## Sue De Coq Revisited Again (ASI#1)

Advanced methods and approaches for solving Sudoku puzzles

### Sue De Coq Revisited Again (ASI#1)

This is a mainly in the form of an introduction to the associated thread ‘The Almost Sue De Coq’. Another reason for it is that there are few presentations of Sue De Coq in tutorial form elsewhere. Andrew Stuart gives a fairly good one in his book ‘The Logic of Sudoku’. The Sudopedia example and associated brief explanation is helpful, but still isn’t enough to guarantee that most who read it will understand the pattern.

Overall, Sue De Coq as a subject of discussion seems to appear and disappear periodically, but, more often than not, it doesn’t seem to be on almost anyone’s regular solving radar. Likely, one of the reasons is that it is a fairly complex pattern and unless you have spent a certain amount of time learning to recognize it, it can be easily missed. However, in more than one way, it is a potentially powerful and useful method and is worth the effort to learn.

A few of the important discussions and/or presentations on Sue De Coq:

The original presentation and description of Sue De Coq (Two-Sector Disjoint Subsets) by rubylips:

http://forum.enjoysudoku.com/viewtopic.php?t=2033

Unfortunately, the following thread has been destroyed by hacker activity, but I'll leave the reference here in memory of it.

[This is an interesting thread ‘Sue De Coq revisited’ started by Ruud. Unfortunately, much of its value is lost since a change in the UK forum software creamed the excellent graphics. It’s still worth reading for some of the original thoughts of Ruud and Myth Jellies on the subject: http://www.sudoku.org.uk/SudokuThread.asp?fid=4&sid=8198&p1=5&p2=11]

The Sudopedia description:

http://www.sudopedia.org/wiki/Sue_de_Coq

One of the interesting revelations in the article by Ruud mentioned above is that, according to a limited study he did, the Sue De Coq pattern may not be nearly as rare as people believe. I know that now that I can recognize it more easily, consistent with Ruud’s findings I’m finding it more frequently than some other patterns (eg. jellyfish, hidden triples, naked quads etc.). For that reason and the fact that it can result in several eliminations, it is worth learning, but there is another good reason that I’ll get to in the other thread.

There are several ways of interpreting and finding a Sue De Coq. My preference is to start by seeing its core as either an AALS or AAALS in a row or column within a box. That is, I will first look for the core in the form of either 4 different digit values (aals) or 5 (aaals) in 2 cells in a row or column, all in the same box or in the form of 5 (aals) or 6 (aaals) different digit values in 3 cells in a row or column all in the same box. Next, there should be, in the same box, a bivalue cell (let’s call it A) containing 2 digits that are also present in the core. Then, in the same row or column (as the case may be) there should be a bivalue cell (let’s call it B) containing 2 other digits from the core (ie. not the same digits as were in the bivalue cell A). In addition to the above, if the Sue De Coq is the aaals-type (ie. 5 digit values in 2 cells or 6 in 3 cells) there must also be one more cell in the row or column (let’s call it C) that contains one more digit equal to a digit value in the core, but not present in the other 2 bivalue cells A and B. Usually, in addition to that digit, cell C can only contain digits that are already present in cell B.

A valid Sue De Coq allows the elimination of any digits in the box (outside of cell A) that are equal to those in cell A. Likewise, all digits in the row or column (outside of cell B and C of course) equal to those in cell B and those in cell C can be removed. Also, if there is one digit value left in the core, not present in A, B or C, all digits equal to that value in the box or in the row or line can be eliminated.

Those newer to solving may find the principle behind the Sue De Coq difficult to understand. Here’s my take: Ultimately, the core will need to have 2 digits (if a core of 2 cells) or 3 digits (if a core of 3 cells) to ‘survive’. If you think about it, cells A and B (the bivalue cells in the box and in the row or column) are sucking away 2 of the possible digit values that the core needs to ‘survive’. Those digits must be either in cells A, B or in the core; that accounts for the basic eliminations in the box and in the row or column. Likewise, if the core is an aaals (ie. 5 digit values in 2 cells or 6 digit values in 3 cells), cell C will potentially suck away a 3rd digit value and accounts for the associated eliminations in the row or column. Finally, this usually leaves one digit value left in the core which must be there for the core to ‘survive’ and it accounts for the associated eliminations of that digit in the box and the row or column.

