Almost Locked Sets (ALS): Advanced Sudoku Technique

Introduction

The Almost Locked Set (ALS) is a powerful advanced Sudoku concept used to identify eliminations based on candidate interactions within a nearly-complete group of cells. Unlike basic strategies such as Naked Pairs or Hidden Triples, ALS is more flexible and can appear in many different puzzle regions, making it a favorite technique among expert solvers.

If you're comfortable with pencil marks, pattern recognition, and mid-level logic, this guide will help you understand ALS and apply it to unlock difficult puzzles.

What Is an Almost Locked Set (ALS)?

An Almost Locked Set (ALS) is an advanced Sudoku technique that identifies eliminations based on candidate interactions within a group of cells containing n cells with n+1 candidates total. This mathematical structure creates tight constraints where the number of candidates is exactly one more than the number of cells, making the set "almost" locked. The single extra candidate enables ALS-based eliminations by creating dependencies between candidates that allow safe removal of candidates from cells that see the entire ALS. Unlike basic strategies like Naked Pairs or Hidden Triples, ALS is more flexible and can appear in rows, columns, or boxes, making it versatile for expert-level solving when puzzles resist basic and intermediate methods.

Key Points

Understanding ALS is essential for expert-level solving:

An Almost Locked Set is a group of cells—within the same row, column, or box—that contains:

• n cells,
• n+1 candidates total,
• with at least one candidate appearing twice.

Because the total number of candidates is just one more than the number of cells, the set is "almost" locked. That single extra candidate is what allows ALS-based eliminations.

Formal definition:

An ALS is a set of cells where the number of candidate digits is exactly one more than the number of cells.

Quick Examples:

• 2 cells → 3 candidates
• 3 cells → 4 candidates
• 4 cells → 5 candidates

This imbalance creates dependency between candidates, forming the basis for eliminations.

• Mathematical structure: ALS requires n cells with n+1 candidates, creating tight constraints
• Powerful eliminations: The extra candidate creates opportunities to eliminate candidates in cells that see the entire ALS
• Flexible application: ALS can appear in rows, columns, or boxes, making it versatile
• Advanced connections: ALS links with AIC, XYZ-Wing, and loop patterns for complex eliminations
• Expert technique: Essential for solving puzzles that resist basic and intermediate methods

How It Works (Step-by-Step)

Here's how to apply the Almost Locked Set technique:

Step 1: Identify ALS Structure

Look for a group of cells in the same row, column, or box where the number of candidates is exactly one more than the number of cells. For example, 3 cells with 4 candidates total.

Step 2: Analyze Candidate Dependencies

Examine how candidates interact within the ALS. The extra candidate creates dependencies that enable eliminations in cells that see the entire ALS.

Step 3: Find Seeing Cells

Identify cells outside the ALS that "see" (are in the same row, column, or box as) all cells in the ALS. These cells are potential elimination targets.

Step 4: Apply Elimination Logic

Use ALS logic to eliminate candidates from seeing cells. The tight constraints of the ALS create logical relationships that guarantee certain eliminations.

Step 5: Connect with Other Techniques

Combine ALS with other advanced methods like AIC (Alternating Inference Chains), XYZ-Wing, or loop patterns for complex eliminations.

Step 6: Verify and Apply

Confirm the ALS pattern is valid, then apply the elimination. ALS provides structured eliminations that break through difficult puzzle positions.

Examples

Here are practical examples of Almost Locked Set technique:

Example 1: Basic ALS

Three cells in a box contain candidates {1,2}, {2,3}, {1,3}—totaling 4 candidates in 3 cells. This ALS structure enables elimination of candidate 1 from a cell that sees all three ALS cells, demonstrating the technique.

Example 2: ALS in Row

Four cells in a row contain 5 candidates total. The ALS structure creates dependencies that eliminate a candidate from a cell outside the ALS that sees all four cells, showing how ALS works in different units.

Example 3: ALS Combined with AIC

An ALS interacts with an Alternating Inference Chain, creating a complex elimination pattern. This demonstrates how ALS connects with other advanced techniques for powerful deductions.

🔧 2. What Makes ALS Powerful?

The strength of ALS comes from relationships between candidates in tightly constrained cell groups.

ALS provides:

• ✔ Strong candidate linking
• ✔ Structured eliminations
• ✔ Flexible pattern interactions
• ✔ Connections with other advanced methods (AIC, XYZ-Wing, loops)

This flexibility makes ALS useful in puzzles where typical techniques fail.

📌 3. Simple Example of ALS

Consider three cells in a box:

• Cell A: {1, 3}
• Cell B: {1, 7}
• Cell C: {3, 7, 9}

Total candidates = 4

Total cells = 3

→ This is an ALS.

Why?

• We have one more candidate (4) than cell count (3)
• Some candidates repeat (1 appears twice, 3 appears twice)

This forms a structure that triggers eliminations when interacting with other candidate patterns.

