Y-Wing is Next Step. What is a Y-Wing?

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Y-Wing is Next Step. What is a Y-Wing?

Postby turnthepage » Tue May 23, 2006 5:56 pm

I am having trouble with the next step in the following puzzle. I ran this puzzle through a Sudoku helper which says that the next step is a Y-Wing.

Y-Wing: r5-c7, r9-c7, r7-c9 (removes 7 from r5-c9 and r6-c9)

I do not understand how the Y-Wing works. Could someone please help?

Also, could someone tell me how to include the Sudoku puzzle in a post including all of the "possibilities" without the puzzle being out of alignment?

Code: Select all
 *-----------*
 |.5.|..1|6..|
 |3.6|..2|...|
 |..9|3..|2.4|
 |---+---+---|
 |..4|53.|182|
 |..3|8.4|...|
 |8.5|12.|4..|
 |---+---+---|
 |6.1|..5|3..|
 |...|6..|9.1|
 |..7|21.|.46|
 *-----------*
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Re: Y-Wing is Next Step. What is a Y-Wing?

Postby ronk » Tue May 23, 2006 8:19 pm

turnthepage wrote:I do not understand how the Y-Wing works. Could someone please help?

The term "Y-Wing" is attributed to Gaby Vanhegan, but his on-line Sudoku Dictionary today says ... "Sometimes XY-wing is incorrectly referred to as Y-wing." The "Y-Wing" technique is described here by one site that still uses the term.
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Postby Carcul » Wed May 24, 2006 1:12 pm

Turnthepage wrote:I am having trouble with the next step in the following puzzle. I ran this puzzle through a Sudoku helper which says that the next step is a Y-Wing.


That hint will not help you much. Try this:

1. [r7c2]-9-[r46c2]=9=[r46c6]-9-[r9c6]=9=[r7c45]-9-[r7c2], => r7c2<>9.

2. [r3c5]=5=[r3c8]-5-[r8c8]=5=[r9c7]-5-[r5c7]-7-[r5c5]-6-[r3c5], => r3c5<>6.

3. [r1c3](-8-[r8c3]-2-[r8c2])-8-[r3c12](-1,7-[r2c2])-1,7-[r3c8]-5-[r8c8]=5=[r9c7]-5-[r9c1]-9-[r9c2]-(UR: r89c26)-3,8-[r8c2]-4-[r2c2]-8-[r1c3],

which implies that r1c3 cannot be "8" and the puzzle is solved. This thread explains the notation.

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Postby tarek » Wed May 24, 2006 2:37 pm

after the hint you could try this (a simple example of a quad implication chain:D ):
Code: Select all
*-----------------------------------------------------------------*
| 247    5      28    | 479    4789   1     | 6      379    3789  |
| 3      1478   6     | 479    45789  2     | 578    1579   5789  |
| 17     178    9     | 3      5678   678   | 2      157    4     |
|---------------------+---------------------+---------------------|
| 79     679    4     | 5      3      679   | 1      8      2     |
| 12     12     3     | 8      679    4     | 57     5679   59    |
| 8      679    5     | 1      2      679   | 4      3679   39    |
|---------------------+---------------------+---------------------|
| 6      2489   1     | 479    4789   5     | 3      27     78    |
| 245    2348   28    | 6      478    378   | 9      257    1     |
| 59     389    7     | 2      1      389   | 58     4      6     |
*-----------------------------------------------------------------*
Candidates in r3c5 will force r5c2 to have only 2

r3c5=5: => r5c5=6 => r4c6<>6 (=>r6c6<>6) => r3c6=6 => r3c2=8 => r8c3=2 => r8c3=8 => r8c6<>8 => r9c6=8 => r9c7=5 => r9c1=9 => r4c1=7 => r3c1=1 => r5c1=2 => r5c2=1

r3c5=6: => r2c5=5 => r2c9<>5 => r5c9=5 => r5c7=7 => r2c7=8 => r9c7=5 => r9c1=9 => r4c1=7 => r3c1=1 => r5c1=2 => r5c2=1

r3c5=7: => r3c1=1 => r5c1=2 => r5c2=1

r3c5=8: => r2c5=5 => r2c9<>5 => r5c9=5 => r5c7=7 => r2c7=8 => r9c7=5 => r9c1=9 => r4c1=7 => r3c1=1 => r5c1=2 => r5c2=1

Therefore r5c2=1
which needs another xy wing to solve.....

