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Sue de Coq
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun May 22, 2011 4:37 am    Post subject: Sue de Coq Reply with quote

Most of you will have noticed that, most of the time, I am only dimly aware of what I am doing. Laughing In the past couple of weeks, I have been accused (at least twice) of using a Sue de Coq. So, I thought I should find out what that is.

The existing explanations (that I could find) seemed to be, in the end, incomplete. Also, there are not enough examples. So, while this thread will probably turn out to be nothing new, I hope it will be helpful.

Here are some links to SdC threads:

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

The original thread: http://forum.enjoysudoku.com/two-sector-disjoint-subsets-t2033.html

Please read the Sudopedia discussion: http://www.sudopedia.org/wiki/Talk:Sue_de_Coq

See also: http://homepages.cwi.nl/~aeb/games/sudoku/solving12.html

The basic idea is this:
Code:
+-----------+-----------+-----------+
|  @  ab @  |  @  @  @  | ( abcde ) |
|  .  .  .  |  .  .  .  |  #  #  #  |
|  .  .  .  |  .  .  .  |  #  #  cd |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
+-----------+-----------+-----------+
., @, #:  Any candidates
a, b, c, d, e:  Specific candidates
An SdC exists in one box and one line, in this case B3 and R1.

The three cells common to the line and the box (R1C789) together contain exactly five distinct candidates a,b,c,d, and e.

A cell in the line but not in the box (here, R1C2) contains only candidates a, b.

A cell in the box but not in the line (here, R3C9) contains only candidates c, d.

We can eliminate a, b, and e from all the cells marked @, and we can eliminate c, d, and e from all the cells marked #.

Explanation: Look at the three cells R1C789. Their solution cannot contain both a and b, nor can it contain both c and d. The solution of those three cells must be 1. (a or b), and 2. (c or d), and 3. (e).

1. is a pseudocell that makes a pair ab in R1.

2. is a pseudocell that makes a pair cd in B3.

3. eliminates e in the cells that are in R1 and not B3, and in the cells that are in B3 and not in R1.

Examples, and questions, to follow.

Keith


Last edited by keith on Wed May 25, 2011 9:55 am; edited 1 time in total
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun May 22, 2011 7:55 am    Post subject: Reply with quote

Nice diagram!

Code:
r1c2 = a  =>  r1c789+r3c9 = bcde  =>  (#) <> bcde
r1c2 = b  =>  r1c789+r3c9 = acde  =>  (#) <> acde

since one must be true            =>  (#) <> cde

Code:
r3c9 = c  =>  r1c789+r1c2 = abde  =>  (@) <> abde
r3c9 = d  =>  r1c789+r1c2 = abce  =>  (@) <> abce

since one must be true            =>  (@) <> abe


Regards, Danny
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keith



Joined: 19 Sep 2005
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Location: near Detroit, Michigan, USA

PostPosted: Sun May 22, 2011 2:14 pm    Post subject: Reply with quote

Example A

Here's an example:
Puzzle: FP042211
Code:
+-------+-------+-------+
| 8 7 . | 1 . . | . . . |
| . . 2 | . . . | 1 . 4 |
| . . . | . 5 9 | 7 8 . |
+-------+-------+-------+
| 3 . . | 4 . 6 | . . . |
| . . 7 | . . . | 9 . . |
| . . . | 8 . 3 | . . 6 |
+-------+-------+-------+
| . 4 5 | 9 . . | . . . |
| 2 . 3 | . . . | 4 . . |
| . . . | . . 7 | . 5 9 |
+-------+-------+-------+
After basics:
Code:
+-------------------+-------------------+-------------------+
| 8     7     69    | 1    23-6   4     | 2356  2369  235   |
| 59    356   2     | 7     36    8     | 1    -369   4     |
| 146   136   146   | 236   5     9     | 7     8     23    |
+-------------------+-------------------+-------------------+
| 3     1258  189   | 4     79    6     | 258   127   12578 |
| 46    68    7     | 25    12    125   | 9     34    38    |
| 59    125   149   | 8     79    3     | 25    1247  6     |
+-------------------+-------------------+-------------------+
| 7     4     5     | 9     12368 12    | 2368  1236  1238  |
| 2     9     3     | 56    168   15    | 4     167   178   |
| 16    168   168   | 23    4     7     | 23    5     9     |
+-------------------+-------------------+-------------------+
ab = 69
cd = 23
e   = 5

The Sue de Coq is in R1B3, making the eliminations shown.

