Sudoku You know how to use Naked Pairs and Pointing Pairs to eliminate candidates within a single house. But what if you could harness the overlap between a row and a box to eliminate candidates from both at the same time? That’s the power of Sue de Coq.
Named after the Sudoku forum member who first described the technique in 2005, Sue de Coq (formally known as Two-Sector Disjoint Subsets) examines cells at the intersection of a line and a box and splits their combined candidate set into disjoint groups using Almost Locked Sets (ALS). The result is a dual-sector elimination that can remove candidates from both the rest of the line and the rest of the box simultaneously.
In this guide we explain the logic behind Sue de Coq, walk through a concrete example with before-and-after diagrams showing 6 candidate eliminations across 5 cells, and show you exactly how to recognise this pattern in your own puzzles.
✅ What is Sue de Coq?
Sue de Coq (Two-Sector Disjoint Subsets, or TSDS) is an expert-level Sudoku technique that exploits the overlap between a line (row or column) and a box to eliminate candidates from both houses.
The technique was first posted in 2005 on the Sudoku Players’ Forum by a contributor using the pseudonym “Sue de Coq.” It was later formalised under the name Two-Sector Disjoint Subsets because it partitions the intersection candidates into two disjoint groups across two sectors (the line and the box).
Sue de Coq looks at N cells at the intersection of a line and a box that together contain N+2 distinct candidates. Those extra two candidates (beyond what can fit in N cells) must be accounted for by an Almost Locked Set in the rest of the line and an ALS in the rest of the box — and their digit contributions must be disjoint.
🧠 How Two-Sector Disjoint Subsets work
Here is the formal structure of Sue de Coq:
Consider N cells at the intersection of a line (row or column) and a box. Let S be the union of all candidates in those N cells, with |S| = N+2.
Because there are only N cells but N+2 candidates, two of those digits cannot all fit within the intersection alone. Sue de Coq resolves this by finding two Almost Locked Sets (ALS) that account for the extra digits:
- Line ALS — an ALS in the rest of the line (same row or column, but outside the box). It contributes a subset of digits DL ⊆ S.
- Box ALS — an ALS in the rest of the box (same box, but outside the line). It contributes a subset of digits DB ⊆ S.
The remaining digits in S are the locked digits — candidates that appear in every intersection cell and must be placed somewhere within the intersection.
1. DL ∩ DB = ∅ (the ALS contributions are disjoint).
2. S = DL ∪ DB ∪ locked digits (every candidate is accounted for).
3. Each ALS has N cells with N+1 candidates (the standard ALS definition). A single cell with two candidates is a valid 1-cell ALS.
Why this allows eliminations
Because the ALS in the rest of the line “owns” the digits DL, those digits are confined to the line ALS and the intersection. No other cell in the box can hold them → eliminate DL from the rest of the box (outside the line).
Symmetrically, the box ALS “owns” the digits DB, confining them to the box ALS and the intersection → eliminate DB from the rest of the line (outside the box).
🔎 Step-by-step example
Let’s walk through a real Sue de Coq application that produces 6 candidate eliminations across 5 cells.
Step 1: Find the intersection
Look at Row 6 ∩ Box 4 (rows 4–6, columns 1–3). Three unsolved cells lie in this intersection:
- R6C1 = {1, 2, 5}
- R6C2 = {5, 6}
- R6C3 = {5, 8}
Combined candidate set S = {1, 2, 5, 6, 8} — that’s 5 digits for 3 cells, giving us N+2 = 5 ✔.
Step 2: Find the ALS partners
Scan the rest of Row 6 (outside Box 4) for a set of cells whose candidates overlap with S:
- Line ALS: R6C5 = {1, 2} — a single-cell ALS with 2 candidates. It contributes DL = {1, 2}.
Now scan the rest of Box 4 (outside Row 6) for another ALS:
- Box ALS: R5C3 = {6, 8} — a single-cell ALS with 2 candidates. It contributes DB = {6, 8}.
