Sue de Coq

Sue de Coq is an elimination method that the Sudoku community named after its inventor, or at least, the clever nom de plume he or she adopted to post the method to a forum. After a possible remote pair chain and a unique rectangle scan, Sue de Coq, or SdC, is among the methods to look for in a bv related scan over every box of the line marked grid.

The signal for SdC is a chute that can be described by the logical expressions N(a+b)(c+d) or MN(a+b). In words, a chute, the intersection of box and line, containing a candidate of number a or number b, and a candidate of number c or number d, and one or more candidates for one more number. Or a chute containing two numbers for sure, and a candidate of number a or a candidate of different number b.

The “or” terms we  call “alternates”.  So we look for a possible clue, slink or aligned triple as the sure number, and two alternates, or we look for two sure numbers and a single alternate.

Actually, in his first post, Sue de Coq  described only the two alternate, original version, and allowed only the bv form of ALS. In Sysudoku, you’ll be introduced to two single alternate versions.

There’s no Sue de Coq yet, only a signal that there may be one. Now we look in the box remainder and the line remainder of the chute for

(1)   two distinct ALS having pairs of different numbers matching the two alternates, or

(2)   one or two ALS having two numbers matching the single alternate with two sure numbers, or

(3)   one ALS having two numbers matching one of the two alternates.

In the signal, there may be more than way to arrange alternates. If so, choose the alternates having  the two matching ALS. Now we have a Sue de Coq constructed: if(1), the original SdC if both ALS are bv.  If (2) we have a single alternate. If (3) we have an extreme form of SdC  suggested In Sysudoku for a last resort, the Single Alternate SdC, or SASdC. The SASdC is a trial method that borders on a logical method, because in some cases, the trial result can be spotted “by eye” whereupon the result is not subject to trial.

In (1) and (2), the matching remainder ALS supplies the alternate candidate that is not in the chute. As a result, any additional candidate of either number in the ALS remainder is removed, because it sees both the supplied ALS candidate and the chute candidate of its number.

Here is an example of the original SdC (1) above, from the reviews. It’s from Frank Longo’s The Nastiest Sudoku Book Ever, puzzle 640

The Sc4 chute is marked. The sure number is 9 and there are choices for possible alternates.  Where a chute has enough numbers, I just look at the remainders for matching ALS. Bv are available for

Sc4 =                      9(3+4)(5+8).

Numbers 5 and 8 are shared between the chute and bv 58 in the box remainder. In the line remainder, the bv 34 and the 2-cell ALS 578 share the (5+8) alternate. There’s no 3 or 4 to eliminate, but in the box remainder, 8r9c6  sees both  the bv 8 and the chute 8’s,

My first post on Sue de Coq was December 22, 2011. It carried my best homework assignment ever, having readers find all of the original SdC in Sue de Coq’s original post, each with its own eliminations. The assignment did not include ALS other than bv.

My next post of December 27, 2011 supplies the surprising checkpoint, and an unreported ALS alternate SdC in the original post. This post describes single alternate forms (2) and (3) as well. An example of the SASdC is included, with an explanation of how it works, but the full story of trials is told later, in the Sysudoku Trials page.

In the many reviews, I have found few SdC(1), no SdC(2) and maybe a dozen SASdC. What I did find was a set of examples on Bernhard Hobiger’s Hodoku site that illustrate the capabilities of ALS alternates in Sue de Coq. I added one of these to the Sysudoku Sue de Coq post of 12/27/11

In my review of Hodoku, the post devoted to Sue de Coq displays two more ALS examples, and makes an assignment for readers to do a third, for a Sysudoku example. One demonstrates a startling fact about remainder ALS of three or more values. Review the example and determine what it is. I’ll check you answer at the end of this page.

A Hodoku reader can choose any of the methods reported on, and order a puzzle designed to illustrate that method. Sue de Coq is included, and more examples of ALS based Sue de Coq could be generated. I’d be interested in any results you get beyond what I have here.

ALS Alternative SdC vs Generalized SdC

Later on the day of Sue de Coq’s historic post, he posted this “generalized version” of his elimination rationale:

Putting this in more familiar terms:

With two or three cells (c) to fill in the chute, and at least two more values (v >=4 or 5), the generalized SdC requires at least one cell in each remainder with candidates of these values only. Call these the dj cells.  The values in the dj cells of the remainders must be disjoint.

Then the chute values not in the dj cells of each remainder can be eliminated from the non-dj cells of the other remainder.

In 640 above, V = 34589. VR = 34, the VB =85, and V/VR = 589 is removed from r9c6 and V/VB = 349,  from r2c4 and r4c4.

Sue-de-Coq’s generalized version was accepted on the forum, and on many expert websites as the preferred way to include cells of more than two values in Sue de Coq. For example, Hobiger’s explanations of the examples linked above are based on the generalized version. The primary reason for the generalization is to allow more than 4 or 5 candidate values in the chute, when extra dj cells can be found.

Sysudoku doesn’t go along, because it seems that full employment by ALS beyond the bv has more focus and is practically as effective as the generalized SdC. Besides, being confined to the values of the chute, multiple dj cells in a remainder tend to be ALS.

The examples shown and linked above illustrate the ALS form satisfies tie subtle requirements of generalized ALS. The remainder ALS often contain  additional values that become locked in the ALS cells as the ALS loses a matching value to the chute. All other candidates of these locked values in the remainder are eliminated.

As a closing illustration, from Andrew Stuart’s The Logic of Sudoku. Andrew uses this case to explain generalized Sue de Coq.

The chute has 6 values and no sure numbers. Generalized coverage of the three chute cells is afforded by three dj cells of 789, 89, and 23.

However, recognizing that the ALS 789 can release only one value, we can describe the contents of NW r1 as NWr1 = 5(2+3)(7+8+9). One chute position that can only be filled with 5. No matter if the matching value is 7, 8 or 9 the other two values are locked in the ALS, producing eliminations.