All of this should be made clearer by the examples below.

This is the simpler aals-type Sue De Coq (5 digit values in the 3 blue cells). The brown cell is the A cell; the green cell is the B cell as described above. The 4 can be eliminated from r3c2 because of the 4 in cell A. The 5 in r3c2 and in r2c4 can be removed because of the digit value 5 in the core not present in either cell A or B. There are no digits available for elimination (ie. equal to 3 or 8) in row 2.

This is the slightly more complex aaals-type Sue De Coq (5 digit values in the two blue cells). The 3s and the 7 can be removed from box 9 due to the digit values in the brown cell A. The 9 can be eliminated from r6c6 due to the 9 in the green cell B. The gold cell C accounts for the 3rd digit, 2, in the aaals of the core, but there are no 2s in the row to eliminate.

This is another aaals-type Sue De Coq which not only represents all of the possible components of a Sue De Coq, but also is an example of the many eliminations that are possible. The 1s and 5 in box 4 are eliminated due to the 1 and 5 in the brown cell A. There are no eliminations possible in row 6 due to the green cell B. 2 can be eliminated due to the 2 in the gold cell C. The 6s in box 4 and row 6 can be eliminated because of the 6 that is not represented in cells A, B, or C and is thus locked to the core.

Again, this description of Sue De Coq is meant primarily as an introduction to the subject of The Almost Sue De Coq. As such, it covers the more common, but not all of the possible forms of the pattern. In summary, the benefit of learning to find and use Sue De Coq can be looked at this way: It can be found more frequently than a number of patterns that manual solvers are used to looking for, but it can often also provide many more eliminations than those patterns. In addition, the Almost Sue De Coq, as described in the follow-up thread, can be one more useful addition to the toolbag for advanced manual solving.

(Puzzle credits: 1st is my own, 2nd from the Player’s forum Zoo, 3rd from Ruud’s ‘Sue De Coq revisited’ thread. ASI stands for Advanced Solving Illustrated.)
Last edited by DonM on Mon Mar 16, 2009 6:54 pm, edited 10 times in total.
DonM
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Very useful stuff, Don. I've never seen anyone point out certain characteristics of this technique as you have. I think I've learned a few things. To wit:

I've always looked as SDCs as simply N candidates in N cells. I never realized they had an "a" and "b" cell in relation to a "core." In fact, I didn't believe it, so I went over my collection of SDCs and this is what I found:

* Each had a "core" of 2 or 3 cells that contained all 5 or 6 values in the pattern. The core cells were always in the same row or column.

* Each had a bivalue "a" cell in the same box as the "core" consisting of core digits.

* Each had a bivalue "b" cell in a different box consisting of "core" digits not in the "a" cell.

Exactly as you pointed out...

Are there valid Sue de Coqs that don't share these characteristics? Are there SDCs with the "a" or "b" cells containing more than two digits?

One small point. I would suggest that in the first example it is misleading to circle the 5 in r2c3 as an elimination. It's merely a by-product of the SDQ (like r2c4<>5) and might cause confusion.
Last edited by Luke on Sun Oct 26, 2008 3:31 pm, edited 2 times in total.

Luke
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Luke451 wrote:One small point. I would suggest that in the first example it is misleading to circle the 5 in r2c3 as an elimination. It's merely a by-product of the SDQ (like r2c4<>5) and might cause confusion.

Good eye Luke. It's an outright careless error. The 5 in r2c4, not r2c3 is supposed to be circled as the text below the example correctly indicates.