Step 3: Verify the split
- Disjoint? DL ∩ DB = {1, 2} ∩ {6, 8} = ∅ ✔
- Locked digits? S − DL − DB = {5}. Digit 5 appears in every intersection cell (R6C1, R6C2, R6C3) ✔
- Complete? DL ∪ DB ∪ {5} = {1, 2} ∪ {6, 8} ∪ {5} = {1, 2, 5, 6, 8} = S ✔
Digit 5 is the locked digit — it appears in all three intersection cells and is “owned” by the intersection itself. It does not need an external ALS partner because it must be placed within the intersection regardless.
Step 4: Eliminate candidates
Now apply the two-sector elimination logic:
Row-side eliminations (remove DB = {6, 8} from rest of Row 6)
The box ALS digits {6, 8} are confined to the box ALS and the intersection. No other cell in Row 6 (outside Box 4) can hold them:
- R6C4 = {1,
6} → eliminate 6 → naked single {1}. - R6C9 = {2,
6, 9} → eliminate 6 → {2, 9}.
Box-side eliminations (remove DL = {1, 2} from rest of Box 4)
The line ALS digits {1, 2} are confined to the line ALS and the intersection. No other cell in Box 4 (outside Row 6) can hold them:
- R4C1 = {
1, 3} → eliminate 1 → naked single {3}. - R5C1 = {
2, 5, 6} → eliminate 2 → {5, 6}. - R5C2 = {
2, 6} → eliminate 2 → naked single {6}.
6 eliminations total, 3 naked singles — a powerful result from a single Sue de Coq!
Step 5: Result
After removing 6 candidates, three cells become naked singles: R6C4 = 1, R4C1 = 3, and R5C2 = 6. These solved cells trigger further simplifications across the grid.
Sue de Coq eliminates candidates from two houses simultaneously — the rest of the row and the rest of the box. Most other techniques target only one house at a time. This dual-sector elimination can break through deadlocks that simpler methods cannot.
🔄 Sue de Coq vs. other techniques
| Feature | Pointing Pairs | ALS-XZ | Sue de Coq |
|---|---|---|---|
| Houses used | Line → box | Two ALS linked by RCC | Line ∩ box intersection |
| Elimination scope | One direction | Cells seeing both ALS | Both line and box |
| ALS involvement | None | Two ALS, one RCC digit | Two ALS with disjoint digits |
| Requires locked digit | No | No | Often yes (N+2 case) |
| Difficulty | Intermediate | Expert | Expert |
| Typical yield | 1–3 eliminations | 1–4 eliminations | 3–8+ eliminations |
Sue de Coq is closely related to ALS-XZ — both use Almost Locked Sets to drive eliminations. The key difference is that ALS-XZ links two ALS through a shared Restricted Common Candidate (RCC), while Sue de Coq links them through the line-box intersection with disjoint digit contributions. Sue de Coq's dual-sector scope often yields more eliminations per application.
🕵️ How to spot Sue de Coq
1. Examine each line-box intersection (18 row-box and 18 column-box intersections exist in a 9×9 grid).
2. Count the unsolved cells (N) and their combined distinct candidates (|S|). Look for |S| = N+2.
3. Search the rest of the line (outside the box) for an ALS whose candidates include some digits from S. These are DL.
4. Search the rest of the box (outside the line) for an ALS whose candidates include the remaining non-locked digits from S. These are DB.
5. Verify DL ∩ DB = ∅ and S = DL ∪ DB ∪ locked.
6. Eliminate DB from the rest of the line and DL from the rest of the box.
Start with intersections containing 2–3 unsolved cells (N=2 or N=3). For N=2 you need |S|=4, for N=3 you need |S|=5. Single-cell ALS partners (bivalue cells) are the easiest to spot — look for cells with exactly two candidates in the rest of the line or box.
⚠️ Common mistakes to avoid
1. Forgetting the disjoint requirement
The line-ALS digits DL and box-ALS digits DB must have no overlap. If both ALS partners share a digit, the split is invalid and the eliminations are wrong.
