Sudoku **Sue De Coq** is a Clustering Counting variation initially introduced by a user with the pseudonym “Sue de Coq” as “Two-Sector Disjoint Subsets,” which is a bit of a mouthful. However, other users quickly began to refer to the approach as “Sue de Coq” (SDC), the inventor’s moniker, and the term has stuck ever since. The approach is simple in its most basic form, but it has been improved upon multiple times.

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Because we recognize Locked Sets, this exotic method is tightly connected to simple patterns like Naked Pairs and Naked Triples. The construction pieces are Almost Locked Sets, but the alignment of these parts is the most intriguing feature.

To re-cap the terms:

- A Naked Pair is an example of a Locked Set, a collection of N cells that can see each other and have N candidates.
- An Almost Locked Set is a collection of N cells that are all visible to each other and share N+1 candidates somehow.

We can take the following steps in order:

- An Almost Locked Set is a collection of N cells that are all visible to each other and share N+2 candidates somehow.
- An Almost Locked Set is a collection of N cells that are all visible to each other and share N+3 candidates in some way. And so forth. Horrible names that are frequently shortened as AALS, AAALS, and so on.

**Image of a Sue de Coq**

Contents

**Examples of Sue-De-Coq**

**Example 1:Â **

Sue-De-Coq, called after the forum handle of the intelligent man who discovered it, begins with an AALS that must be aligned in a row or column AND completely enclosed within a box. As a result, the AALS group is limited to two or three cells.

The two yellow cells (N=2) in the first example contain 2,3,5,8, which is N+2, or four possibilities. Box 4 is where the group is kept. We are unaware of the value 2,3,5,8; either which one will answer D2 and E2, but we may be certain that two of them will be. We can now locate single cells with two possibilities if we look along with the alignment unit in column 2 and within the box. 2,8 (the green cell) is found in B2, whereas 3,5 is found in F3. These cells are visible to the AALS, which is crucial!

We now know that the AALS D2, E2 solution cannot be 2/8 or 3/5 since it would leave nothing in cells B2 and F3.

The reasoning goes like this: If neither 2/8 nor 3,5 can complete the AALS, another combination must be used to fill it, leaving a digit open for the single bi-value cells. As a result, 2,3,5,8 must successfully occupy all colored cells. Because the overall group has four cells and four candidates, we’ve classified it as a Locked Set. This suggests that all candidates X who view all X in the whole group can be removed. This eliminates the 8 in C2 and J2 (aligned in the column), the 2 in G2 while the 3 in E3 both of them are alligned in the columns (shares the box).

**Sue-De-Coq Example 2:Â **

Example of a Load or: From the Beginning We identified a four-cell Locked Set in the example above, a rather simple pattern. Sue-De-Coq can also be utilized in more complex designs, such as the second one. To build the 4-cell locked sets in the first example, we used bi-value single cells as ‘hooks.’ Bi-value cells contain two candidates in one cell; they are Almost Locked Sets by definition. Sue-De-Coq can build the pattern with bigger ALSs.

We combine an AAALS (N+3) in E7, E8 holding 1,3,6,7,8 with two regular ALSs D9, F9, and E2 carrying 1,3,7 and 6/8 correspondingly in the second case. The key is that the total number of cells, 5, equals the total number of candidates in all 1,3,6,7,8 cells. Thus, a 5-cell Locked Set is given to us.

We look at who can see ALL the candidates INSIDE the pattern from outside the pattern to remove candidates. For example, in row E, these are the 6s and 8s, and in box 6, these are the 1s, 3s, and 7s.

Sue-De-general Coq’s norms

In broad terms, the pattern’s rule is as follows:

- Group C is a 2-cell or 3-cell group within a box aligned on a row or column.
- V is a group of candidates in C that must be two or more than the number of cells in C (N+2, N+3, ALS, and so on).
- We must discover at least one bi-value cell (or bigger ALS) in the row or column that solely includes candidates from set V referred to as D.
- In the box, we need to discover at least one bi-value cell (or bigger ALS) that solely includes candidates from set V, dubbed E.
- Each of the candidates in D and E must be unique.
- Remove any candidates in the row or column common to C+D but are not in the cells covered by C or D.
- Remove any candidates in the box common to C+E but are not in the cells covered by C or E.

