Almost Locked Sets (ALS)

An Almost Locked Set is a group of N cells containing exactly N+1 different candidates. When two ALSs share a Restricted Common Candidate (RCC), powerful eliminations become possible.

Note: ALS patterns are visualised with convex hulls around each set, making the relationship between sets clear. The RCC and elimination targets are highlighted distinctly.

Understanding ALS

What Makes a Set "Locked"?

A Locked Set (like a Naked Pair) has N cells with exactly N candidates. Each candidate MUST go in one of those cells.

An Almost Locked Set has N cells with N+1 candidates — one candidate "too many." It's almost locked.

Examples

Naked Pair (Locked):

• 2 cells with {2, 5} — exactly 2 candidates in 2 cells

ALS:

• 2 cells with {2, 5, 7} — 3 candidates in 2 cells (one too many)
• 3 cells with {1, 3, 4, 8} — 4 candidates in 3 cells

The Key Property

If you remove any one candidate from an ALS, it becomes locked. The remaining N candidates MUST fill the N cells.

Restricted Common Candidate (RCC)

The magic happens when two ALSs share a Restricted Common Candidate:

What is an RCC?

A candidate is an RCC between two ALSs when:

1. It appears in both ALSs
2. ALL cells containing it in ALS1 can see all cells containing it in ALS2

Why It Matters

If the RCC is in ALS1, it cannot be in ALS2 (they see each other). This "locks" ALS2:

• ALS2 loses the RCC
• Remaining candidates must fill ALS2's cells
• Any other common candidates are forced

The Elimination Rule

When two ALSs share an RCC:

1. Find other common candidates (besides the RCC)
2. Find cells that see ALL occurrences of that candidate in BOTH ALSs
3. Eliminate the candidate from those cells

Logic

• The RCC is in exactly one of the two ALSs
• Whichever ALS doesn't have the RCC becomes locked
• The other common candidates in that ALS are forced
• External cells seeing all of them cannot contain that digit

Example 1: Two 2-Cell ALSs

This example shows a classic ALS-XZ pattern with two small ALSs connected by digit 5.

puzzle: S9B09014A07501U1816034A06024J43030717090703057N7P040L08064B4A090307024R064R5702038J058J4B074B1F05071F040809030202074Y04C38Z030Z4J054A0102030706094A0309565F4Z1V4R0207
mode: guided
technique: Almost Locked Sets
initial:
  layers:
    hints: true
steps:
  - text: >
      We're looking for Almost Locked Sets — groups of N cells with N+1 candidates.
      Two ALSs sharing a Restricted Common Candidate enable eliminations.
    hint: subtle
    technique: ALS

  - text: >
      **ALS A**: R1C3 {4,8} and R1C8 {4,5} form a 2-cell ALS.
      Together they have 3 candidates {4,5,8} — that's 2 cells with 3 candidates.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R1C3, R1C8]
      annotations:
        - cells: [R1C3, R1C8]
          label: "ALS A"
          style: pattern

  - text: >
      **ALS B**: R2C8 {1,4,5} and R7C8 {1,5} form another 2-cell ALS.
      Together they have 3 candidates {1,4,5} — again 2 cells with 3 candidates.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R2C8, R7C8]
      annotations:
        - cells: [R1C3, R1C8]
          label: "ALS A"
          style: pattern
        - cells: [R2C8, R7C8]
          label: "ALS B"
          style: pattern

  - text: >
      The **Restricted Common Candidate** is 5. In ALS A, only R1C8 has 5.
      In ALS B, both R2C8 and R7C8 have 5. R1C8 sees both (same column).
      All 5s in ALS A see all 5s in ALS B — this makes 5 the RCC.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R1C8, R2C8, R7C8]
      focus:
        enabled: true
        digits: [5]
      annotations:
        - cells: [R1C3, R1C8]
          label: "ALS A"
          style: pattern
        - cells: [R2C8, R7C8]
          label: "ALS B"
          style: pattern
        - cells: [R1C8, R2C8, R7C8]
          label: "RCC: 5"
          style: chain

  - text: >
      The RCC means 5 must be in exactly one of the two ALSs.
      Whichever ALS loses the 5 becomes a locked set.
    hint: obvious
    technique: ALS
    state:
      annotations:
        - cells: [R1C3, R1C8]
          label: "ALS A"
          style: pattern
        - cells: [R2C8, R7C8]
          label: "ALS B"
          style: pattern

  - text: >
      **Other common candidate**: 4 appears in both ALSs.
      ALS A has 4 in R1C3 and R1C8. ALS B has 4 in R2C8.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R1C3, R1C8, R2C8]
      focus:
        enabled: true
        digits: [4]
      annotations:
        - cells: [R1C3, R1C8]
          label: "ALS A"
          style: pattern
        - cells: [R2C8, R7C8]
          label: "ALS B"
          style: pattern

  - text: >
      R1C7 sees ALL occurrences of 4 in both ALSs:
      R1C3 (same row), R1C8 (same row), R2C8 (same box).
      Since 4 must be in one ALS or the other, R1C7 cannot be 4.
      **Eliminate 4 from R1C7.**
    hint: detailed
    technique: ALS
    state:
      selection:
        cells: [R1C3, R1C7, R1C8, R2C8]
      focus:
        enabled: true
        digits: [4]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Example 2: 2-Cell + 3-Cell ALS