📘 4. How ALS Creates Eliminations (Core Logic)

Here is the essential idea:

• In an ALS, n cells must contain n of the candidates.
• This means one candidate is "extra"—but we don't know which one.
• If another cell outside the ALS sees all instances of this extra candidate within the ALS…
• …then that external cell cannot contain that candidate.

In other words:

If a candidate must appear inside an ALS, then it cannot appear outside the ALS in any cell that sees all ALS occurrences.

This sounds abstract, but becomes clearer with patterns (examples below).

🧠 5. ALS + AIC: The Core Application

ALS often shows up as part of an Alternating Inference Chain (AIC).

Example:

• Candidate 8 appears in two cells in an ALS
• A third cell (outside ALS) sees both of these 8s
• Therefore, that outside cell cannot be 8

This is known as the ALS-xz rule, a common elimination mechanism.

✨ 6. The ALS-XZ Rule: The Most Famous Form

The ALS-XZ rule is the most widely recognized ALS pattern.

Requirements:

• Two ALS sets
• Candidate X appears in both ALS
• Both ALS are linked through a common candidate Z

When these conditions happen, candidate Z can be eliminated from specific cells.

This rule appears often in tough puzzles and is the foundation of many advanced strategies.

🧩 7. Visual Example of ALS Eliminations

Imagine an ALS in Row 4:

• Cells: R4C2, R4C3, R4C7
• Candidates: {2, 3, 4, 9}

This is an ALS because:

• 3 cells
• 4 candidates

Now imagine another ALS in Column 7:

• Cells: R2C7, R6C7
• Candidates: {3, 9, 7}

This is also an ALS:

• 2 cells
• 3 candidates

Shared candidates:

• 3 and 9

These links create a chain → enabling eliminations

If R5C7 sees all 9s in both ALS, then R5C7 cannot be 9.

ALS can detect these subtle interactions even when conventional strategies fail.

📚 8. ALS in Practical Sudoku Solving

ALS is most useful when:

• ✔ The puzzle reaches a mid-to-late stage
• ✔ Standard tools (pairs, triples, locked candidates) stop helping
• ✔ Candidate density increases
• ✔ You need single-elimination logic to progress

ALS often unlocks progress in hard and expert puzzles.

⚠️ 9. Common Mistakes When Using ALS

Mistake 1: Miscounting candidates

ALS requires very precise counting:

• n cells
• n+1 candidates

Get this wrong, and the pattern collapses.

Mistake 2: Overlooking interactions

ALS is powerful only when linked to:

• Another ALS
• A chain
• A shared seeing cell

Mistake 3: Confusing ALS with Hidden Pairs/Triples

Hidden sets have fewer candidates.

ALS has one extra candidate, which is the key difference.

Mistake 4: Forcing ALS where none exist

ALS must appear naturally within the grid.

💡 10. Tips for Identifying ALS Quickly

• ✔ Look for "tight" cell clusters

Boxes often produce ALS naturally.

• ✔ Identify repeating candidates

Repeated candidates hint at internal structure.

• ✔ Focus on mid-game

ALS is rare in early game due to insufficient pencil marks.

• ✔ Use pencil marks clearly

Clean notation helps identify ALS shapes.

❓ FAQ

Q1: Do beginners need to learn ALS?

Not at all. ALS is an advanced topic best suited for expert-level solvers who have mastered intermediate techniques.

Q2: Is ALS used often in puzzles?

In medium puzzles: rarely. In hard puzzles: sometimes. In expert puzzles: frequently. ALS becomes more common as puzzle difficulty increases.

Q3: Is ALS similar to chains?

Yes—ALS often integrates tightly with chain logic. Many ALS eliminations work through chain-like relationships between candidate sets.

Q4: Why is ALS hard to spot?

Because ALS structures vary widely and are not visually obvious. They require careful analysis of candidate distributions and interactions within cell clusters.

Q5: How does ALS relate to other advanced techniques?

ALS connects with many advanced methods including AIC (Alternating Inference Chains), XYZ-Wing, and various loop patterns. Understanding ALS provides a foundation for these more complex techniques.

Q6: When should I look for ALS patterns?

Look for ALS when basic and intermediate techniques fail. If you've applied Naked Pairs, Hidden Pairs, and basic eliminations but still have many candidates, ALS may provide the breakthrough you need.

Summary

Almost Locked Sets may seem intimidating at first, but once you learn to identify cell clusters with tight candidate structures, ALS becomes a powerful tool for breaking through difficult Sudoku puzzles. By mastering ALS logic—especially ALS-XZ patterns—you'll gain access to solving pathways unavailable through simpler techniques.

If you are aiming to reach expert-level solving, ALS is a technique you'll definitely want in your toolkit.

Ready to practice? Try our Sudoku puzzles and apply ALS techniques to solve challenging puzzles!

Related Articles

• What Is Sudoku Complete Guide
• Sudoku Basic Rules
• Naked Pairs and Triples
• Hidden Pairs and Triples
• XY-Wing Technique
• Unique Rectangle Technique

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