Also, although much of the above is my own spin on the concept of SDC, in all fairness, some of it also comes from Andrew Stuart's view of it.
DonM
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Just as an example, here's a SDC with a four digit core.
c = core
a = bivalue in core box
b = other bivalue

Eight eliminations!
Code: Select all
`  *--------------------------------------------------------------------* | 3      14     7      | 1458   1248   9      | 2458   2458   6      | | 5      1469   1469   | 1468   12348  7      | 2489   23489  3489   | | 8      2      469    | 456    34     36     | 1      7      3459   | |----------------------+----------------------+----------------------| | 29     5      23489  | 7      6      28     | 2489   23489  1      | | 1269   1689   12689  | 3      5      4      | 7      289    89     | | 7      348    2348   | 18     9      128    | 2458   6      3458   | |----------------------+----------------------+----------------------| |a69     36789  5      | 468    3478   368    | 4689   1      2      | | 126    13678  12368  | 9      13478  13568  | 4568   458    458    | | 4     c1689  c1689   | 2     b18     1568   | 3      589    7      | *--------------------------------------------------------------------*`
From Scanraid

Luke
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How common is Sue de Coq really, and how commonly is it found by manual solvers?
As of two weeks ago, Sue de Coq joined my list of "Techniques that I have only once encountered in puzzles" alongside Jellyfish, "Y-wing with two strong links", and (as of even more recently) WXYZ-wing. (Would you say that Sue de Coq is more, or less, common than e.g. Jellyfish?)

It occurred in #19 from the top95:
Code: Select all
`    14      2      3 ||     7      5      9 ||   148     148       6     8      7     14 ||     2      6    134 ||     5       9     134     9     56     56 ||   138    138   1348 ||     7       2     134=====================||=====================||======================    26    156  12568 ||  1358      4    138 ||     9       7     158     3    145      7 ||   158      9      6 ||   148    1458       2    14   1459  14589 ||   158      2      7 ||    36      36    1458=====================||=====================||======================     5   1369   1269 ||     4      7    138 || 12368    1368     189    67  13469   1469 ||    69    138      2 || 13468  134568  145789   267      8  12469 ||    69     13      5 || 12346    1346    1479`

Bivalue cells: r6c1, r3c2
Core: r45c2
Eliminations: r4c3<>1, r6c3<>14, r7c2<>6, r8c2<>6, r6c2<>145

(Then we have a single r6c2=9 and a grouped turbot fish/ER in 4r6b3 => r1c1<>4 and it's all singles and locked candidates.)
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

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After the Simple Sudoku Technique Set (SSTS), this puzzle can be solved with a Sue de Coq, a naked triple, a naked pair and singles. Can you find the Sue de Coq Is there a simpler solution path
Code: Select all
`top1465 #136.9.....8...7.1...4............6...4.2.....3..3....5...1.5...7.8...9..........2..After SSTS: 6      57     9      | 234    2345   2345   | 1347   1245   8 23     58     23     | 7      458    1      | 469    4569   569 4      578    1      | 69     2358   69     | 37     25     2357----------------------+----------------------+--------------------- 157    9      8      | 123    6      2357   | 17     12     4 157    2      46     | 1489   1457   45789  | 16789  3      1679 17     3      46     | 12489  1247   2479   | 5      12689  12679----------------------+----------------------+--------------------- 239    1      23     | 5      34     3468   | 34689  7      369 8      46     57     | 12346  9      23467  | 1346   1456   1356 39     46     57     | 13468  1347   34678  | 2      145689 13569`

hidden answer (triple click text area to see) wrote:Sets: A = {r13c8} = {1245}; B = {r2c789} = {4569}; C = {r4c8} = {12}

Sets A,B share digits 4,5; sets A,C share digits 1,2

Elims: r1c7<>4, r3c9<>5, r6c8<>12, r89c8<>1
Last edited by ronk on Wed Oct 29, 2008 2:40 pm, edited 3 times in total.
ronk
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ronk wrote:Can you find the Sue de Coq
No! Dangnabbit. Give me a hint: is it an "almost" or a clean SDC?
If it's not "almost" then I think boxes 2, 4, 5, 8 and 9 can't be involved.

At least this is for sure: ripe type 1 UR on <23> means r7c1=9.

Luke
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Luke451 wrote:
ronk wrote:Can you find the Sue de Coq
Give me a hint: is it an "almost" or a clean SDC?

