Skyscraper Sudoku Technique

The Skyscraper technique is an advanced Sudoku solving method that uses the concept of strong and weak links to eliminate candidates. It's named for its visual resemblance to skyscrapers when drawn on a Sudoku grid. This powerful technique can help you solve even the most challenging puzzles.

What is the Skyscraper Technique?

The Skyscraper technique is a pattern recognition method that works when a specific digit appears in exactly two cells in two different rows (or columns), and these cells share a common column (or row). The pattern creates a logical chain that allows you to eliminate candidates from other cells.

The technique gets its name from the visual pattern it creates when drawn on the grid - it looks like two skyscrapers connected by a base.

Understanding Strong and Weak Links

Before learning the Skyscraper technique, you need to understand two key concepts:

Strong Link

A strong link exists when a digit can appear in exactly two cells in a row, column, or box. If the digit is not in one cell, it must be in the other.

Weak Link

A weak link exists when a digit can appear in two or more cells in a row, column, or box. If the digit is in one cell, it cannot be in the others.

How the Skyscraper Pattern Works

For a Skyscraper pattern to be valid, you need:

1. A specific digit that appears in exactly two cells in two different rows (or columns)
2. These two rows (or columns) must share a common column (or row)
3. The digit must form a strong link in each row (or column)
4. The pattern must create a logical chain for elimination

Step-by-Step Skyscraper Identification

Step 1: Choose a Target Digit

Start by selecting a digit that appears frequently in your puzzle. Look for digits that have candidates in multiple rows and columns.

Step 2: Find Two Rows with Strong Links

Identify two rows where your target digit appears in exactly two cells each. These create strong links.

Step 3: Check for Common Column

Verify that these two rows share exactly one common column where the digit appears.

Step 4: Apply the Elimination

If the pattern is valid, eliminate the target digit from cells in the common column that are not part of the Skyscraper pattern.

Skyscraper Example

Let's say we're looking for digit 7 in a Skyscraper pattern:

This creates a Skyscraper pattern where:

• Two rows (2 and 6) contain digit 7 in exactly two cells each
• These rows share column 1
• Strong links exist in both rows

You can now eliminate digit 7 from all other cells in column 1 that are not in rows 2 and 6.

Visual Representation

The Skyscraper pattern looks like this when drawn:

The pattern forms two "skyscrapers" (the two rows) connected by a "base" (the common column).

Common Skyscraper Variations

Row-Based Skyscraper

When you look for the pattern across two rows, you eliminate candidates in the corresponding common column.

Column-Based Skyscraper

When you look for the pattern across two columns, you eliminate candidates in the corresponding common row.

Box Skyscraper

A variation where the strong links are formed within 3×3 boxes instead of rows or columns.

Tips for Finding Skyscraper Patterns

1. Use Pencil Marks

Always use pencil marks to track all possible candidates. Skyscraper patterns are impossible to spot without seeing all the candidates for each digit.

2. Look for Digits with Many Candidates

Focus on digits that appear as candidates in many cells. Digits with only a few candidates are less likely to form Skyscraper patterns.

3. Check Both Rows and Columns

Remember that Skyscraper can work in either direction - look for patterns in both rows and columns.

4. Practice Pattern Recognition

The more you practice, the easier it becomes to spot these patterns. Start with simpler techniques before moving to Skyscraper.

When to Use Skyscraper

Use the Skyscraper technique when:

• Basic techniques (singles, pairs, triples) no longer provide progress
• You've already tried X-Wing and Y-Wing techniques
• You're working on expert-level puzzles
• A digit appears frequently across multiple rows and columns

Common Mistakes to Avoid

1. Incorrect Strong Link Identification

Make sure you have exactly two candidates in each row (or column). Having three or more candidates doesn't create a strong link.

2. Missing Common Column/Row

Ensure the two rows (or columns) share exactly one common column (or row) where the digit appears.

3. Wrong Elimination

Only eliminate candidates from cells that are NOT part of the Skyscraper pattern. Don't eliminate from the pattern cells themselves.

4. Confusing with Other Techniques

Don't confuse Skyscraper with X-Wing or other fish patterns. Each technique has its own specific requirements.

Advanced Skyscraper Concepts

1. Multi-Skyscraper

A variation where multiple Skyscraper patterns work together to create more complex eliminations.

2. Skyscraper Chains

Extended Skyscraper patterns that form longer chains of logical connections.

3. Finned Skyscraper

A variation where one of the strong links has an extra candidate that breaks the perfect pattern.

Practice Exercises

To master the Skyscraper technique:

1. Start with puzzles that are known to contain Skyscraper patterns
2. Practice identifying the pattern before applying eliminations
3. Work through examples step by step
4. Try creating your own Skyscraper examples

Related Techniques

The Skyscraper technique is related to other advanced methods:

• X-Wing - Similar pattern recognition
• Swordfish - Extended fish patterns
• Forcing Chains - Logical chain techniques

Tips for Success

• Practice regularly to improve pattern recognition
• Start with easier puzzles and work your way up
• Use pencil marks consistently
• Don't get discouraged if you don't spot patterns immediately
• Combine Skyscraper with other techniques for maximum effectiveness