2. Miscounting the intersection candidates
S must be the union of candidates across all intersection cells. Don’t count a digit twice just because it appears in multiple cells. Verify that |S| = N+2 exactly.
3. Eliminating from the wrong sector
A common error is eliminating in the wrong direction. Remember: line-ALS digits are eliminated from the box and box-ALS digits are eliminated from the line. Each ALS “claims” its digits, and the elimination happens in the other sector.
4. Ignoring locked digits
Not every digit in S needs an ALS partner. Digits that appear in every intersection cell are locked — they stay in the intersection regardless and don’t need to be covered by an ALS.
5. Incomplete pencil marks
Sue de Coq depends on accurate candidate lists. A missing or incorrect pencil mark can make you miss the N+2 condition or identify the wrong ALS partner. Always ensure all singles and basic eliminations have been applied first.
📅 When to look for Sue de Coq
- Basic: Naked Singles, Hidden Singles, Full House.
- Intermediate: Naked Pairs, Hidden Pairs, Naked Triples, Pointing Pairs, Box/Line Reduction.
- Advanced (single-digit): X-Wing, Skyscraper, Simple Colouring.
- Advanced (multi-digit): XY-Wing, XYZ-Wing, W-Wing.
- Expert: ALS-XZ, 3D Medusa, Sue de Coq, Swordfish, Unique Rectangles.
Sue de Coq is rated Expert. It is one of the rarest techniques to encounter in generated puzzles but also one of the most rewarding. Puzzles requiring it are typically rated Extreme. Try our hard puzzles for practice.
🚀 Beyond Sue de Coq
| Technique | What it adds | Complexity |
|---|---|---|
| Pointing Pairs | One-direction line-box elimination | Intermediate |
| ALS-XZ | Two ALS linked by RCC | Expert |
| Sue de Coq | Two ALS with disjoint digits at line-box intersection | Expert |
| 3D Medusa | Multi-digit colouring chains | Expert |
| Forcing Chains | Multi-path “what if” chains | Master |
| Forcing Nets | Branching inference networks | Master |
Sue de Coq is closely related to ALS-XZ (both leverage Almost Locked Sets) and can be seen as a specialised form of ALS interaction focused on line-box intersections. Once comfortable with Sue de Coq, advanced solvers often explore full ALS chains, 3D Medusa, and forcing-chain methods for even deeper eliminations.
🎯 Practice Sue de Coq
Hard Sudoku
Challenging puzzles where Sue de Coq and other expert techniques are regularly needed.
▶ Play Hard Sudoku3D Medusa Guide
Another powerful expert-level technique using multi-digit colouring chains.
▶ Read 3D Medusa GuideSudoku Solver
Enter your puzzle and watch the solver identify techniques automatically.
▶ Open SolverFrequently asked questions
Sue de Coq (Two-Sector Disjoint Subsets) is an advanced elimination technique. It finds N cells at the intersection of a line and a box whose combined N+2 candidates can be split between an Almost Locked Set in the rest of the line and an ALS in the rest of the box, with disjoint digit contributions. Digits from each ALS are then eliminated from the opposite sector.
The intersection candidates are partitioned into three groups: digits contributed by the line ALS (DL), digits contributed by the box ALS (DB), and locked digits present in every intersection cell. You eliminate DB from the rest of the line (outside the box) and DL from the rest of the box (outside the line).
An Almost Locked Set (ALS) is a group of N cells containing exactly N+1 distinct candidates. It is “almost” locked because removing any one digit would make the remaining N digits lock into the N cells. In Sue de Coq the simplest ALS is a single cell with two candidates — one of which must be placed there.
After exhausting simpler techniques including Naked Pairs, Pointing Pairs, X-Wing, and Wings. Sue de Coq is an expert-level method best suited for hard and extreme puzzles. Look for it when line-box intersections have cells whose combined candidates exceed the cell count by two.
The technique was first described in 2005 by a Sudoku forum member using the pseudonym “Sue de Coq.” It was later formalised under the name Two-Sector Disjoint Subsets (TSDS). The name stuck and is widely used in the Sudoku community today.