]

I use a different program so I don't know if you have the option, but to find things like x-wing, I find it very helpful to run through highlighting all squares with a certain candidate - eg all the squares that can still be 1. If you go through all the numbers then you should find any cycles of that sort, though I have to say that even so I frequently miss things.

Hope that helps.

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

Aha! Sorry, I've got it now. It's not a simple x-wing that you've got, but an xy wing. If you consider r6c1, this can either be 6 or 7. If this is a 7, then 7 is ruled out from the squares in r6 c4,5,6. If this is a 6, we follow the chain to get 3 in r4c3 and 7 in r4c5. Likewise, the candidate 7 is ruled out from the same squares in row 6. Either way, you can cancel 7 from those squares.

I'm sure I'm pretty crap at explaining, so check out someone a bit more articulate than me if you haven't come across this before, eg:

http://www.simes.clara.co.uk/programs/sudokutechnique11.htm

which has some helpful diagrams as well and will give you the more general explanation for the specific case that you have.

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

### X-Wing Confusion

ChrisT wrote:Aha! Sorry, I've got it now. It's not a simple x-wing that you've got, but an xy wing.

Thanks for your prompt response Chris in identifying this as an XY-Wing pattern as did also - as I now humbly realize - the author of this SS puzzle solver. I looked (and kept looking) trying to see where I was wrong because Angusj never seems to make mistakes. How I misread the hint as X-Wing pattern and not the correctly displayed "XY-Wing " pattern I don't know.

Your explanations were easy to follow Chris and again thanks for your help.

Bonsai Cec
Cec

Posts: 1039
Joined: 16 June 2005

### Re: X-Wing Confusion

Ahh, I thought that puzzle looked familiar

http://forum.enjoysudoku.com/viewtopic.php?p=12148#p12148
angusj

Posts: 306
Joined: 12 June 2005

Wow! Your puzzles are like your children - you can recognise them in a crowd!
emm

Posts: 987
Joined: 02 July 2005