Advanced methods and approaches for solving Sudoku puzzles

Does this pattern have a technique associated with it?

Code: Select all
`# [r1c7]-7-[r4c7]=7=[r4c8]-7-[r8c8] => [r1c7]=9 -or- [r8c8]=9 => [r3c8]<>9 *--------------------------------------------------* | 5    2    3    | 679  4    679  | 79   8    1    | | 4    69   8    | 5    79   1    | 3    2    679  | | 7    1    69   | 3    8    2    | 5    6-9  4    | |----------------+----------------+----------------| | 69   5    1    | 4    2    8    | 79   679  3    | | 689  7    2    | 69   5    3    | 1    4    689  | | 689  3    4    | 1    679  679  | 2    5    689  | |----------------+----------------+----------------| | 2    69   7    | 8    1    69   | 4    3    5    | | 1    8    5    | 2    3    4    | 6    79   79   | | 3    4    69   | 679  679  5    | 8    1    2    | *--------------------------------------------------*`

[Edit: Corrected chain notation. Thanks ronk!]
Last edited by daj95376 on Tue Aug 21, 2007 12:23 pm, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

It at least has 3 names, semi-remote naked pair or Y-wing (style) or W-wing.
There is a pair 79 connected by a strong link for 7. Either r4c7=7 => r1c7=9 or r4c8=7 => r8c8=9.
The same technique can be used to remove 9 from r56c9 and from r6c6, r9c4.
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:It at least has 3 names, semi-remote naked pair or Y-wing (style) or W-wing.

That the xy-wing term is already taken is unfortunate, because that's the name this technique should have IMO ... and the now xy-wing should be properly called the y-wing.

Why? Then maybe eventually all continuous and discontinuous loops where strong inferences due to ...
1) bilocation only would be "x-something",
2) bivalues only would be "y-something",
3) both bilocation and bivalues would be "xy-something".
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

I'd like to ask a simpler question.

Let's suppose you have already concluded (somehow) that the only cells where a 4 can occur in row 8 are in box 7. You can then conclude that, conversely, the only cells where a 4 can occur in box 7 are in row 8.

In other words, if 4 is not a candidate in r8c4, r8c5, r8c6, r8c7, r8c8, r8c9, then you can conclude that 4 is not a candidate in r7c1, r7c2, r7c3, r9c1, r9c2, r9c3 either.

What do you call this technique?

I'm sure there's an answer buried in Advanced Techniques somewhere, but that thread is a bit large and heavy for me.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

Smythe Dakota wrote:I'd like to ask a simpler question.

Let's suppose you have already concluded (somehow) that the only cells where a 4 can occur in row 8 are in box 7. You can then conclude that, conversely, the only cells where a 4 can occur in box 7 are in row 8.

In other words, if 4 is not a candidate in r8c4, r8c5, r8c6, r8c7, r8c8, r8c9, then you can conclude that 4 is not a candidate in r7c1, r7c2, r7c3, r9c1, r9c2, r9c3 either.

What do you call this technique?

I'm sure there's an answer buried in Advanced Techniques somewhere, but that thread is a bit large and heavy for me.

Bill Smythe

Locked Candidates.
re'born

Posts: 551
Joined: 31 May 2007

Thanks ravel and ronk for setting me straight on this PM !!!

The eliminations in [r56c9] are an obvious extension of what I'd already found. I should have caught them! However, the eliminations in [r6c6],[r9c4] are not obvious to me and I'm going to need to look harder.

I hope Smythe Dakota isn't suggesting that I should have researched this pattern. However, he would have a good point if that was his intent. When is it wiser to ask than to search threads in Advanced Techniques?

If you know the name of the technique, then it's obvious that you should search for relevant information on it. If you don't know the technique, then SD is right that there are a lot of threads out there!

[Edit: Okay. Strong link in middle with weak links to identical bivalue cells.]

Code: Select all
`# 9-[r5c4]-6-[r6c5]=6=[r9c5]-6-[r7c6]-9 => [r6c6],[r9c4]<>9`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:[Edit: Okay. Strong link in middle with weak links to identical bivalue cells.]