It's a "clean SDC"; your deduction re box numbers is correct so far.
ronk
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999_Springs wrote:How common is Sue de Coq really, and how commonly is it found by manual solvers? As of two weeks ago, Sue de Coq joined my list of "Techniques that I have only once encountered in puzzles" alongside Jellyfish, "Y-wing with two strong links", and (as of even more recently) WXYZ-wing. (Would you say that Sue de Coq is more, or less, common than e.g. Jellyfish?)

Although it is in the link above, for interest sake, I'll print Ruud's study here:

Ruud: If you think Sue De Coq is too rare, you might want to reconsider looking for naked quads, hidden triples, hidden quads, swordfish, jellyfish, remote pairs, aligned pairs, simple coloring, multi coloring, BUGs and several types of unique rectangles, because they appear less frequent than Sue De Coq. This statement is based on empirical data, as I counted the frequency of each solving technique in a set of 33000 non-singles sudokus. Here are the complete results:

Technique Per 10,000
Naked pair 4,143
Naked triple 866
Hidden pair 3,303
Hidden triple 270
X-Wing 1,388
Swordfish 340
Jellyfish 15
Remote pair 488
XY-Wing 2,920
XYZ-Wing 1,155
Sue De Coq 581
Aligned pair 85
2-string kite 2,143
Skyscraper 2,658
BUG+1 271
Empty Rectangle 924
Unique Rectangle #1 631
Unique Rectangle #2 123
Unique Rectangle #3 207
Unique Rectangle #4 105
Simple coloring 200
Finned X-Wing 607
Finned Swordfish 456
Finned Jellyfish 19
Sashimi X-Wing 115
Sashimi Swordfish 104
Sashimi Jellyfish 1
Multi-coloring 114
XY-Chain 3,130
ALS-XZ rule 1,897
3D Medusa (1 cluster) 1,165
3D Medusa (2 clusters) 678
3D Medusa (>2 clusters) 511
Nishio 130
Forcing nets 287

Obviously, this is one study and doesn't prove the point, but it does raise the question. I would think that the accuracy of anyone's study on this subject would depend on things such as the sample of puzzles used (any or all levels of difficulty?), how accurate is the random generator & how many samples should be taken to guarantee, within reasonable limits accuracy and finally, how accurate is the programming of the solver in identifying all the variations of Sue De Coq?

Ruud's study raised my interest partly because he spent considerable time programming his solver to accurately recognize the latest/greatest patterns so I was reasonably confident that it was able to find more of the Sue De Coq patterns than other solvers might.
DonM
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But the main information is missing:
- what were the priorities on the various techniques used?
- said otherwise, is a SdC counted every time simpler rules could do the same job?

Can you provide a list of puzzles where it is used?
denis_berthier
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ronk wrote:
Luke451 wrote:
ronk wrote:Can you find the Sue de Coq
Give me a hint: is it an "almost" or a clean SDC?

It's a "clean SDC"; your deduction re box numbers is correct so far.
When I do chess puzzles in the paper I have a rule. If I can't find the answer within five minutes, I lose! I think I'll start applying that to this game too.

I will say the solution here must be a wrinkle outside the "core-a-b" pattern mentioned above.

Luke
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ronk wrote:After the Simple Sudoku Technique Set (SSTS), this puzzle can be solved with a Sue de Coq, a naked triple, a naked pair and singles. Can you find the Sue de Coq Is there a simpler solution path
Code: Select all
`top1465 #136.9.....8...7.1...4............6...4.2.....3..3....5...1.5...7.8...9..........2..After SSTS: 6      57     9      | 234    2345   2345   | 1347   1245   8 23     58     23     | 7      458    1      | 469    4569   569 4      578    1      | 69     2358   69     | 37     25     2357----------------------+----------------------+--------------------- 157    9      8      | 123    6      2357   | 17     12     4 157    2      46     | 1489   1457   45789  | 16789  3      1679 17     3      46     | 12489  1247   2479   | 5      12689  12679----------------------+----------------------+--------------------- 239    1      23     | 5      34     3468   | 34689  7      369 8      46     57     | 12346  9      23467  | 1346   1456   1356 39     46     57     | 13468  1347   34678  | 2      145689 13569`

