## How does X-Wing and Swordfish work?

Advanced methods and approaches for solving Sudoku puzzles

### How does X-Wing and Swordfish work?

Hi. I just started playing Sudoku, and I keep hearing about these techniques, and I read about them somewhere, but I can't seem to understand them, or how to use them, at all! If someone could explain it in an easy way I would really appreciate it!

Thanks.
ofezo

Posts: 1
Joined: 17 July 2005

Here and here are my attempts at explaining them.
Last edited by simes on Sun Dec 11, 2011 10:16 am, edited 1 time in total.
simes

Posts: 324
Joined: 11 March 2005
Location: UK

chabo

Posts: 5
Joined: 23 July 2005

Your dissertation about generalized x-wing is fatally flawed, for a simple reason:
it is true that you can have a x-wing pattern involving boxes, but it's useless. It's useless because in all cases when such a pattern exists, it can simply be solved with the "single unit candidate" rules.

Let's take your first example, "2 boxes with only 2 candidates for a value (marked in green), these candidates lie also on 2 common rows".
The red cells can be excluded simply because in the second row the number can only be in the third box.
Nick70

Posts: 156
Joined: 16 June 2005

Glad to learn that the X-Wing can be applied to boxes as well as rows and columns. Although the elimination of candidates can be concluded by more trival logic, the generalizion seems reasonable. The idea is definitely not fatally flawed. Take it easy, Nick.
George

Posts: 20
Joined: 20 July 2005

George wrote:Glad to learn that the X-Wing can be applied to boxes as well as rows and columns.

Did you need someone to tell you? You invented an advanced technique like the open chains of sudo and didn't notice it?

You see, the idea of a generalized x-wing is not new. It has already been considered, and dismissed.

IJ wrote:Note - I believe Rubylips comment about generalising X-wing to boxes is a red herring because it would always be solved by rule 1 anyway.

Note that the sentence before that one is copied & pasted in the page linked above, in section 6. Swordfish.
Nick70

Posts: 156
Joined: 16 June 2005

Nick70 wrote:Did you need someone to tell you? You invented an advanced technique like the open chains of sudo and didn't notice it?

Thanks Nick. I thought you didn't read the open chain technique at all. Firstly, I didn't invent the open chain, but rather built on what was there before. In fact, the generalised x-wing involving boxes is just an open chain with a conjugate link and 2 like links. The elimination process is the same.

However, what I was trying to say was that although the underlying logic is trivial and the method may be of little practical use, your cannot rule out these are subsets of the generalized x-wing. The words "dismiss" are "red herring" are generally used to describe things that don't exist or shouldn't exist.

May I say that when the X-wing is applied to box/row or box/column, it reduces to a simple case which can be solved by Rule 1, whatever what Rule 1 is.

Cheers
George
George

Posts: 20
Joined: 20 July 2005