## Solver indicates XY Wing but doesn't follow rules?

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### Solver indicates XY Wing but doesn't follow rules?

Hi, I'm new to the forum but very keen on Sudoku. I got stuck nearing the completion of a 'hard' puzzle and used an online Sudoku solver for a hint. The hint suggests there is an XY wing as shown in the pic but gives the number 1 as the candidate value and the one to eliminate. All the rules I've read about XY wings state that the candidate value is the common value contained in the 'wing' cells - in this case the number 5. Is the solver simply wrong or am I missing something?
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XY Wing query.JPG (129.86 KiB) Viewed 423 times
RayC333

Posts: 7
Joined: 20 April 2017

### Re: Solver indicates XY Wing but doesn't follow rules?

Welcome to the Sudoku Players Forum!

D5 is the pivot cell and F4 & G5 are the wing cells (I would call them pincer cells). The common digit shared by the two wing cells is 1.

Your interpretation would have G5 as the pivot, but G5 can't "see" F4, so that would not be a valid XY-Wing.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Solver indicates XY Wing but doesn't follow rules?

458291763193...2487268435919314..68.5873..9.4264.893.7642..58393159284768796341..

Jason wrote : D5 is the pivot cell and F4 & G5 are the wing cells (I would call them pincer cells). The common digit shared by the two wing cells is 1.

Continuing on, the pincer cells F4 and G5 can't see each other, but they can both see the grey cells E5 and G4, so the 1's in them can be eliminated, so it is a valid XY Wing as indicated in the diagram.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

### Re: Solver indicates XY Wing but doesn't follow rules?

Thanks for your replies and welcome. The reason I assumed G5 was the pivot is that it can see D5 vertically and F4 diagonally. However, I don't understand how D5 can be the pivot when it can't see F4 horizontally, vertically or diagonally?
RayC333

Posts: 7
Joined: 20 April 2017

### Re: Solver indicates XY Wing but doesn't follow rules?

Maybe I have a fundamental misunderstanding of the term 'see each other'. My interpretation was that F4 and F5 can see each other because they are diagonally adjacent, whereas the flaw for me would be that the pincer suggested at F4 cannot see pivot suggested at D5 in any direction. Can it see it because it's in the same box? I've never seen that given as a rule for XY wings.
RayC333

Posts: 7
Joined: 20 April 2017

### Re: Solver indicates XY Wing but doesn't follow rules?

You need to go back to The One Rule:
Every row, every column, and each of the 3x3 blocks must contain all of the digits from 1 through 9 exactly once.

Rows, columns, and 3x3 blocks are called houses. "See" means shares a house with. That mean that diagonals don't mean anything, and sharing a 3x3 block is very important.

The one rule is assumed, rather than repeated, in all of the solving techniques.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Solver indicates XY Wing but doesn't follow rules?

Thanks JasonLion, I appreciate your help and clear explanation. The 'one rule' in itself was clear to me, but I hadn't fully understood 'houses' and their role in 'seeing' each other.
RayC333

Posts: 7
Joined: 20 April 2017

### Re: Solver indicates XY Wing but doesn't follow rules?

Hi,

JasonLion wrote:Rows, columns, and 3x3 blocks are called houses. "See" means shares a house with.

Or "see" means within "peer cells".

Well, normally there are nine rows, nine columns and nine boxes in the Sudoku puzzle. Each row, column and box contain exactly nine cells. [Also, each cell has 20 peer cells.]

Now consider your above given puzzle XY-Wing state. Rows are denoted as alphabet A to I and columns are denoted as number 1 to 9. Each cell is denoted as product of row and column, for e.g., A1 means row A and column 1.

Pivot cell D5 means row D and column 5. Pincer cell F4 means row F and column 4; and pincer cell G5 means row G and column 5. Note that pincer cell F4 shares same box as pivot cell D5 and pincer cell G5 shares same column as pivot cell D5 but both pincer cells F4 and G5 neither share same row nor same column nor same box.

Now in this case, there are cells that share box of one pincer and column of other pincer at a same time, means, that see both pincer cells at a time, i.e., [D5 also but it's pivot cell so ignore it,] E5 [and F5 but it's already solved so ignore it also] share box with pincer cell F4 and column with pincer cell G5; and G4 [, H4 and I4 but it's already solved so ignore them as well] share box with pincer cell G5 and column with pincer cell F4. therefore both pincer cells common digit must be eliminated from these cells.

To check, one of the pincer cells must contain digit 1. In each case, both E5 and G4 cells must not contain digit 1.

Hope that clarify your "see" [or peer] problem.

R. Jamil
rjamil

Posts: 300
Joined: 15 October 2014
Location: Karachi, Pakistan