All depends on what you call simpler. Personally, starting from your PM, I consider the following short nrct-chains, each of which has a single additional t-candidate, as simpler than a SdC.

nrct-chain[3] {n1 n7}r4c7 - n7{r6 r3 r5#n7r4c7}c9 - n2{r3 r6}c9 ==> r6c9 <> 1
nrc-chain[4] {n3 n7}r3c7 - {n7 n1}r4c7 - {n1 n2}r4c8 - n2{r6 r3}c9 ==> r3c9 <> 3
interaction column c9 with block b9 for number 3 ==> r8c7 <> 3, r7c7 <> 3
nrct-chain[4] {n5 n2}r3c8 - {n2 n1}r4c8 - {n1 n7}r4c7 - n7{r6 r3 r5#n7r4c7}c9 ==> r3c9 <> 5
nrct-chain[4] {n1 n7}r4c7 - n7{r6 r3 r5#n7r4c7}c9 - n2{r3 r6}c9 - {n2 n1}r4c8 ==> r6c8 <> 1, r5c9 <> 1
interaction column c9 with block b9 for number 1 ==> r9c8 <> 1, r8c8 <> 1, r8c7 <> 1
naked-pairs-in-a-row {n4 n6}r8{c2 c7} ==> r8c9 <> 6, r8c8 <> 6, r8c8 <> 4
...singles...
679325148
283741965
451986327
598263714
124857639
736419582
912534876
867192453
345678291
denis_berthier
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ronk wrote:Is there a simpler solution path

I was unable to find one. And I was unable to find a simpler step for your path either. The elimination, that unlocks your path, seems to be r1c7<>4, but the only steps (other then the Sue de Coq) I could find were a Nice Loop, that uses the same ALS as the Sue de Coq and a MINL. Not really easier...
hobiwan
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ronk wrote:After the Simple Sudoku Technique Set (SSTS), this puzzle can be solved with a Sue de Coq, a naked triple, a naked pair and singles. Can you find the Sue de Coq Is there a simpler solution path
Code: Select all
`top1465 #136.9.....8...7.1...4............6...4.2.....3..3....5...1.5...7.8...9..........2..After SSTS: 6      57     9      | 234    2345   2345   | 1347   1245   8 23     58     23     | 7      458    1      | 469    4569   569 4      578    1      | 69     2358   69     | 37     25     2357----------------------+----------------------+--------------------- 157    9      8      | 123    6      2357   | 17     12     4 157    2      46     | 1489   1457   45789  | 16789  3      1679 17     3      46     | 12489  1247   2479   | 5      12689  12679----------------------+----------------------+--------------------- 239    1      23     | 5      34     3468   | 34689  7      369 8      46     57     | 12346  9      23467  | 1346   1456   1356 39     46     57     | 13468  1347   34678  | 2      145689 13569`

denis_berthier wrote:All depends on what you call simpler. Personally, starting from your PM, I consider the following short nrct-chains, each of which has a single additional t-candidate, as simpler than a SdC.

hobiwan wrote:I was unable to find one. And I was unable to find a simpler step for your path either. The elimination, that unlocks your path, seems to be r1c7<>4, but the only steps (other then the Sue de Coq) I could find were a Nice Loop, that uses the same ALS as the Sue de Coq and a MINL. Not really easier...

After the following AIC loop, you need only a single pair to crack the puzzle.
(sorry for the probably non-accademic AIC notation) :

7r3c9=7r56c9 - (7=1)r4c7 - (1=2)r4c8 - 2r13c8=2r3c9 - loop
==> r3c9<>35, r5c7<>7, r4c14<>1, r6c8<>2

Mage
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a SDC puzzle
Code: Select all
`. . .|8 . 2|. . .. . 4|. . .|3 . .. 6 .|. . .|. 8 .-----+-----+-----9 . .|4 . 8|. . 5. . .|. . .|. . .8 . .|2 . 5|. . 4-----+-----+-----. 1 .|. . .|. 2 .. . 6|. . .|1 . .. . .|3 . 7|. . .`
tarek

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