## At what point have I cheated ?

Advanced methods and approaches for solving Sudoku puzzles

### X-wings

Hello!

Maybe I'm not getting exactly what an X-wing is - my intrerpretation is that by looking at 2 rows (or columns), where the digit (i.e. 6) is missing and there are only 2 blanks left in each and these blanks are "parallel", since it has to be in either "cross" of those rows (or columns), I can then eliminate this digit from all other fields in the columns (or rows) in which they go.

In the example, the only X-wing I find is that 6 has to go in either R1C6 and R9C9 or in R1C9 and R9C6, and then I can eliminate 6 from R7C6, R8C6, R4C9 and R7C9. But by this technique, R3C5 still remains a candidate for 6 and I cannot eliminate it in favour of R1C6.

Sorry if I don't know the right terminology, I just started with Sudokus this Tuesday, but I hope you see what I mean.
Anette

Posts: 55
Joined: 09 June 2005

'blank cells' is not the correct word... as in row 1 has three blank cells...

What you really mean is that you look for a row/column where the digit has only two candidate cells.

Take a really good look at r7c9... And remember what the X-wing allows you to do... can you fill it in?
Animator

Posts: 469
Joined: 08 April 2005

Hello!

Thanks! I was staring so hard at other places that I didn't see that by eliminating the 6 from there, I had only one value left.

So, now I know what the X-wing technique is. Thanks a lot.

/Anette
Anette

Posts: 55
Joined: 09 June 2005

### Re: Pencil and paper, every time.

Togidubunus wrote:.... When I find an anchor number I put a circle round it. If the whole puzzle goes completely tits-up, I ink in the anchors and rub out the whole thing.

I know this is an old post, but this bit caught my eye. What exactly is an anchor number? Why are they important? I searched the whole forum for 'Anchor' but only this post seems to contain a reference to it.

Cheers,

Tabber.
tabber

Posts: 25
Joined: 31 May 2005

### Re: Is this "double guessing" / cheating?

Anette wrote:Is this cheating?

I have started out with the “Very Hard” sudoku from Times like this:

*43*8*25*
6********
*****1*94
9****4*7*
***6*8***
*1*2****3
82*5*****
********5
*34*9*71*

After solving according to logic so far, I ended up with the following:

*4398*25*
6**425***
2****1*94
9****4*7*
3**6*8***
41*2*9**3
82*5*****
****4***5
53489*71*

Then I could see no more “simple” logic ways to solve it, so I started looking at the 2 possibilities in Column 1 and did the following:

Option A: If R1C1 = 7, then 7 can go nowhere else in Row 1. For R1C6, the only possibility is then 6

Option B: If R1C1 = 1, then R8C1 has to be 7. Then R8C4 has to be 1. Then R3C4 has to be 7. Then R1C6 cannot be 7, and the only possibility for it is 6.

So either way, R1C6 had to be 6, and from there, I could solve the puzzle.

Is it considered cheating to set up 2 alternatives like that? I did draw some rings and squares around the pencil marks, but might as well have done it in my head since the chain wasn't that long.

/Anette

No, it isn't cheating. -- You solved the puzzle using only your brain.
No, it isn't trial and error. -- You made no trial and found no contradiction.
No, it isn't guessing. -- You *certainly* didn't guess.

You simply proved the contents of a cell by clear, reproducible, straightforward, logic.

I realize I'm responding to an older post, but we've it we've been talking about this elsewhere. It seems that this idea comes up again and again, but often gets shot down.

Certainly, if you can do it in your head, you simply have no choice but to use it -- you can't simply pretend you don't see the answer. And if you are already using pencil marks, it just a matter of degree how much information you can cram into each cell.

Animator wrote:The technique you are missing in your example-grid is an X-wing in the number 6.

I might as well say that if instead you had solved by searching and searching until you found the X-wing, you would have missed solving the grid by the Forced Chain Proof.

It seems that if one cannot put a name to the tactic they use, cannot describe its exact parameters, form and function -- they're just guessing.

See:
http://forum.enjoysudoku.com/viewtopic.php?t=692
http://forum.enjoysudoku.com/viewtopic.php?t=594
tso

Posts: 798
Joined: 22 June 2005

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