Almost Locked Set (ALS)

What is an Almost Locked Set?

An Almost Locked Set (ALS) is one of the most important concepts in advanced Sudoku solving. It's a group of N cells within a single unit (row, column, or box) that contains exactly N+1 different candidates among them.

For example, if you have two cells in the same row containing candidates {2,5} and {5,7}, that's an ALS: 2 cells with 3 candidates {2,5,7}. Similarly, three cells containing {1,4}, {1,6}, and {4,6} form an ALS: 3 cells with 4 candidates {1,4,6} (where 1,4,6 are the unique values).

The key insight is that an ALS is "almost" a Naked Subset. A naked pair has 2 cells with exactly 2 candidates (locked). An ALS has 2 cells with 3 candidates (almost locked—one candidate too many). This "almost" property creates special logical opportunities when multiple ALS interact.

Why is it called "Almost Locked Set"?

It's called "Almost Locked Set" because it's one candidate away from being a locked set (like a Naked Pair or Naked Triple). If you could remove one candidate from the ALS, it would become a locked subset that eliminates candidates from the rest of the unit.

The "almost" property is what makes ALS special: they're constrained enough to create logical patterns, but not locked enough to work alone. They need to interact with other ALS or structures to produce eliminations.

Why They Matter

Almost Locked Sets matter because they're the foundation for several powerful master-level techniques:

  • ALS-XZ — Two ALS connected by restricted common candidates
  • ALS Chains — Multiple ALS linked together in chains
  • Sue de Coq — ALS patterns at box-line intersections
  • Death Blossom — Complex ALS patterns involving multiple units

Understanding ALS is essential for mastering the hardest Sudoku puzzles. While a single ALS doesn't create eliminations on its own, recognizing ALS patterns is the first step to applying advanced techniques.

Step-by-Step: How to Identify an ALS

  1. Choose a unit — Focus on a row, column, or box.
  2. Select N cells — Choose a group of cells (typically 2-5 cells).
  3. Count unique candidates — List all different candidates that appear in those cells.
  4. Check the N+1 property — If N cells contain exactly N+1 unique candidates, it's an ALS.
  5. Note the candidates — Record which candidates are in the ALS for later use in advanced techniques.

ALS Examples

Simple ALS (2 cells)

Two cells in Row 5: R5C2={3,8} and R5C7={3,9}. This is an ALS with 2 cells and 3 candidates {3,8,9}.

Larger ALS (3 cells)

Three cells in Box 1: R1C2={2,5}, R2C1={5,7}, R3C2={2,7}. This is an ALS with 3 cells and 4 candidates {2,5,7}. Note that 5 appears in only one cell, 2 appears in two cells, and 7 appears in two cells.

Extended ALS (4 cells)

Four cells in Column 6: R2C6={1,4}, R3C6={4,6}, R5C6={1,6}, R7C6={1,9}. This is an ALS with 4 cells and 5 candidates {1,4,6,9}.

Not an ALS

Two cells: R1C1={2,5} and R1C8={7,9}. This is NOT an ALS because 2 cells contain 4 candidates {2,5,7,9}. The N+1 property requires exactly 3 candidates for 2 cells.

Visual Example

Imagine three cells in Box 4:

  • R4C1: {2,6,8}
  • R5C2: {2,8}
  • R6C3: {6,8}

Analysis: Count unique candidates: {2,6,8} = 3 unique candidates. We have 3 cells and 3 candidates, so this is NOT an ALS—it's actually a Naked Triple (locked set).

Now modify one cell: R4C1: {2,6,8,9}. Now we have 3 cells and 4 candidates {2,6,8,9}. This IS an ALS (3 cells, 4 candidates).

Strategies for Finding ALS

  1. Start with small sets — Look for 2-cell ALS first (easiest to spot).
  2. Focus on bi-value cells — Cells with exactly 2 candidates often participate in ALS.
  3. Scan each unit systematically — Check rows, columns, and boxes one at a time.
  4. Count candidates carefully — It's easy to miscount when cells share candidates.
  5. Use candidate highlighting — Digital solvers can color-code candidates to make ALS visible.
  6. Look for "almost patterns" — If you spot something that's almost a Naked Triple or Quad, it might be an ALS.

