Sue-de-Coq

Sue-de-Coq is one of the rarest and most powerful Sudoku techniques. It combines an Almost Almost Locked Set (AAALS) with block and aligned cell interactions to create eliminations impossible with simpler methods.

Understanding the Pattern

The Core (C)

The pattern starts with 2-3 aligned cells in a box:

Cells are in the same row OR same column
Together they contain N+2 or more candidates (an AAALS)
This is the "core" of the pattern

The Block Cells (B)

Other cells in the same box as the core:

Share at least 2 candidates with the core
Form an ALS-like relationship with the core

The Aligned Cells (A)

Cells in the same row/column as the core but outside the box:

Share at least 2 candidates with the core
Form another ALS-like relationship

The Critical Constraint

(Core ∩ Block) ∩ (Core ∩ Aligned) = ∅

In plain English: The candidates shared with block cells and the candidates shared with aligned cells must NOT overlap. They must be completely separate sets.

Visual Pattern

          ║         C5         ║
══════════╬════════════════════╬════════════
          ║                    ║
    Box 1 ║       Box 2        ║    Box 3
          ║  ┌───────────────┐ ║
          ║  │ Core: {1,2,5,7}│ ║   Aligned
R4        ║  │  R4C4  R4C5   │──────{2,7}
          ║  └───────────────┘ ║
          ║         │          ║
          ║    Block: {1,5}    ║
          ║                    ║
══════════╬════════════════════╬════════════

In this example:

Core (C): R4C4-R4C5 with {1, 2, 5, 7}
Block (B): Other cells in Box 2 with {1, 5}
Aligned (A): R4C7-R4C8 with {2, 7}
Shared with Block: {1, 5}
Shared with Aligned: {2, 7}
Constraint: {1, 5} ∩ {2, 7} = ∅ ✓

Elimination Rules

Once the pattern is verified:

Rule 1: Box Eliminations

Cells in the box (outside Core ∪ Block) cannot contain candidates from Core ∩ Block.

Rule 2: Line Eliminations

Cells in the row/column (outside Core ∪ Aligned) cannot contain candidates from Core ∩ Aligned.

Why It Works

The logic is subtle but powerful:

The core cells must contain certain candidates
Some of those candidates ({1, 5}) can ONLY come from Block cells
Other candidates ({2, 7}) can ONLY come from Aligned cells
Because these sets don't overlap, we know exactly where candidates can go
This "locks" candidates into specific regions, allowing eliminations elsewhere

Example

Core: R4C4-R4C5 = {1, 2, 5, 7}  (4 candidates in 2 cells = AAALS)
Block: R5C4 = {1, 5}           (shares {1, 5} with core)
Aligned: R4C8 = {2, 7}         (shares {2, 7} with core)

Verification: {1, 5} ∩ {2, 7} = ∅ ✓

Eliminations:

Other cells in Box 2: Cannot contain 1 or 5
Other cells in Row 4: Cannot contain 2 or 7

Walkthrough: Core + Aligned Pattern

This example shows a Sue-de-Coq with Core and Aligned cells only (no Block cells). The Core forms an AAALS in column 1, and the Aligned cells complete the locked set.

puzzle: S9B2I010U0905081Q3E02B844060304070501B6055YBI0602014ED65UB94K074B0610BF03B70648BD635U0O4BD6054304125V0912026Q6R5X784L5U03094Z50044C094C050106074403036Q43025U04C305C3
mode: guided
technique: SDC
initial:
  layers:
    hints: true
steps:
  - text: >
      We're looking for a Sue-de-Coq pattern — an AAALS (Almost Almost Locked Set)
      combined with block and/or aligned cells to form a powerful elimination.
    hint: subtle
    technique: SDC

  - text: >
      **Core**: R1C1 {4,7} and R2C1 {2,8,9} are aligned in column 1 within Box 1.
      Together they have 5 candidates {2,4,7,8,9} — that's an AAALS (2 cells, 5 candidates).
    hint: obvious
    technique: SDC
    state:
      selection:
        cells: [R1C1, R2C1]
      annotations:
        - cells: [R1C1, R2C1]
          label: "Core"
          style: pattern

  - text: >
      **No Block cells**: Looking at other cells in Box 1, none share the required
      candidates with the core to form a valid block component.
    hint: obvious
    technique: SDC
    state:
      annotations:
        - cells: [R1C1, R2C1]
          label: "Core"
          style: pattern

  - text: >
      **Aligned cells**: R4C1, R6C1, and R7C1 are in the same column as the core
      but outside Box 1. Together they share candidates {2,7,8,9} with the core.
    hint: obvious
    technique: SDC
    state:
      selection:
        cells: [R4C1, R6C1, R7C1]
      annotations:
        - cells: [R1C1, R2C1]
          label: "Core"
          style: pattern
        - cells: [R4C1, R6C1, R7C1]
          label: "Aligned"
          style: pattern

  - text: >
      **Locked Set formed**: Core (2 cells) + Aligned (3 cells) = 5 cells with
      exactly 5 candidates {2,4,7,8,9}. This forms a locked set in column 1.
    hint: obvious
    technique: SDC
    state:
      selection:
        cells: [R1C1, R2C1, R4C1, R6C1, R7C1]
      focus:
        enabled: true
        digits: [2, 4, 7, 8, 9]
      annotations:
        - cells: [R1C1, R2C1]
          label: "Core"
          style: pattern
        - cells: [R4C1, R6C1, R7C1]
          label: "Aligned"
          style: pattern

  - text: >
      R8C1 {2,8} is in column 1 but outside the locked set.
      Since {2,4,7,8,9} are locked in the 5 pattern cells, R8C1 cannot contain
      any of the shared candidates.
      **Eliminate 2 and 8 from R8C1.**
    hint: detailed
    technique: SDC
    state:
      selection:
        cells: [R1C1, R2C1, R4C1, R6C1, R7C1, R8C1]
      focus:
        enabled: true
        digits: [2, 8]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Complexity

Sue-de-Coq is an expert-level technique — arguably the hardest standard technique:

Extremely rare: Appears in less than 0.01% of puzzles
Complex verification: Must check candidate separation constraint
Multiple components: Core + Block + Aligned all must align correctly
Computational cost: Exponential subset enumeration

Why the Name?

Sue-de-Coq is named after the SuDoku forum member who first described the technique. It's sometimes called Two-Sector Disjoint Subset in academic literature.

Finding Sue-de-Coq

Practically, you won't find these manually:

Let the app find it — The hint system detects Sue-de-Coq automatically
Understand the principle — Knowing WHY it works helps verify hints
Appreciate its rarity — If you see one, the puzzle is genuinely difficult

Relationship to Other Techniques

Technique	Pattern
Almost Locked Sets	N cells with N+1 candidates
Sue-de-Coq	AAALS (N cells with N+2+ candidates) + block/aligned
Pointing Pair/Triple	Simpler box-line interaction

Sue-de-Coq is essentially a very advanced form of box-line reduction using ALS concepts.

Tips

Don't hunt for these — They're too rare to search for manually
Trust the hint system — If Sue-de-Coq is available, the app will find it
Verify the constraint — Check that shared-with-block and shared-with-aligned don't overlap
Appreciate difficulty — Puzzles requiring Sue-de-Coq are among the hardest

More Puzzles

Related Techniques

Almost Locked Sets — Related concept
Pointing Pair/Triple — Simpler box-line pattern
Claiming — Another box-line interaction