This example shows how ALSs of different sizes can work together. A 2-cell ALS combines with a 3-cell ALS, enabling multiple eliminations.

puzzle: S9B9G037O06089O019M0506BG01059O03649M9O9WBG847O9O0168069S7P7P04089H0506032C08067S7S9S9O2K05010P05070P1T1O09080S890794048P08127N8M897P94078P8K1A7V08047N087R058I2E02AE
mode: guided
technique: Almost Locked Sets
initial:
  layers:
    hints: true
steps:
  - text: >
      This puzzle contains a larger ALS pattern. We'll find a 2-cell ALS
      interacting with a 3-cell ALS through a shared RCC.
    hint: subtle
    technique: ALS

  - text: >
      **ALS A**: R1C1 {2,7,9} and R1C3 {2,9} form a 2-cell ALS.
      Together: {2,7,9} — that's 3 candidates in 2 cells.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R1C1, R1C3]
      annotations:
        - cells: [R1C1, R1C3]
          label: "ALS A"
          style: pattern

  - text: >
      **ALS B**: R3C1 {2,5,7,9}, R3C3 {2,5,9}, and R3C4 {2,9} form a 3-cell ALS.
      Together: {2,5,7,9} — that's 4 candidates in 3 cells.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R3C1, R3C3, R3C4]
      annotations:
        - cells: [R1C1, R1C3]
          label: "ALS A"
          style: pattern
        - cells: [R3C1, R3C3, R3C4]
          label: "ALS B"
          style: pattern

  - text: >
      The **Restricted Common Candidate** is 7. In ALS A, only R1C1 has 7.
      In ALS B, only R3C1 has 7. R1C1 and R3C1 are in the same column.
      All 7s in ALS A see all 7s in ALS B — 7 is the RCC.
    hint: obvious
    technique: ALS
    state:
      selection:
        cells: [R1C1, R3C1]
      focus:
        enabled: true
        digits: [7]
      annotations:
        - cells: [R1C1, R1C3]
          label: "ALS A"
          style: pattern
        - cells: [R3C1, R3C3, R3C4]
          label: "ALS B"
          style: pattern
        - cells: [R1C1, R3C1]
          label: "RCC: 7"
          style: chain

  - text: >
      **Other common candidates**: Both 2 and 9 appear in both ALSs.
      The RCC (7) locks one ALS, forcing 2 and 9 in the other.
    hint: obvious
    technique: ALS
    state:
      focus:
        enabled: true
        digits: [2, 9]
      annotations:
        - cells: [R1C1, R1C3]
          label: "ALS A"
          style: pattern
        - cells: [R3C1, R3C3, R3C4]
          label: "ALS B"
          style: pattern

  - text: >
      R3C2 {2,4,8,9} sees ALL occurrences of 2 in both ALSs:
      R1C1 and R1C3 (same box), R3C1, R3C3, R3C4 (same row).
      **Eliminate 2 from R3C2.**
    hint: detailed
    technique: ALS
    state:
      selection:
        cells: [R1C1, R1C3, R3C1, R3C2, R3C3, R3C4]
      focus:
        enabled: true
        digits: [2]

  - text: >
      R3C2 also sees ALL occurrences of 9 in both ALSs (same logic).
      **Eliminate 9 from R3C2.**
      Final eliminations: R3C2~2, R3C2~9.
    hint: detailed
    technique: ALS
    state:
      selection:
        cells: [R1C1, R1C3, R3C1, R3C2, R3C3, R3C4]
      focus:
        enabled: true
        digits: [9]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Finding ALSs

Where to Look

ALSs exist within units (rows, columns, boxes):

• Row ALS: 2-4 cells in a row with 3-5 candidates
• Column ALS: 2-4 cells in a column with 3-5 candidates
• Box ALS: 2-4 cells in a box with 3-5 candidates

Practical Tips

1. Start small — Look for 2-cell ALSs first (easiest to spot)
2. Count candidates — Cells + 1 = required candidate count
3. Check visibility — Both ALSs must see each other via the RCC
4. Look for commons — Need at least 2 shared candidates (RCC + elimination target)

Complexity

ALS is an expert-level technique because:

• Must identify valid ALSs across multiple units
• Must verify RCC property (all instances see each other)
• Must track multiple candidates across both sets
• Computationally expensive — many combinations to check

Relationship to Other Techniques

ALS is a generalisation of simpler patterns:

Tips

1. Don't search manually — ALS patterns are computationally intensive
2. Trust the hint system — The app finds ALSs automatically
3. Understand the logic — Knowing WHY it works helps verify hints
4. Look for bi-value cells — These are 1-cell ALSs (2 candidates in 1 cell)

More Puzzles

• Almost Locked Sets ex. 1
• Almost Locked Sets ex. 2
• Almost Locked Sets ex. 3
• Almost Locked Sets ex. 4
• Almost Locked Sets ex. 5
• Almost Locked Sets ex. 6
• Almost Locked Sets ex. 7
• Almost Locked Sets ex. 8

Related Techniques

• Naked Pair — Simpler locked set
• Sue-de-Coq — Related exotic technique
• XYZ-Wing — Uses similar bi-value logic