Sue de Coq
What is Sue de Coq?
Sue de Coq is a master-level Sudoku technique named after its discoverer, Sue de Coq. It's a specialized pattern that combines Almost Locked Set logic with geometric constraints at box-line intersections.
The pattern involves three components: an ALS at the intersection of a box and line (row or column), a companion set in the same line outside the box, and another companion set in the same box outside the line. When these sets partition candidates in a specific way, multiple eliminations become possible.
What makes Sue de Coq elegant is how it exploits the overlapping structure of Sudoku units. The intersection cells belong to both a line and a box, creating unique logical opportunities that don't exist elsewhere in the grid.
Why is it called "Sue de Coq"?
Unlike most Sudoku techniques named descriptively (like X-Wing or Naked Pairs), Sue de Coq is named after a person—Sue de Coq, who discovered and documented this pattern. It's a tribute to her contribution to advanced Sudoku solving techniques.
It's sometimes abbreviated as "SdC" in solving forums and literature.
Why It Matters
Sue de Coq matters because it:
- Enables powerful eliminations — Can eliminate candidates in both the line and box simultaneously
- Exploits geometric structure — Uses box-line intersections in ways other techniques don't
- Combines ALS with position — Shows how abstract sets interact with grid geometry
- Appears in difficult puzzles — Many expert-level puzzles require Sue de Coq or similar techniques
- Generalizes simpler patterns — Can be viewed as an extension of Pointing Pairs and Box-Line Reduction
Step-by-Step: How to Find Sue de Coq
- Find a box-line intersection — Focus on the three cells where a row or column intersects a box.
- Check for ALS in intersection — The intersection cells should form an ALS (N cells with N+1 candidates).
- Identify line companion set — Find cells in the same line (outside the box) that contain some of the ALS candidates.
- Identify box companion set — Find cells in the same box (outside the line) that contain some of the ALS candidates.
- Verify candidate partition — The total candidates should partition into: intersection-only, line-companion-only, and box-companion-only sets.
- Eliminate candidates — Remove line-only candidates from the rest of the line, and box-only candidates from the rest of the box.
Sue de Coq Example
Setup
Focus on Row 5 intersecting Box 6 (cells R5C7, R5C8, R5C9):
- Intersection ALS: R5C7={2,8}, R5C8={2,5,8} → 2 cells with 3 candidates {2,5,8}
- Line companion (Row 5, outside Box 6): R5C2={5,9}, R5C4={9} → candidates {5,9}
- Box companion (Box 6, outside Row 5): R4C9={2,7}, R6C8={7} → candidates {2,7}
Analysis
Total candidates in all sets: {2,5,7,8,9}. Count total cells: 2 (intersection) + 2 (line companion) + 2 (box companion) = 6 cells. But we only have 5 unique candidates? Let me recount...
Actually, for Sue de Coq to work, the union of candidates should equal the total number of cells involved. Let me provide a corrected example:
Corrected Setup
- Intersection: R3C1={4,8}, R3C2={4,7,8} → candidates {4,7,8}
- Line companion (Row 3, outside Box 1): R3C5={7,9} → candidates {7,9}
- Box companion (Box 1, outside Row 3): R1C2={4,5}, R2C1={5,9} → candidates {4,5,9}
Logic
The intersection cells contain {4,7,8}. Candidates {7,9} appear in the line companion. Candidates {4,5,9} appear in the box companion. Since the intersection, line, and box must collectively lock these candidates, you can eliminate {7,9} from other cells in Row 3, and {4,5,9} from other cells in Box 1.
Visual Example
Imagine Row 7 intersecting Box 9:
- Intersection (R7C7, R7C8, R7C9): Contains candidates {1,3,6}
- Rest of Row 7: Candidate 3 appears in R7C2={3,5}
- Rest of Box 9: Candidate 6 appears in R8C7={6,8}
Partition:
- Candidate 1: intersection only
- Candidate 3: intersection + line companion
- Candidate 6: intersection + box companion
Eliminations: Since 3 is handled by intersection+line, eliminate 3 from rest of Row 7 (excluding R7C2 and intersection). Since 6 is handled by intersection+box, eliminate 6 from rest of Box 9 (excluding R8C7 and intersection).