**Types of Sue De Coq**

**Type 1**

If you can locate two Bi-Value Cells that,

- There isn’t a single candidate that everyone agrees on.
- The first Cell of a Square (Square-1) and the second Cell of a Row (Row-2) share Square-1.
- However, they are not on the same Row.

If two of the Cells common to Square-1 and Row-2 only include combinations of the Candidates present in the two Bi-Value Cells, these four Cells create a Sue De Coq Type 1 pattern.

The removal of such a pattern is possible when;

- all candidates present in Square-1’s initial Bi-Value Cell
- the second Bi-Value Cell from Row-2, all Candidates are present.

Except for the cells that are part of the pattern

Indeed, the pattern’s four Cells only include combinations of four Candidates who view each other. Each of these Candidates must be the answer in one of the pattern’s Cells. When “Row” is replaced with “Column,” the same logic applies.

Type 1 is entirely based on the Bi-value Cells J7 and A8 and Cells H8 and J8 in the example above. Candidate 9 must be the solution in either J7, J8, or H8, which excludes it from H7 and H9. Candidate 6 must be the solution in either A8 or H8, which eliminates it from E8. Candidate 8 must also be the answer in A8, H8, or J8, which rules it out of E8.

**Type 2**

If you can locate two Bi-Value Cells that,

- have nothing in common candidate
- with the first Cell of a Square (Square-1) and the second Cell of a Row (Row-2) that shares Cells with Square-1
- they are not on the same Row.

If the Cells common to Square-1 and Row-2 only include combinations of the Candidates present in the two Bi-Value Cells plus one extra candidate, the pattern Sue De Coq Type 2 is formed. The removal of such a pattern is possible when

- all candidates present in Square-1’s initial Bi-Value Cell
- the second Bi-Value Cell from Row-2, all Candidates are present.
- both Square-1 and Row-2’s other candidate

except for the cells that are part of the pattern

The pattern’s five Cells only contain combinations of five Candidates who view each other. Each of these Candidates must be the answer in one of the pattern’s Cells. When “Row” is replaced with “Column,” the same logic applies.

The Sue De Coq Type 2 in the example above is made up of Bi-Value Cells B7 and A2 and Cells A7, A8, and A9. Candidate 5 must be the solution in either B7, A7, A8, or A9, which removes it from C7 and C9; candidate two must be the solution in either A2 or A9, which eliminates it A3 and A6. Candidate 8 must also be the answer in A2, A7, or A9, which rules it out of A3. Finally, candidate three must be the correct answer in A7, A8, or A9, ruling it out of A6 and C7.

**The Techniques Of Sue De Coq**

The Sue de Coq approach employs two intersecting sets A and B, where A is a set of N cells with N candidates in a line, B is a set of N cells with N candidates in a box, and the sets A – B and B – A have no candidates in common. The cells in the line that are not in A and the cells in the box that are not in B can be removed as candidates.

This strategy was first mentioned on the Sudoku Players’ forum by a member named Sue de Coq, who called it Two-Sector Disjoint Subsets, but a statement that this was a real Sue de Coq gave it its current name.

This approach may be expanded to create Three-Sector Disjoint Subsets. However, this is a very uncommon use. The Sue de Coq method is demonstrated in the image below;

Consider the point where row 3 and box 3 meet. It has 1,2,5,8,9 candidates. It can’t have both 2 and 9 in it since it would clash with r3c2. It can’t have both 5 and 8 because that would be incompatible with r1c7. 1 + (2 or 9) + must be present at the intersection (5 or 8). This allows us to rule out candidates for digit one from row 3 and box three, candidates for digits 2 and 9 from the rest of row 3, and candidates for digits 5 and 8 from the rest of box 3. (if there were any). These exclusions are shown in red.

Sue de Coq is a graceful and successful strategy that frequently results in several eliminations. Yet, despite this, the method is rarely employed.