Keith
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keith



Joined: 19 Sep 2005
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PostPosted: Sun May 22, 2011 2:29 pm    Post subject: Reply with quote

Example B

Here's another example:
Code:
Puzzle: M6306219sh(37)
+-------+-------+-------+
| 1 8 . | . . . | . 4 9 |
| . 9 4 | . . 1 | 6 7 . |
| . . . | . . 5 | . . . |
+-------+-------+-------+
| . 2 9 | . . 3 | . . . |
| . . . | 1 . 8 | . . . |
| . . . | 5 . . | 3 8 . |
+-------+-------+-------+
| . . . | 7 . . | . . . |
| . 4 1 | 2 . . | 8 9 . |
| 9 5 . | . . . | . 2 6 |
+-------+-------+-------+
After basics:
Code:
+----------------+----------------+----------------+
| 1    8    235  | 6    237  27   | 25   4    9    |
| 235  9    4    | 38   238  1    | 6    7    35   |
| 2367 367  2367 | 9    4    5    | 12   13   8    |
+----------------+----------------+----------------+
| 8    2    9    | 4    6    3    | 157  15  1-57  |
| 3457 37   357  | 1    27   8    | 9    6    24   |
| 467  1    67   | 5    9    27   | 3    8    24   |
+----------------+----------------+----------------+
| 236  36   2368 | 7    1358 9    | 4   -135  135  |
| 37   4    1    | 2    35   6    | 8    9    357  |
| 9    5    378  | 38   138  4    | 17   2    6    |
+----------------+----------------+----------------+
ab = 35
cd = 17
e  = 6
The Sue de Coq is in C9B9, making the eliminations shown. (Edited to add "e = 6" above.)

By the way, the elimination in R4C9 is also made by an XY-wing 13-5. After that:
Code:
+----------------+----------------+----------------+
| 1    8    235  | 6    237  27   | 25   4    9    |
| 235  9    4    | 38   238  1    | 6    7    35   |
| 2367 367  2367 | 9    4    5    | 12   13   8    |
+----------------+----------------+----------------+
| 8    2    9    | 4    6    3    | 157  15   17   |
| 3457 37   357  | 1    27   8    | 9    6    24   |
| 467  1    67   | 5    9    27   | 3    8    24   |
+----------------+----------------+----------------+
| 236  36   2368 | 7    1358 9    | 4   *135  135  |
| 37   4    1    | 2    35   6    | 8    9    357  |
| 9    5    378  | 38   138  4    | 17   2    6    |
+----------------+----------------+----------------+
I am not sure I would ever recognize this as an SdC. Are there other ways to see that R7C8 <>1?

Keith


Last edited by keith on Sun May 22, 2011 5:45 pm; edited 2 times in total
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JC Van Hay



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Location: Charleroi, Belgium

PostPosted: Sun May 22, 2011 3:43 pm    Post subject: Reply with quote

"M-Loop" : 1r7c9-(1=7)r4c9-7r4c7=(7-1)r9c7@ => -1r7c8
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keith



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Location: near Detroit, Michigan, USA

PostPosted: Sun May 22, 2011 5:49 pm    Post subject: Reply with quote

JC Van Hay wrote:
"M-Loop" : 1r7c9-(1=7)r4c9-7r4c7=(7-1)r9c7@ => -1r7c8
JC's logic is fine, though it is a different pattern from a Sue de Coq. (And, it answers the question I asked.)

Keith
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ronk



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Posts: 397

PostPosted: Sun May 22, 2011 7:14 pm    Post subject: Reply with quote

JC Van Hay wrote:
"M-Loop" : 1r7c9-(1=7)r4c9-7r4c7=(7-1)r9c7@ => -1r7c8

Instead of that, I see ... (1)r7c9 = (1-7)r4c9 = (7)r4c7 - (7=1)r9c7 - loop
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keith



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PostPosted: Sun May 22, 2011 8:08 pm    Post subject: Reply with quote

I have edited the Sudopedia article

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

so I now believe it is less incorrect.

