The New Sudoku Players' Forum

[Kent]

from the example below, can we say that the 1's with * form an x-wing?? What is the foundation of an X-wing?? When can u call it X-wing and when it's not an X-wing?? I need some examples.Any What's a finned-swordfish??
Thanks

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1 #1 #1  |  .  .  .  |
| . -1  1  | +1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  .  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

[TKiel]

Kent,

There is an explanation of that example here www.sudoku.com/boards/viewtopic.php?t=2793, but it is not, strictly speaking, an x-wing. The grid you posted was used as an example to illustrate the 'Filet-O-Fish' (formulated by myth jellies in the link above) concept. An x-wing is two rows (or columns) each with only two cells containing the candidate and those four cells must align in the same two columns (or rows). If the hashmarked cells did not contain a 1, then the * cells would be an x-wing.

[Kent]

But according to the link u gave me, jellies described it as X-wing.Since it is not an X-wing in the puzzle noted, then wh did jellies said that the 1 with hashmardked can be excluded? I tried putting 1 at the hashedmarked and it is possible to have a 1 there.

In X-wing, does the 2 candidates have to be the only 2 candidates in the row AND column or only row OR column(either one)??? Can u illustrate some examples??

Another thing.whats's the difference between a finned swordfish and a normal swordfish?? Thanks.

[Cec]

".. What is the foundation of an X-wing?? When can u call it X-wing and when it's not an X-wing.."

It seems you have requested an explanation of an X-wing. Have you read, and if so, is there any part of the X-wing description which is explained in the angusj link which, together with other links on solving techniques, was previously suggested to you in this THREAD.?
Cec

[TKiel]

Kent,

Myth jellies said it would be an x-wing if the hashmarked cells did not contain a 1. If you have questions about the proof of the 'Filet-O-Fish' concept, maybe you should post your question on that thread.

The swordfish is explained in many threads in this forum, but basically it is three rows each with only 2 or 3 cells and those cells must align in three columns. It can also be columns aligning with rows.

If you haven't done so, read up on the links cecbevwr provided. They provide much useful information.

Tracy

(Edited to delete boneheaded answer about x-wing. My only defense is it was early in the morning, I hadn't had enough coffee, I was in a hurry, my shoes were too tight and the sun was in my eyes. Sorry for the confusion, consternation, bewilderment or urge to tell me to stop answering posts if I'm just going to screw it up.)

[ronk]

then wh did jellies said that the 1 with hashmardked can be excluded? I tried putting 1 at the hashedmarked and it is possible to have a 1 there.

Your opening post illustrates a finned x-wing. IOW it would be a x-wing ... if none of the fins were there. The finned x-wing "rule" directly leads to an elimination -- under the right circumstances -- not a placement. If the elimination is in a bivalued cell, then you would have a placement as a consequence of the elimination.

Besides, why would you try to place a 1 in one of two hashmarked cells in the same row? How could you possibly know which one of the two was the correct one?

Ron

P.S. The elimination is marked '+' in your illustration.

[Myth Jellies]

I'll give it a try

If you had the following candidate grid, the starred cells would form an X-Wing, and you could eliminate the 1's from the cells marked with a '-'.

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1  .  .  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  .  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

Unfortunately when you look at your candidates, you find that there are a couple of lousy hashed cells which prevent you from having that X-Wing.

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1 #1 #1  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  .  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

Fortunately, the candidates that are blocking you from making an X-Wing are both in the same box as one of your potential reductions. Thus you can salvage something from your search and form a finned X-Wing (or an X-Wing filet) to make that one reduction and eliminate the 1 in r5c4.

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| .  1  1  |  1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1 #1 #1  |  .  .  .  |
| .  1  1  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  .  |  1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

That's all there is to it. You can extend this concept to apply to other things such as a swordfish.

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| .  1  1  |  1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1 #1 #1  |  .  . *1  |
| .  1  1  | -1  1  1  |  .  .  .  |
| .  .  .  | *1 #1 #1  |  .  . *1  |
+----------+-----------+-----------+
| .  .  .  |  1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

Here the hashed 1's are preventing the starred cells from forming a swordfish. However, you can still make that one elimination using a finned swordfish (or swordfish filet)

[Kent]

Myth Jellies

Thus you can salvage something from your search and form a finned X-Wing (or an X-Wing filet) to make that one reduction and eliminate the 1 in r5c4.

[/quote]

I still don't get how u can eliminate 1 in r5c4.Why is that the only 1 u can eleminate?? How about other 1?In the following example that u gave, which is the 1 that u can eliminate??