Code: Select all
`# 9-[r5c4]-6-[r6c5]=6=[r9c5]-6-[r7c6]-9 => [r6c6],[r9c4]<>9`

A more intuitive version would use the strong link of 6 in r1c46 together with the bivalue cells {69} in r5c4+r7c6
Code: Select all
`*--------------------------------------------------*| 5    2    3    |A679  4   A679  |B79   8    1    || 4    69   8    | 5    79   1    | 3    2   B679  || 7    1    69   | 3    8    2    | 5    69   4    ||----------------+----------------+----------------|| 69   5    1    | 4    2    8    |B79   679  3    || 689  7    2    |A69   5    3    | 1    4   68-9  || 689  3    4    | 1    679  67-9 | 2    5   68-9  ||----------------+----------------+----------------|| 2    69   7    | 8    1   A69   | 4    3    5    || 1    8    5    | 2    3    4    | 6    79  B79   || 3    4    69   | 67-9 679  5    | 8    1    2    |*--------------------------------------------------*`

And for the uninspired the elimination r56c9<>9 is based on the strong link of 7 in r1c7+r2c9 (or r48c8) and the bivalue cells {79} in r4c7+r8c9.

My gut feeling tells me that this topic should really exist in the Advanced solving techniques forum and I have the ability to move it to there. If it's okay with Danny I'll do it for you.
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:
daj95376 wrote:[Edit: Okay. Strong link in middle with weak links to identical bivalue cells.]

Code: Select all
`# 9-[r5c4]-6-[r6c5]=6=[r9c5]-6-[r7c6]-9 => [r6c6],[r9c4]<>9`

A more intuitive version would use the strong link of 6 in r1c46 together with the bivalue cells {69} in r5c4+r7c6

I don't see how the strong link in r1 is any more "intuitive" than the strong link in c5. Are you saying you find it easier to see links in rows/columns than in boxes?

ravel wrote:It at least has 3 names, semi-remote naked pair or Y-wing (style) or W-wing.

Presumably the "semi-" of semi-remote naked pair is because only one of the two digits is eliminated, instead of both. Hmm, wouldn't that make it semi-naked instead of semi-remote?

The puzzle below contains a variant that is neither semi-remote nor semi-naked. It yields four exclusions followed by cascading singles to solve the puzzle.
Code: Select all
`#385 of top1465....4.87..61..................6...312...7....4.........5.1.8...7.....2.....3.....# after SSTS 3     29    259   | 59    4     1     | 8     7     6 589   6     1     | 7     38    59    | 359   24    24 589   47    47    | 2     38    6     | 1     59    359-------------------+-------------------+------------------ 59    78    78    | 6     59    2     | 4     3     1 2     1     3569  | 4589  7     3459  | 569   5689  589 4     39    3569  | 589   1     359   | 5679  25689 25789-------------------+-------------------+------------------ 6     5     2349  | 1     29    8     | 379   49    3479 7     389   389   | 459   6     459   | 2     1     3589 1     2489  2489  | 3     259   7     | 569   45689 4589`

triple click to see the spoiler ronk wrote:r56c6 -5- r4c5 -9- r4c1 -5- r23c1 =5= r1c23 -5- r1c4 -9- r2c6 -5- r56c6, implies r56c6<>5

r56c6 -9- r4c5 -5- r4c1 -9- r23c1 =9= r1c23 -9- r1c4 -5- r2c6 -9- r56c6, implies r56c6<>9
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:I don't see how the strong link in r1 is any more "intuitive" than the strong link in c5. Are you saying you find it easier to see links in rows/columns than in boxes?