Keith
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keith



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PostPosted: Sun May 22, 2011 10:13 pm    Post subject: Reply with quote

Example C

The original Sue de Coq:
http://forum.enjoysudoku.com/two-sector-disjoint-subsets-t2033.html
Code:
 4 . . | 2 . . | 1 . .
 . . 6 | . . 4 | . . .
 7 . . | 8 5 . | . . .
-------+-------+------
 2 5 . | 4 . . | . . 1
 . . . | . . . | . . .
 8 . . | . . 3 | . 9 7
-------+-------+------
 . . . | . 7 9 | . . 3
 . . . | 1 . . | 6 . .
 . . 8 | . . 2 | . . 4
After basics:
Code:
+-------------------+-------------------+-------------------+
| 4     389  -35    | 2     39    6     | 1     7     58    |
|1-359  12389 6     | 7     39    4     | 289   238   258   |
| 7     239   23    | 8     5     1     | 249   234   6     |
+-------------------+-------------------+-------------------+
| 2     5     9     | 4     8     7     | 3     6     1     |
| 36    367   37    | 9     1     5     | 248   248   28    |
| 8    -14    14    | 6     2     3     | 5     9     7     |
+-------------------+-------------------+-------------------+
| 16   -1246  14    | 5     7     9     | 28    128   3     |
| 35    237   2357  | 1     4     8     | 6     25    9     |
| 159   19    8     | 3     6     2     | 7     15    4     |
+-------------------+-------------------+-------------------+
ab = 19
cd = 23
e  = 8
The line is C2, the box is B1. Making the eliminations shown.

In this same grid, there is a second SdC:
Code:
+-------------------+-------------------+-------------------+
| 4     389   35    | 2     39    6     | 1     7     58    |
|1-35-9 1-2-38-9 6  | 7     39    4     | 289   238   258   |
| 7     239   23    | 8     5     1     |-249  -234   6     |
+-------------------+-------------------+-------------------+
| 2     5     9     | 4     8     7     | 3     6     1     |
| 36    367   37    | 9     1     5     | 248   248   28    |
| 8     14    14    | 6     2     3     | 5     9     7     |
+-------------------+-------------------+-------------------+
| 16    1246  14    | 5     7     9     | 28    128   3     |
| 35    237   2357  | 1     4     8     | 6     25    9     |
| 159   19    8     | 3     6     2     | 7     15    4     |
+-------------------+-------------------+-------------------+
ab = 39
cd = 58
e = 2
The line is R2, the box is b3. Making the eliminations shown.

Our drag queen (the boy named Sue), then says:
Quote:
and that {r7c1,r7c2,r7c3} contains three of {1,3,5,6,9} with the other three values in r5c1 and r9c2, so we eliminate r2c1=9, r2c2=3, r2c2=9 and r7c3=1.
This appears to be a typo: {r7c1,r7c2,r7c3} should be r789c1.

There is a third SdC in C1 and B7:
Code:
+-------------------+-------------------+-------------------+
| 4     389   35    | 2     39    6     | 1     7     58    |
|1-3-59 12389 6     | 7     39    4     | 289   238   258   |
| 7     239   23    | 8     5     1     | 249   234   6     |
+-------------------+-------------------+-------------------+
| 2     5     9     | 4     8     7     | 3     6     1     |
| 36    367   37    | 9     1     5     | 248   248   28    |
| 8     14    14    | 6     2     3     | 5     9     7     |
+-------------------+-------------------+-------------------+
| 16   -1246 -14    | 5     7     9     | 28    128   3     |
| 35    237   23-57 | 1     4     8     | 6     25    9     |
| 159   19    8     | 3     6     2     | 7     15    4     |
+-------------------+-------------------+-------------------+
ab = 36
cd = 19
e  = 5
Making the eliminations shown.

(Edit: Corrected, thanks to Danny.)

Does anyone agree or disagree with this analysis?

Keith


Last edited by keith on Mon May 23, 2011 2:37 am; edited 2 times in total
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daj95376



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Posts: 3855

PostPosted: Sun May 22, 2011 11:58 pm    Post subject: Reply with quote

HoDoKu v2.0.1 does not agree ...

(Keith: Yes. Correction made.)

Note: on an earlier puzzle where you use a given, e=6, HoDoKu only uses two cells.

Code:
r78c9 - {1357} (r2c9 - {35}, r9c7 - {17}) => r7c8<>1, r4c9<>5


(Edited by Keith to remove comment details now that corrections have been made.)
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keith



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PostPosted: Mon May 23, 2011 1:16 am    Post subject: Reply with quote

Danny,

Thank you. I have made some corrections.
daj95376 wrote:
Note: on an earlier puzzle where you use a given, e=6, HoDoKu only uses two cells.