Common Pitfalls

  • Miscounting unique candidates — If candidate 5 appears in three cells of your ALS, it still counts as only ONE unique candidate.
  • Mixing units — All cells in an ALS must be in the same unit (row, column, or box). You can't combine cells from different rows.
  • Expecting eliminations from single ALS — An ALS alone doesn't eliminate anything. You need ALS interactions.
  • Confusing with Naked Subsets — If N cells have exactly N candidates, it's a locked subset, not an ALS.
  • Ignoring larger ALS — Don't only look for 2-cell ALS. Some patterns require 3-4 cell ALS.

Practice: Identify the ALS

Scenario: In Row 3, you have these cells:

  • R3C2: {4,7}
  • R3C5: {4,9}
  • R3C8: {7,9}

Question: Is this an ALS? If so, how many cells and how many candidates?

Answer: Yes, this is an ALS. It has 3 cells and 4 unique candidates {4,7,9}. Wait—let me recount: {4,7,9} is only 3 candidates. Actually, this is NOT an ALS because 3 cells with 3 candidates forms a Naked Triple (locked set, not almost locked). For this to be an ALS, you'd need a 4th candidate in at least one cell.

Why Almost Locked Sets Matter

Almost Locked Sets are crucial because they:

  • Form the theoretical foundation for multiple advanced techniques
  • Capture "constraint-almost-satisfied" patterns that create logical opportunities
  • Enable eliminations in extremely difficult puzzles where simpler techniques fail
  • Demonstrate the mathematical elegance of Sudoku's logical structure

While identifying ALS is just the first step, mastering this concept unlocks the door to master-level solving techniques.

Quick Recap

Technique How it Works Difficulty
Almost Locked Set N cells in a unit with N+1 candidates (foundation for other techniques) Master
Naked Pair 2 cells with exactly 2 candidates (locked set) Intermediate
Naked Triple 3 cells with exactly 3 candidates (locked set) Intermediate

Final Thought

Almost Locked Sets are like Sudoku's building blocks for advanced logic. While they don't solve puzzles on their own, they're essential pieces that combine to create powerful elimination patterns. Master ALS recognition, and you'll be ready to tackle the most sophisticated solving techniques.

Frequently Asked Questions

What is an Almost Locked Set in Sudoku?

An Almost Locked Set (ALS) is a group of N cells within a single unit (row, column, or box) that contains exactly N+1 different candidates. For example, three cells containing candidates {2,5,7,9} among them form an ALS because 3 cells have 4 candidates. ALS are the foundation for several advanced solving techniques.

How is an ALS different from a Naked Subset?

A Naked Subset has N cells with exactly N candidates, forming a locked set that eliminates those candidates from other cells. An Almost Locked Set has N cells with N+1 candidates—one candidate too many to be locked. This 'almost' property enables different elimination patterns when ALSs interact.

Can an ALS be used alone to make eliminations?

No, a single ALS by itself doesn't allow eliminations. ALS are building blocks that must be combined with other ALS or logical structures. Techniques like ALS-XZ, ALS-Chains, and Sue de Coq use ALS interactions to create eliminations.

What makes ALS powerful in Sudoku?

ALS are powerful because they capture 'almost constraints'—patterns that are one candidate away from being locked. When multiple ALS interact through shared candidates (restricted commons), they create elimination opportunities that simpler techniques miss. This makes ALS fundamental to master-level solving.

How do I identify an Almost Locked Set?

To identify an ALS, find N cells in the same unit (row, column, or box) and count the total unique candidates among those cells. If there are exactly N+1 unique candidates, you've found an ALS. For example, two cells with candidates {3,7} and {3,8} form an ALS: 2 cells, 3 candidates {3,7,8}.

Practice Almost Locked Sets

Ready to use ALS? Learn ALS-XZ or Sue de Coq.

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