I guess it's a personal thing. My major point is that in my "more intuitive version" the 4 linked cells are in the form of a right-angled trapezoid, while Danny's version they are forming an irregular skewed shape. Some people are more affected by the visual geometry and I think I was speaking on behalf of those people. Unfortunately you're not one of them.

ronk wrote:
Code: Select all
`#385 of top1465....4.87..61..................6...312...7....4.........5.1.8...7.....2.....3.....# after SSTS 3     29    259   | 59    4     1     | 8     7     6 589   6     1     | 7     38    59    | 359   24    24 589   47    47    | 2     38    6     | 1     59    359-------------------+-------------------+------------------ 59    78    78    | 6     59    2     | 4     3     1 2     1     3569  | 4589  7     3459  | 569   5689  589 4     39    3569  | 589   1     359   | 5679  25689 25789-------------------+-------------------+------------------ 6     5     2349  | 1     29    8     | 379   49    3479 7     389   389   | 459   6     459   | 2     1     3589 1     2489  2489  | 3     259   7     | 569   45689 4589`

triple click to see the spoiler ronk wrote:r56c6 -5- r4c5 -9- r4c1 -5- r23c1 =5= r1c23 -5- r1c4 -9- r2c6 -5- r56c6, implies r56c6<>5

r56c6 -9- r4c5 -5- r4c1 -9- r23c1 =9= r1c23 -9- r1c4 -5- r2c6 -9- r56c6, implies r56c6<>9

triple click to see the spoiler udosuk wrote:I see this as a "grouped turbot chain". r1c23 & r23c1 each form an essential bivalue unit of {59} in the chain. To write it out:
One of r1c23 & r23c1 must have 5 & the other must have 9
=> One of r1c4 & r4c1 must be 5 & the other must be 9
=> One of r2c6 & r4c5 must be 5 & the other must be 9
=> r56c6 can't be 5 or 9.
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:I see this as a "grouped turbot chain".

I posted that puzzle because the step is more than remotely-linked (pun intended) to the "semi-remote naked pair/y-wing/w-wing" topic. The somewhat ironic, and perhaps too subtle, point was that a remote pair is made even more remote by an additional pair of identical bivalued cells.

Unfortunately, the pairs of bivalued cells are conjugately linked (for both values), so it's not the greatest of examples -- as you may have pointed out -- but it is at least an example.

udosuk wrote:
ronk wrote:I don't see how the strong link in r1 is any more "intuitive" than the strong link in c5. Are you saying you find it easier to see links in rows/columns than in boxes?

I guess it's a personal thing. [...] Some people are more affected by the visual geometry and I think I was speaking on behalf of those people. Unfortunately you're not one of them.

Smiley face notwithstanding, I don't consider being less affected by "visual geometry" as unfortunate. However, I'm trying to adopt Mike Barker's policy of not getting involved in discussions involving Points of Personal Preference (POPP), so I have no further comment.

udosuk wrote:I see this as a "grouped turbot chain". r1c23 & r23c1 each form an essential bivalue unit of {59} in the chain.

As a point of fact, rather than a POPP, a "grouped turbot chain" is a single-digit technique.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:Smiley face notwithstanding, I don't consider being less affected by "visual geometry" as unfortunate. However, I'm trying to adopt Mike Barker's policy of not getting involved in discussions involving Points of Personal Preference (POPP), so I have no further comment.

The word "unfortunate" was merely pointing to the fact that my comment made you feel the need to argue, not about your personal attributes. As a matter of fact, I think people who are less affected by "visual geometry" are smarter. But the majority of people are not that smart.
ronk wrote:As a point of fact, rather than a POPP, a "grouped turbot chain" is a single-digit technique.

My bad. I missed the word "doubly-linked". So I should say it's a "doubly-linked grouped turbot chain", or a "grouped remote pair". I always think a remote pair is just a "doubly-linked turbot chain".
udosuk

Posts: 2698
Joined: 17 July 2005

ronk wrote:
ravel wrote:It at least has 3 names, semi-remote naked pair or Y-wing (style) or W-wing.

Presumably the "semi-" of semi-remote naked pair is because only one of the two digits is eliminated, instead of both. Hmm, wouldn't that make it semi-naked instead of semi-remote?

As the inventor of semi-remote naked pair (the name, not the technique), I will tell you where it came from and how I interpret it. First I agree with ronk that the semi is really connected to the naked pair and not the remote, however I didn't like the sound of remote semi-naked pair and so I put it at the front with unwritten parenthesis, i.e.,

semi- (remote naked pair)

is how I think about it.
re'born

Posts: 551
Joined: 31 May 2007