Code:
r78c9 - {1357} (r2c9 - {35}, r9c7 - {17}) => r7c8<>1, r4c9<>5
Originally, in Example B, I did not include the solved cell R9C9 = 6 as e. Then, I realized that the basic original template still applies when you do include it. Sure, you can make a special case when only two of the three common cells are unknown, but why?

I guess I was very surprised to find an error in the original Sue de Coq post. It's been around for years!

Keith
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keith



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PostPosted: Mon May 23, 2011 3:36 am    Post subject: Reply with quote

Example D

http://forum.enjoysudoku.com/post16664.html#p16664

ronk has a Sue de Coq example which makes a lot of eliminations, and solves an intractable puzzle:
Code:
Puzzle: ronkSdC
+-------+-------+-------+
| . 6 . | . . . | 8 3 . |
| . 2 5 | . . . | . 1 . |
| . . . | . 1 6 | . . . |
+-------+-------+-------+
| . . 7 | . 6 . | . . . |
| 8 . . | 4 . 5 | 7 . 3 |
| . . . | . . . | . 8 . |
+-------+-------+-------+
| . . 2 | . . . | 1 9 . |
| . 5 . | . . 8 | . . . |
| 4 . . | . . 7 | . . . |
+-------+-------+-------+
After basics:
Code:
+----------------------+----------------------+----------------------+
| 179    6      149    | 2579 -24-57-9 249    | 8      3      24579  |
| 379    2      5      | 379    8      349    | 469    1      4679   |
| 379    34789  3489   | 23579  1      6      | 2459   2457   24579  |
+----------------------+----------------------+----------------------+
| 25     349    7      | 8      6      1239   | 2459   245    12459  |
| 8      19     169    | 4      29     5      | 7      26     3      |
| 25     349    3469   | 2379 -237-9   1239   | 24569  8      124569 |
+----------------------+----------------------+----------------------+
| 367    378    2      |-3-56   345    34     | 1      9      45678  |
| 13679  5      139    |12-369  2349   8      | 2346   2467   2467   |
| 4      1389   1389   |12-3-569 2359  7      | 2356   256    2568   |
+----------------------+----------------------+----------------------+
ab = 29
cd = 34
e  = 5

The SdC is in C5B8, making the eliminations shown. [Edited to fix a typo in R9C4.]

Keith


Last edited by keith on Mon May 23, 2011 8:11 pm; edited 1 time in total
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ronk



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Posts: 397

PostPosted: Mon May 23, 2011 4:12 am    Post subject: Reply with quote

keith, the SDC is subsumed by the doubly-linked ALS-xz.
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keith



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PostPosted: Tue May 24, 2011 1:00 am    Post subject: Reply with quote

ronk wrote:
keith, the SDC is subsumed by the doubly-linked ALS-xz.
ronk, you are correct, but (except for more examples), I'm going to stop here with the theory. The linked ALS patterns get very complicated very quickly.

My goal is to lay out patterns that might be useful for pencil and paper solvers. Let's see how useful this basic pattern turns out to be. If what has been laid out so far is not useful, there is no point in going farther.

Keith
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Tue May 24, 2011 2:30 am    Post subject: Reply with quote

keith wrote:
ronk wrote:
keith, the SDC is subsumed by the doubly-linked ALS-xz.
ronk, you are correct, but (except for more examples), I'm going to stop here with the theory. The linked ALS patterns get very complicated very quickly.

My goal is to lay out patterns that might be useful for pencil and paper solvers. Let's see how useful this basic pattern turns out to be. If what has been laid out so far is not useful, there is no point in going farther.

Keith


Keith, I didn't see the following link above. It is in the way of a mini-primer for manual solvers with some graphic examples (hide the kids Smile ):
http://forum.enjoysudoku.com/sue-de-coq-revisited-again-asi-1-t6410.html

My interest in Sue-de-Coq developed mainly as a pattern that should be of great interest to manual/pencil&paper solvers, but which seemed to be very under-used. In the 2+ years since the thread above, I have found the SDC to be relatively easy-to-learn (and find) and frequent enough to be well-worth adding to one's toolbag, especially considering how powerful it is.

