Solving Tips

Sudoku Skyscraper Technique: Advanced Elimination Using Strong Links

2025-01-27 · 10 min read

Skyscraper is an advanced Sudoku technique based on strong links. Its name comes from the visual pattern it creates—two parallel "pillars" connected by a "beam," resembling two skyscrapers. The core concept is: when a candidate forms a strong link in each of two rows (or columns), and these two strong links are connected through the same column (or row), the cells that can see both "dangling" endpoints can eliminate that candidate.

         What is a Strong Link?

        When a candidate appears in only two cells within a row (or column, or box), these two cells form a strong link. A strong link means: exactly one of these two cells will contain that number. If one doesn't have it, the other definitely does.

Before reading this article, it's recommended to master Sudoku row-column-box naming conventions and the X-Wing technique, which will help you understand the analysis examples below.

Example Analysis 1: Skyscraper with Candidate 2

Let's look at the first Skyscraper example involving candidate 2.

Figure: Candidate 2 forms a Skyscraper pattern in rows 3 and 6

Analysis Process

1 Observe Row 3: In row 3, candidate 2 appears in only two positions: B3 and C3. These two cells form a strong link (green horizontal line).

2 Observe Row 6: In row 6, candidate 2 also appears in only two positions: A6 and C6. These two cells also form a strong link (green horizontal line).

3 Find the Common Column: Notice that C3 and C6 are both in column C. This means the two strong links are connected through column C (orange dashed line).

4 Identify Skyscraper Pattern: Now we have:

Base: C3 and C6 (in the same column, connected by orange dashed line)
Dangling Endpoints: B3 and A6 (the two "rooftops")

5 Understand the Logic: Due to the nature of strong links:

The 2 in row 3 is either at B3 or C3
The 2 in row 6 is either at A6 or C6
If C3 is 2, then C6 cannot be 2 (same column), so A6 must be 2
If C3 is not 2, then B3 must be 2

Conclusion: In either case, at least one of B3 or A6 contains 2.

6 Execute Elimination: Since at least one of B3 or A6 contains 2, cells that can be seen by both B3 and A6 cannot contain 2. Which cells can be seen by both B3 and A6?

A1: In column A (A6 can see it) and in box 1 (B3 can see it) — can eliminate candidate 2

Conclusion:
Candidate 2 forms a Skyscraper pattern in rows 3 (B3-C3) and 6 (A6-C6), connected through column C. Cell A1, which can be seen by both dangling endpoints B3 and A6, must have candidate 2 eliminated.

Example Analysis 2: Skyscraper with Candidate 6

Let's look at the second Skyscraper example involving candidate 6.

Figure: Candidate 6 forms a Skyscraper pattern in rows 3 and 7

Analysis Process

1 Observe Row 3: In row 3, candidate 6 appears in only two positions: C3 and E3. These two cells form a strong link.

2 Observe Row 7: In row 7, candidate 6 also appears in only two positions: C7 and F7. These two cells also form a strong link.

3 Find the Common Column: Notice that C3 and C7 are both in column C. This means the two strong links are connected through column C.

4 Identify Dangling Endpoints:

Base: C3 and C7 (in the same column)
Dangling Endpoints: E3 and F7 (the two "rooftops")

5 Execute Elimination: At least one of E3 or F7 contains 6. Cells that can be seen by both E3 and F7:

E7: In row 7 (F7 can see it) and in column E (E3 can see it) — can eliminate candidate 6
F2: In column F (F7 can see it) and may share box with E3 — needs confirmation

Conclusion:
Candidate 6 forms a Skyscraper pattern in rows 3 (C3-E3) and 7 (C7-F7), connected through column C. Cells that can be seen by both dangling endpoints E3 and F7 must have candidate 6 eliminated.

Forms of Skyscraper

Skyscraper can have multiple forms depending on the direction of strong links and how they connect:

1. Row-based Skyscraper

This is the case in the examples above:

Basic Structure: Each of two rows has one strong link
Connection: The two strong links share an endpoint in the same column
Dangling Endpoints: The two endpoints not in the common column

2. Column-based Skyscraper

Opposite form but same principle:

Basic Structure: Each of two columns has one strong link
Connection: The two strong links share an endpoint in the same row
Dangling Endpoints: The two endpoints not in the common row

         Memory Tip:

        Imagine two skyscrapers:

        • Bases are on the same "street" (the common row or column)

        • Rooftops are the dangling endpoints

        • Places that both rooftops can see simultaneously are the elimination targets

How to Find Skyscraper?

Finding Skyscraper requires systematic observation:

1 Select a Candidate: Focus on one candidate (one of 1-9), analyze one at a time. Candidates appearing 5-8 times are easier to find.

2 Look for Strong Links: Identify which rows or columns have that candidate appearing in exactly two cells. Each such row or column contains a strong link.

3 Find Connection Points: Check if any two strong links each have one endpoint in the same column (or row).

4 Identify Dangling Endpoints: Find the two endpoints of the strong links that are not in the common column (or row)—these are the "dangling endpoints."

5 Find Elimination Targets: Find cells that can be seen by both dangling endpoints (same row, column, or box). These cells can eliminate that candidate.

Important Notes:

Strong links require the candidate to appear in exactly two cells in that row (or column)
The two strong links must be connected through the same column (or row)
"Seen by both" includes: same row, same column, and same box
If the two dangling endpoints have no cells they can both see, no elimination is possible
Skyscraper is an "imperfect" variant of X-Wing—when X-Wing's four corners are incomplete, it might form a Skyscraper

Skyscraper's Relationship with Other Techniques

Skyscraper vs X-Wing

Both involve strong links in two rows (or columns), but have important differences:

X-Wing: All four corners align perfectly, forming a complete rectangle, can eliminate entire columns (or rows)
Skyscraper: Only three points align (two bases + one common column), one endpoint "dangles," can only eliminate specific cells

Skyscraper vs 2-String Kite

Skyscraper is actually a special form of the 2-String Kite:

Two strong links connected through a common point
Uses "at least one endpoint is true" logic for elimination

Technique Summary

Key points for applying Skyscraper technique:

Identification Criteria: A candidate appears exactly twice in each of two rows (or columns), and one column (or row) contains an endpoint from both strong links
Pattern Formation: Two strong links + one common column (or row) + two dangling endpoints
Elimination Rule: Cells that both dangling endpoints can "see" can eliminate that candidate
Application Scenario: Alternative method when X-Wing conditions aren't met
Identification Difficulty: Intermediate to advanced, requires understanding strong links

         Practical Advice:

        Skyscraper is more common in practice than X-Wing because its conditions are more relaxed. Suggestions:
        First master identifying strong links
When looking for X-Wing, if the four corners are incomplete, check if a Skyscraper can form
Focus on candidates with fewer occurrences—easier to find strong links
Use candidate highlighting to focus on one number at a time

    

Practice Now

Practice Suggestions:
Start a difficult or expert-level Sudoku game and try using the Skyscraper technique! Suggestions:

Choose difficult level—easy puzzles usually don't require advanced techniques
Mark all candidates first, then look for strong links one number at a time
After finding two strong links, check if they share a common row or column
Once you identify dangling endpoints, look for cells they can both see

X-Wing Swordfish Techniques Index