dailysudoku.com

Cherylpc · Joined: 17 Jul 2006 Posts: 1

Please explain what an X-Wing and an XY-Wing is?

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Hi, Cheryl! Welcome to the forum.

Please try reading this explanation of the "X-Wing" pattern. Then check out this explanation of the XY-Wing.

If you still have questions after reading that stuff, please feel free to ask again. dcb

jake3988 · Joined: 22 Sep 2006 Posts: 5

Like Cheryl (but 2 months removed) am looking for an explaination. However, most explainations have horrible-looking diagrams associated (like on forums and such).

This has that advantage, but the explaination is utterly horrendous. First he says you can use it with rectangles. But, there's at least 3 other rectangles you can form with the 1's, never explaining why you can't use those.

Plus, there's no reasoning on why this method works, either. I won't just 'take his word for it', I have to have a reasoning as to why it works.

If anyone else can clearly explain it, or point me somewhere else, that would be immensely helpful.

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Hi, Jake!

I'm a little confused by your post. Are you asking abou the "X-Wing" pattern? Or about the "XY-Wing"? Since you mentioned a rectangle, I suppose you're asking about the "X-Wing".

The first thing you might try is to use the search button at the top of this page, and run a search on x-wing in this forum. That should get you 15 or 20 examples, many of them clearly explained.

Here, I'll explain it one more time.

There are two possible kinds of X-Wings: an X-Wing on rows and an X-Wing on columns.

An X-Wing on rows occurs when three conditions are satisfied for a particular candidate digit x.

-- In row a, there are only two spots where digit "x" can occur.
-- In row b, there are only two spots where digit "x" can occur.
-- The pairs of possible spots for "x" in rows a and b fall in the same two columns -- let's call them m and n.

The "X-Wing rule" now says that any other possible "x"s in columns m and n can be eliminated. The logic is simple.

Either there's an "x" at Row a Column m and an "x" at Row b Column n, or else there's an "x" at Row a Column n and an "x" at Row b Column m; no other configurations are possible.

Another way to think of it is as follows. If an "x" occurred in column m and not in row a or row b, it would be impossible to complete rows a and b.

An X-Wing on columns is exactly analagous, but now you have two columns (in each of which "x" can only fit in two spots) and the "candidate cells" in these columns lie in just two rows. You can transform an X-Wing on rows into an X-Wing on columns by turning the puzzle sideways, so these are really the same pattern, just rotated by 90 degrees. dcb

jake3988 · Joined: 22 Sep 2006 Posts: 5

Thanks for the reply.. I still don't understand the logic. Nor could I ever pick it out.

Let's say, we have something like:
(This is the exact [recreated] situation from the site refferal. Note, all the '1's are candidates for the one.)
1xx|x1x|xx1
xxx|x1x|xx1
1xx|x11|1xx
----------------
xxx|xxx|xxx
xxx|x11|1x1
xxx|x1x|xx1

Edit: Actually, according to your given definition, it would make the one specified on the website work. So I understand that.

However, on the website, it claims R3C6 is the upper-left corner of 'another' x-wing which don't NOT apply to that definition. Which makes it really confusing.

Although, I'm not the type of guy who writes every single candidate for every single box. That's just sadistically overboard. So I guess this whole thing is moot anyway.

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

The other X-wing is in columns. Columns 6 & 7 both have only two places for the 1 and those places are in rows 3 & 5. Eliminates all other 1 candidates in those two rows.

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Hi, Jake! Thanks for writing back. And thanks for the diagram. Specific examples are easier to follow than abstract explanations.

jake3988 · Joined: 22 Sep 2006 Posts: 5

thanks again. I still don't understand the logic, but I guess if I spot more examples I'll try and deduce why it actually works in my head. It'll come with practice.

That is, try and place ones in the other cells in that column and see why its impossible. I just don't see it from the example.

Marty R. · Posted: Sun Sep 24, 2006 3:50 pm Post subject:

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

jake3988,

Do you understand the concept of 'strong links' (also known as conjugate links)? It's pretty much essential to understanding X-wings.

Here is the link to an excellent post that explains the general concepts of 'strong links' and specifically explains the logic behind an X-wing:

http://www.sudoku.com/forums/viewtopic.php?t=3326

jake3988 · Joined: 22 Sep 2006 Posts: 5

kinda. If he made his post about half as long and stayed with the quasi-reallife situation instead of making it confusing as heck with green letters and code, I would likely have it really understood.

He does a good job explaining the logic though in a very simple way.

But anyway, I found a real life situation in today's puzzle (the logic is completely different, and it wouldn't really qualify as a x-wing, but basically the same logic applied.

That is, I had:

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

Here is the position to which you refer:

jake3988 · Joined: 22 Sep 2006 Posts: 5

Right. Thanks. And yes, that's pretty much the exact point in the puzzle I saw it.

Solved it completely shortly thereafter too. (This hard was immensely easier than the previous day's very hard. It was indeed much harder than the medium and easy, but the very hard I only got about 2 numbers of the whole puzzle.)