Following up on your point above: In spite of having also put up 2 ALS-primer threads including dual-linked ALS-xz examples (those threads specifically aimed at manual solvers), I have found that a Sue-de-Coq pattern is much easier to find than the associated dual-linked ALS patterns. I don't think this just applies to me, because I practically never see dual-link ALS patterns in the solutions of others.
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keith



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PostPosted: Tue May 24, 2011 3:16 am    Post subject: Reply with quote

DonM wrote:
Keith, I didn't see the following link above. It is in the way of a mini-primer for manual solvers with some graphic examples (hide the kids Smile ):
http://forum.enjoysudoku.com/sue-de-coq-revisited-again-asi-1-t6410.html

My interest in Sue-de-Coq developed mainly as a pattern that should be of great interest to manual/pencil&paper solvers, but which seemed to be very under-used. In the 2+ years since the thread above, I have found the SDC to be relatively easy-to-learn (and find) and frequent enough to be well-worth adding to one's toolbag, especially considering how powerful it is.

Following up on your point above: In spite of having also put up 2 ALS-primer threads including dual-linked ALS-xz examples (those threads specifically aimed at manual solvers), I have found that a Sue-de-Coq pattern is much easier to find than the associated dual-linked ALS patterns. I don't think this just applies to me, because I practically never see dual-link ALS patterns in the solutions of others.

DonM,

I think we are in violent agreement! I had not seen the specific thread you mention, but there are a couple of similar ones. I did not quote them, because they stray to more general patterns than are defined and described in this thread.

I also have the feeling that the utility of the Sue de Coq may have been diminished in the last couple of years by M-wings, W-wings, and the like. Not that they are variants of the same pattern as the SdC, but they can often be used to make the same eliminations.

Nonetheless, I think the basic Sue de Coq pattern is incredibly elegant, and easy to recognize. It belongs in our toolboxes.

Keith
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DonM



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Posts: 51

PostPosted: Sun May 29, 2011 6:46 pm    Post subject: Reply with quote

keith wrote:
DonM wrote:
Keith, I didn't see the following link above. It is in the way of a mini-primer for manual solvers with some graphic examples (hide the kids Smile ):
http://forum.enjoysudoku.com/sue-de-coq-revisited-again-asi-1-t6410.html

My interest in Sue-de-Coq developed mainly as a pattern that should be of great interest to manual/pencil&paper solvers, but which seemed to be very under-used. In the 2+ years since the thread above, I have found the SDC to be relatively easy-to-learn (and find) and frequent enough to be well-worth adding to one's toolbag, especially considering how powerful it is.

Following up on your point above: In spite of having also put up 2 ALS-primer threads including dual-linked ALS-xz examples (those threads specifically aimed at manual solvers), I have found that a Sue-de-Coq pattern is much easier to find than the associated dual-linked ALS patterns. I don't think this just applies to me, because I practically never see dual-link ALS patterns in the solutions of others.

DonM,

I think we are in violent agreement! I had not seen the specific thread you mention, but there are a couple of similar ones. I did not quote them, because they stray to more general patterns than are defined and described in this thread.

I also have the feeling that the utility of the Sue de Coq may have been diminished in the last couple of years by M-wings, W-wings, and the like. Not that they are variants of the same pattern as the SdC, but they can often be used to make the same eliminations.

Nonetheless, I think the basic Sue de Coq pattern is incredibly elegant, and easy to recognize. It belongs in our toolboxes.

Keith


In my Sudoku discussions I think that some of my opinions have pushed one or two people to a point of violence, but never from a position of agreement! Very Happy

Interestingly enough, I went back into my solving archives and found it ironic (given my comment in bold above) that the only puzzle solution I've ever posted in Other Puzzles here (I think) was a dual-linked ALS (towards the bottom of the following thread-I still don't know how to link to a specific post):

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=20026#20026


Last edited by DonM on Sun May 29, 2011 8:13 pm; edited 2 times in total
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun May 29, 2011 7:27 pm    Post subject: Reply with quote

Quote:
I still don't know how to link to a specific post


http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=22493#22493

Look at the second sticky topic in the site help section.

Keith
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Sun May 29, 2011 8:13 pm    Post subject: Reply with quote

keith wrote:
Quote:
I still don't know how to link to a specific post


http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=22493#22493

Look at the second sticky topic in the site help section.