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Postby ronk » Wed May 24, 2006 3:26 pm

tarek wrote:
Code: Select all
*-----------------------------------------------------------------*
| 247    5      28    | 479    4789   1     | 6      379    3789  |
| 3      1478   6     | 479    45789  2     | 578    1579   5789  |
| 17     178    9     | 3      5678   678   | 2      157    4     |
|---------------------+---------------------+---------------------|
| 79     679    4     | 5      3      679   | 1      8      2     |
| 12     12     3     | 8      679    4     | 57     5679   59    |
| 8      679    5     | 1      2      679   | 4      3679   39    |
|---------------------+---------------------+---------------------|
| 6      2489   1     | 479    4789   5     | 3      27     78    |
| 245    2348   28    | 6      478    378   | 9      257    1     |
| 59     389    7     | 2      1      389   | 58     4      6     |
*-----------------------------------------------------------------*

Can anyone see a way to use the AUR(679) Type E3 in r46c26?
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Postby RW » Wed May 24, 2006 7:46 pm

ronk wrote:Can anyone see a way to use the AUR(679) Type E3 in r46c26?


I'm not quite sure what your looking for, at least I would eliminate 6 from r6c6:

Code: Select all
If r4c1=7 => r46c2=69 & r4c26=69 => r6c6<>69
If r4c2=7 => r6c2=6 => r6c6<>6
If r6c2=7 => r4c1=9 => r4c2=6 => r4c6=7 => r6c6<>6


Might be some other eliminations too if you search hard. But I don't recognize this as a pattern I would regularly use.

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Postby ronk » Wed May 24, 2006 8:43 pm

RW wrote:I'm not quite sure what your looking for ...

Sorry, I was looking for something that used a strong link, err ... a strong inference ...
Code: Select all
 .    679 .    | .    .    679      (row 4)
 .    .   .    | .    .    .
 .    679 .    | .    .    679

... e.g., if r4c26<>6, then r6c26=6 ... or if r24c2<>6, then r24c6=6 ... or either of the preceding using 7 or 9 instead of 6.

RW wrote:... at least I would eliminate 6 from r6c6:

Code: Select all
If r4c1=7 => r46c2=69 & r4c26=69 => r6c6<>69
If r4c2=7 => r6c2=6 => r6c6<>6
If r6c2=7 => r4c1=9 => r4c2=6 => r4c6=7 => r6c6<>6

That's more than I had found so far.:) My excuse is ... this wine I'm drinking is GREAT!:D
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Postby RW » Wed May 24, 2006 9:37 pm

The elimination r6c6<>6 could be expressed in a better(?) way using some kind of interference with box 6:

Code: Select all
If r6c6=6 => r4c2=6
     either r5c5=7 (=> r4c6=9) => r6c8=7 => r6c2=9 => UR in r46c26
         or r5c5=9 (=> r4c6=7) => r6c89=9 => r6c2=7 => UR in r46c26
=> r6c6<>6


I can't find any valid eliminations using strong interference inside the pattern only...

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Re: Y-Wing is Next Step. What is a Y-Wing?

Postby Cec » Thu May 25, 2006 12:18 am

turnthepage wrote:"...Also, could someone tell me how to include the Sudoku puzzle in a post including all of the "possibilities" without the puzzle being out of alignment?.."

To post a puzzle (including the candidate grid) from the SS program to the Forum you manually load your puzzle into SS or copy and paste the puzzle direct from the Forum into the SS program. In the top Menu bar of the SS program puzzle click on Edit / Copy or, alternatively, select (Ctrl+C) on your keyboard.

Click on the appropriate button in the Forum to open a "Post a reply" window box. Click on the code tag and paste (Ctrl +V) the puzzle into this window box and click the code tag again at the end of the puzzle. Note the / must precede the second code tag. To demonstrate this to you I have to use these {} brackets to explain this to you whereas you must type these [] brackets. Your "Post a reply" window would look like this:

{code}
Puzzle pasted here
{/code}

Now copy and paste your puzzle as explained above from SS to this window using these correct brackets [] when showing the code tags. Note that the candidate grid is automatically shown simply from just copying the puzzle grid.
The candidate grid will appear out of alignment in your "Post a reply" window box but corrects itself when you click the "Preview" button which you should do anyway before submitting your post to the forum.