[ronk]

I still don't get how u can eliminate 1 in r5c4.Why is that the only 1 u can eleminate?? How about other 1?

Maybe this explanation will help.

Code: Select all

+----------+-----------+-----------+
| .  .  .  |  .  .  .  |  .  1  .  |
| . *1  .  | *1  .  .  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
+----------+-----------+-----------+
| . *1  .  | *1 #1 #1  |  .  .  .  |
| . -1  1  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  .  .  1  |
+----------+-----------+-----------+
| .  .  .  | -1  1  1  |  .  .  .  |
| .  .  .  |  .  .  .  |  1  .  .  |
| 1  .  .  |  .  .  .  |  .  .  .  |
+----------+-----------+-----------+

Either the r24c24 pattern (the starred cells) is an x-wing or it isn't.

1. If it is an x-wing, 1s marked with a minus sign may be eliminated.
2. If it isn't an x-wing, it's because a 1 at one of the hashmarked cells -- a cell preventing the x-wing outcome -- must be true.

It follows then ... that any candidate normally eliminated by an x-wing, is still eliminated if that candidate can "see" all the candidates that can prevent the x-wing. In this case, the only candidate fitting that description is at r5c4.

Ron

[Myth Jellies]

Good approach, Ron. To be honest, I never really thought of it in that fashion before, but that works well as an alternate way of explaining it.

Only two choices; either the x-wing applies or it doesn't.

If it applies then you could eliminate all of the candidates marked with a '-'.

If it does not apply, then one of the candidates marked with '#' must be true, and you could remove all candidates in box 5 not marked with a '#'.

In either case, you can remove the candidate in r5c4. Nice logic, and easier to see/explain than my approach.

[Kent]

Thanks Ron and Myth.I get it clear now.Just another question about colouring. From the example below, if i start colouring r2c1 with +, then is r2c3 + or r2c5 +?? How do u colour this puzzle??

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 | 2    .    2    | .    2    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    .    | .    2    .    |
 | .    .    2    | .    .    .    | 2    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    2    | .    2    .    |
 | 2    .    .    | .    .    .    | 2    .    .    |
 | .    2    .    | .    .    2    | .    .    .    |
 *--------------------------------------------------*

[MCC]

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 |+2    .   -2    | .   (2)   .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    .    | .   +2    .    |
 | .    .   +2    | .    .    .    |-2    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    2    | .   -2    .    |
 |-2    .    .    | .    .    .    |+2    .    .    |
 | .    2    .    | .    .    2    | .    .    .    |
 *--------------------------------------------------*

The (2) can be eliminated as it can see both a + and a -.

This can also be viewed as a swordfish in columns.
The *2's make up the swordfish.

Code: Select all

*--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 |*2    .   *2    | .    2    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    .    | .    2    .    |
 | .    .   *2    | .    .    .    |*2    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    2    | .    2    .    |
 |*2    .    .    | .    .    .    |*2    .    .    |
 | .    2    .    | .    .    2    | .    .    .    |
 *--------------------------------------------------*

MCC

[Kent]

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 |*2    .   *2    | .    .    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .        .    | .    .    .    | .       .    |
 | .    .   *2    | .    .    .    |.    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .        .    | .    .        | .        .    |
 |*2    .    .    | .    .    .    |.    .    .    |
 | .        .    | .    .        | .    .    .    |
 *-------------------------------------------------*

Can say the number 2 with * form an X-wing???

[Cec]

"..Can say the number 2 with * form an X-wing???

The following is part of the explanation of an "X-wing" pattern described in the angusj link. Of particular importance are the sentences I have bolded out.

"...For every Sudoku, a value can exist only once in each row, column and box. If a value has only 2 possible locations in a given row (ie it has a candidate in only 2 cells in that row), then it must be assigned to one of these 2 cells. Given a particular puzzle that has two rows where a given candidate 'C' is restricted to exactly the same two columns (and no more than 2 columns), and since
1) candidate C must be assigned once in each of these two rows, and
2) no column can contain more than one of candidate C
then candidate C must be assigned exactly once in each of these two columns within these two rows.Therefore, it's not possible for any other cells in these two columns to contain candidate C. This same logic applies when a puzzle that has two columns where candidate C is restricted to exactly the same two rows."

In your example the 2's occupy two columns but not the same two rows. This pattern does not satisfy the above conditions so it cannot be an X-wing pattern.
Cec

[Kent]

Thanks for your explaination.