Keith


Well, that was easy! (Have edited the link.) Thanks Keith.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Jun 15, 2011 4:39 pm    Post subject: Reply with quote

I was traveling this past month so didn't see this thread. As someone who occasionally spots and utilizes Sue de Coq, I would quibble only slightly with the definition above as being over-determined, as I'll try to explain. Also, the definitions in the various links seem overly complicated given the basic pattern involved. How easy this pattern is to spot probably varies from person to person but describing it shouldn't make the job more difficult than necessary.

Here's my attempt to define the pattern most generally in the simplest "visual pattern" terms I can think of. I use abbreviations that match the pattern's structure. I'll label an example with the abbreviations to help make it clear.


A Sue de Coq involves n candidates in n cells arranged in a particular way within two houses, a Box (B) and a Row or Column (RC) that overlaps with the Box. I'll use "S" to refer to each of the n Sue de Coq cells. These n cells fall into 3 groups: (1) at least 2 of the 3 overlap cells ("OLS"); (2) at least one of the RC cells not in the overlap ("RCS"); and (3) at least one of the B cells not in the overlap ("BS"). The final requirement is that the RCS and BS cells can have no digit in common.

The victim cells fall into 2 groups: (1) non-Sue de Coq cells within the Box ("BV"); and (2) non-Sue de Coq cells within the Row or Column ("RCV").

Eliminations: (1) All digits in the RCS cells can be eliminated from the RCV cells, and (2) all digits in the BS cells can be eliminated from the BV cells, and (3) if the OLS cells contain a digit not found in either the BS or RCS cells that digit can be eliminated from all of the victim cells.


Using the second example in the "Example C" post:
Code:
+----------------------+-------------------+--------------------+
| 4  OLS:389  OLS:35   | 2     39    6     | 1     7  RCS:58    |
|1-35-9  1-2-38-9 6    | 7     39    4     | 289   238    258   |
| 7   BS:239   BS:23   | 8     5     1     | 249   234    6     |
+----------------------+-------------------+--------------------+
| 2      5        9    | 4     8     7     | 3     6      1     |
| 36     367      37   | 9     1     5     | 248   248    28    |
| 8      14       14   | 6     2     3     | 5     9      7     |
+----------------------+-------------------+--------------------+
| 16     1246     14   | 5     7     9     | 28    128    3     |
| 35     237      2357 | 1     4     8     | 6     25     9     |
| 159    19       8    | 3     6     2     | 7     15     4     |
+----------------------+-------------------+--------------------+

This is a 5-digit, 5-cell Sue de Coq. The BS digits are 239; the RCS digits are 58 (these two groups have no digits in common, as required). In this case, there are no eliminations in the potential RC victim cells and there is no digit unique to the OLS cells for the third sort of elimination. (I removed the eliminations shown in r3c78 in the previous post because they are consequential eliminations due to locked candidates and not eliminations immediately due to the Sue de Coq.)

To avoid clutter I didn't label the potential victim cells. To make sure they are clear, here is a diagram:
Code:
+----------------+---------------+-------------+
| RCV/BV   S   S | RCV  RCV  RCV | RCV  RCV  S |
|     BV  BV  BV |   -    -    - |   -    -  - |
|     BV   S   S |   -    -    - |   -    -  - |
+----------------+---------------+-------------+


Additional comments...

The smallest possible SdC requires 4 cells and the largest could involve, conceivably, 9 cells (though whether such a creature occurs in the real world I don't know).

There can be multiple RCS cells and multiple BS cells and they aren't limited to bivalue cells. (The example above has two BS cells, one a trivalue cell.)

In the example, I show 2 OLS cells rather than three. Since the third OL cell is a solved cell, it could be included (forming a 6-cell/digit SdC) without contradicting the definition. However, we don't usually consider solved cells to be parts of solving patterns. In addition, I believe that such a non-SdC third OL cell does not necessarily need to be a solved cell and is thus a potential victim (though I don't have an example to prove this).

At most there can be only one digit in the OLS cells not contained in either the RCS or BS cells and causing the third sort of elimination from all possible victim cells.

As already mentioned, all Sue de Coqs can be seen as overlapping ALS closed AIC loops. For those familiar with such things, that is probably the easiest way to understand the underlying logic. Otherwise, one must do a bunch of "if-then" reasoning exhausting the solution possibilities to convince oneself that the pattern works as described. While this ALS connection is interesting and worth pursuing, definitions of the pattern that rely on ALS (or AALS or AAAAAALS) descriptions strike me as too many trees and not enough forest.
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