Hopefully your candidate grid will look like this:
Code: Select all
 
 *--------------------------------------------------------------------*
 | 247    5      28     | 479    4789   1      | 6      379    3789   |
 | 3      1478   6      | 479    45789  2      | 578    1579   5789   |
 | 17     178    9      | 3      5678   678    | 2      157    4      |
 |----------------------+----------------------+----------------------|
 | 79     679    4      | 5      3      679    | 1      8      2      |
 | 1279   12679  3      | 8      679    4      | 57     5679   579    |
 | 8      679    5      | 1      2      679    | 4      3679   379    |
 |----------------------+----------------------+----------------------|
 | 6      2489   1      | 479    4789   5      | 3      27     78     |
 | 245    2348   28     | 6      478    378    | 9      257    1      |
 | 59     389    7      | 2      1      389    | 58     4      6      |
 *--------------------------------------------------------------------*


Incidently, have you checked your PM inbox? or have you disabled your "Notify me when a reply is posted" window box?

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Postby daj95376 » Thu May 25, 2006 12:33 am

Bad post ... ignore.
Last edited by daj95376 on Wed May 24, 2006 10:02 pm, edited 1 time in total.
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Postby ronk » Thu May 25, 2006 1:18 am

daj95376 wrote:I took the output from my solver and manually derived these results. Are they strong enough for you?

I see you've made progress on the puzzle. But perhaps you misunderstood my question about strong inferences using an AUR Type E3.
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Postby RW » Thu May 25, 2006 6:51 am

Thanks for the link, hadn't seen that thread before. The E3 examples discussed on the thread alway included an x-wing in the cells, which made them easier to use. Just to show the difference:

Code: Select all
abc      abc
 |        |
 |a       |a
 |        |
abc      abc


Here you Can use the strong interference "if one corner is b => the opposite corner is not".

In this puzzle

Code: Select all
abc      abc
 |
 |a
 |
abc      abc


you cannot make such eliminations.

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Postby daj95376 » Fri May 26, 2006 4:52 pm

If you scan cells in reverse order.

Code: Select all
*-----------------------*
| . 5 . | . . 1 | 6 . . |
| 3 . 6 | . . 2 | . . . |
| . . 9 | 3 . . | 2 . 4 |
|-------+-------+-------|
| . . 4 | 5 3 . | 1 8 2 |
| . . 3 | 8 . 4 | . . . |
| 8 . 5 | 1 2 . | 4 . . |
|-------+-------+-------|
| 6 . 1 | . . 5 | 3 . . |
| . . . | 6 . . | 9 . 1 |
| . . 7 | 2 1 . | . 4 6 |
*-----------------------*

    b4  -  679   Naked  Triple
r9c7    ~  7     XY-Wing
r9c7    =  5     [r9c7]=8 => [c6]=INVALID

Singles complete remainder of puzzle.

Details:

[r9c7]=8,[r7c9]=7,[r7c8]=2,[r8c8]=5,[r9c1]=5,
[r3c5]=5,[r3c6]=6,[r3c2]=8,[r1c3]=2,[r8c3]=8 =>[c6]=INVALID
Last edited by daj95376 on Wed Sep 13, 2006 5:32 am, edited 1 time in total.
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Thanks to all

Postby turnthepage » Tue May 30, 2006 3:55 pm

I appreciate everyone's help! I haven't had the opportunity to get on my computer again until today. My oldest daughter has been sick for 3 weeks and my mother has been in the hospital as well. I'm anxious to get back to this puzzle so that I can try to complete it.

Thanks again to all of you:)
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Re: Y-Wing is Next Step. What is a Y-Wing?

Postby angusj » Wed May 31, 2006 12:03 am

ronk wrote:The term "Y-Wing" is attributed to Gaby Vanhegan, but his on-line Sudoku Dictionary today says ... "Sometimes XY-wing is incorrectly referred to as Y-wing." The "Y-Wing" technique is described here by one site that still uses the term.

Are you saying that the XY-Wing is attributed to Gaby Vanhegan? If so, then I don't think that's correct. I believed it was first described here - http://www.setbb.com/phpbb/viewtopic.php?t=63&mforum=sudoku - by Mat Newman.
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