Strategies for Finding Sue de Coq
- Scan box-line intersections — Focus on the 27 intersection points (9 boxes × 3 lines each).
- Look for ALS in intersections — Check if the intersection cells form an ALS.
- Check for candidate extensions — See if intersection candidates extend into both the line and box.
- Count carefully — Verify that total cells equals total unique candidates for the lock to work.
- Use candidate highlighting — Color-coding makes partitioning visible.
- Practice with software — Use solvers that identify Sue de Coq to learn pattern recognition.
Common Pitfalls
- Incorrect candidate counting — The total unique candidates must match the total cells for the pattern to work.
- Missing the ALS — The intersection cells must form an ALS (N cells with N+1 candidates).
- Wrong elimination targets — Only eliminate candidates that are exclusive to line companion or box companion, not shared ones.
- Confusing with simpler techniques — Sometimes what looks like Sue de Coq is actually a simpler Pointing Pair or Box-Line Reduction.
- Incomplete verification — Must verify all components (intersection ALS, line companion, box companion) before making eliminations.
Practice: Identify Sue de Coq
Scenario: Column 4 intersects Box 2 at R1C4, R2C4, R3C4. These cells contain {2,6,7}. In Column 4 outside Box 2, cells contain candidate 7. In Box 2 outside Column 4, cells contain candidate 2.
Question: Is this a valid Sue de Coq, and what can you eliminate?
Answer: Let's verify: Intersection has 3 cells with 3 candidates {2,6,7}. This is a Naked Triple (locked set), not an ALS. For Sue de Coq, you need an ALS (N cells with N+1 candidates). This pattern might allow eliminations through the Naked Triple rule, but it's not Sue de Coq. For Sue de Coq, you'd need the intersection to have, for example, 3 cells with 4 candidates.
Why Sue de Coq Matters
Sue de Coq demonstrates the power of combining set theory with geometric structure. It shows that:
- Box-line intersections create unique logical opportunities
- ALS patterns can be enhanced with positional constraints
- Complex eliminations can arise from structured pattern recognition
- Named techniques contribute to the solving community's shared knowledge
While rare and complex, Sue de Coq is a valuable tool for expert-level puzzles and demonstrates the mathematical beauty of Sudoku's structure.
Quick Recap
| Technique | How it Works | Difficulty |
|---|---|---|
| Sue de Coq | ALS at box-line intersection with companions creates dual eliminations | Master |
| ALS-XZ | Two ALS connected by RCC enable eliminations | Master |
| Pointing Pairs | Candidates confined to box-line intersection eliminate from line | Intermediate |
Final Thought
Sue de Coq is a testament to the Sudoku community's creativity—a pattern discovered by a solver exploring the intersection of set theory and geometry. It's named recognition for original logical insight, and mastering it honors that contribution while adding a powerful tool to your solving arsenal.
Frequently Asked Questions
What is Sue de Coq in Sudoku?
Sue de Coq is a master-level Sudoku technique discovered by Sue de Coq. It involves a specific pattern at box-line intersections where an Almost Locked Set combines with two companion sets. The pattern enables multiple eliminations through geometric and set-based logic.
How does Sue de Coq work?
Sue de Coq requires an ALS in the intersection of a box and line (row or column), plus two companion sets: one in the same line outside the box, and one in the same box outside the line. The candidates partition into sets that eliminate from both the line and box.
What is required for a valid Sue de Coq pattern?
A valid Sue de Coq needs: (1) an ALS at a box-line intersection, (2) a set of cells in the same line outside the box, (3) a set of cells in the same box outside the line, (4) the union of all candidates equals the number of cells involved, creating a locked configuration.
Who discovered Sue de Coq?
Sue de Coq was discovered by and named after Sue de Coq, a Sudoku enthusiast who identified this pattern in the mid-2000s. It's one of the few Sudoku techniques named after a person rather than a descriptive name.
Is Sue de Coq related to ALS-XZ?
Yes, Sue de Coq is a specialized ALS-based technique. While ALS-XZ connects any two ALS through restricted commons, Sue de Coq has a specific geometric structure at box-line intersections with particular elimination patterns. Both use Almost Locked Set logic.
Practice Sue de Coq
Explore more ALS techniques: ALS-XZ or ALS Chains.