**Sue De Coq Mathematical Algorithm’sÂ Â **

Sue de Coq is the name given to an elimination procedure by its creator in a forum post. One of the strategies to search for in a scan of every box of the line-marked grid is Sue de Coq or SdC. The original form and other comparable variants that are ideally suited for the bv scan are described first.

To track down a Sue de Coq Scan the bending areas, the intersections of box and line, the box and line remainders, and the chute (wall) with four matching possibilities.

When the genuine contents of the chute can be stated using the logical formula N(a+b)(c+d), where N is considered as a clue while the digit two is considred as a remainders include an ALS with value groups a and b, and another with value groups c and d, you have an original SdC.

One of the two chute cells accessible to candidates must have the letters an orb, while the other must include c or d. There are two possible logical expressions for the chute candidates. Only one of an ALS’s values can be given up; therefore, those in the ALS remainders alternate in the chute. Extra candidates in each remaining group, but outside of its ALS-matching chute, are eliminated. Extra applicants for the chute are weeded out.

Instead of a hint, a slink or aligned triple in one candidate satisfies the logical expression. Thus, for candidate N to be present in the chute solution, it must be present.

Frank longo’s Nasiest Book regarding Sudoku contains an example of the original SdC.

The Sc4 chute has been identified. The certain number is nine, and there are other options for alternates. I merely check at the remainders for matching ALS when a chute has enough numbers. Sc4 = 9(3+4)(5+8) has Bv accessible.

Both chute and bv 58 in the box remaining share the numbers 5 and 8. Therefore, the additional eight candidates are eliminated. The bv 34 requires 3 and 4 to alternate in the chute in the line remains, but there are no other candidates to remove. It demonstrates why the bv is the most effective ALS for Sue de Coq.

The original Sue de Coq is available in two variations. One arises when two values, generally two hints, must be present in the chute. To drive alternation in the single free cell, just one ALS is necessary.

The SASdC or Single Alternate SdC trial is a second single alternate form, with just one matching ALS in the remainings. In addition, a second word is added to the logical formula for chute contents to account for the chance that one set of alternatives is absent from the chute. The SASdC is discussed in further detail in The Guide’s Trials section.

The generalized SdC requires at least one cell in each remainder with candidates of these values alone, with two or three cells (c) to fill in the chute and at least two more values (v >=4 or 5). These are known as DJ cells. The values in the remainders’ DJ cells must be distinct.

The chute values that aren’t in each remainder’s DJ cells can then be removed from the non-DJ cells of the other remainder.

V = 34589 in 640 above. VR = 34, VB = 85, and V/VR = 589 have been deleted from r9c6 and V/VB = 349 has been removed from r2c4 and r4c4.

On the forum and many expert websites, Sue-de-generalized Coq’s version was the ideal technique to include cells with more than two values in Sue de Coq. Hobiger’s explanations of the cases mentioned above, for example, are based on the generalized version. When more DJ cells can be located, the fundamental reason for the generalization is to enable more than 4 or 5 candidate values in the chute.

Sudoku disagrees because total employment by ALS beyond the bv appears to have greater focus and is almost as successful as the generic SdC. In addition, multiple DJ cells in a leftover are likely to be ALS because they are restricted to the values of the chute.

The examples above demonstrate how the ALS form meets the subtle criteria of generalized ALS. As the ALS loses a matching value to the chute, the remaining ALS typically contains additional values that become stuck in the ALS cells. Thus, in the remainder, all alternative options for these locked values are ruled out.

Andrew Stuart’s The Logic of Sudoku is used as a final example. Andrew uses this example to illustrate Sue de Coq in general.

There are six values in the chute, but no certain numbers. Therefore, three DJ cells of 789, 89, and 23 provide generalized coverage of the three chute cells.

Recognizing that the ALS 789 may only release one value, the contents of NW r1 can be described as NWr1 = 5(2+3)(7+8+9). Thus, there is just one chute position that can hold five people. The other two values are locked in the ALS, resulting in eliminations, regardless of whether the matched value is 7, 8, or 9.

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