Skyscraper Sudoku Technique
The Skyscraper is an advanced Sudoku technique that belongs to the family of single-digit patterns. It uses two rows (or two columns) where a candidate appears in exactly two positions each, connected by a shared column (or row). The Skyscraper is one of the most accessible advanced techniques and is often the first pattern-based strategy solvers learn after X-Wing.
Prerequisites
Before learning the Skyscraper, you should be comfortable with:
- Candidate notation (pencil marks) — you need complete candidates in every empty cell
- Naked singles and hidden singles — the foundation of Sudoku solving
- Naked pairs and hidden pairs — basic subset elimination
- X-Wing — the Skyscraper is closely related to X-Wing logic
What is a Skyscraper?
A Skyscraper occurs when a candidate appears in exactly two cells in each of two different rows, and one cell from each row shares the same column. The shared column creates a strong link between the two rows, and the two cells that are NOT in the shared column are the “tops” of the Skyscraper. Any cell that can see both tops can have the candidate eliminated.
Think of it like two buildings (the rows) connected at the base (the shared column), with the tops sticking up in different positions. The candidate must be in one of the two tops — so anything that sees both tops can’t contain that candidate.
How it Relates to X-Wing
The X-Wing requires both pairs to align in the same two columns. The Skyscraper is what happens when one pair shifts — they share only one column:
| Pattern | Shared columns | Eliminations |
|---|---|---|
| X-Wing | 2 (both align) | Entire columns outside the pattern |
| Skyscraper | 1 (offset) | Cells that see both non-shared endpoints |
The Skyscraper is sometimes called a “Turbot Fish” or a type of “Turbot Crane.”
How to Find a Skyscraper: Step-by-Step
Step 1: Pick a Candidate Number
Choose a digit to focus on. Scan the grid for digits that appear frequently in pencil marks but are narrowed to exactly two positions in some rows or columns.
Step 2: Find Two Rows with Exactly Two Positions
Look for two rows where your chosen candidate appears in exactly two cells each. Note which columns those cells occupy.
Example: Looking for the candidate 5:
- Row 2: 5 appears in columns 3 and 7
- Row 6: 5 appears in columns 3 and 9
Both rows have 5 in column 3 — that’s the shared base.
Step 3: Verify the Shared Column
Confirm that exactly one column is shared between the two rows. If both columns match, you have an X-Wing instead. If no columns match, there’s no Skyscraper.
In our example:
- Shared column: column 3 (the base)
- Non-shared endpoints: Row 2, Col 7 and Row 6, Col 9 (the tops)
Step 4: Identify the Elimination Zone
The candidate must be placed in one of the two tops. Any cell that can see both tops (shares a row, column, or box with both) can have the candidate eliminated.
In our example, any cell that can see both R2C7 and R6C9 can have 5 removed. This could be a cell in column 7 row 6 (if it sees R6C9 through the same row) — but more typically, the elimination happens in cells that share a box with both endpoints.
Worked Example
Let’s walk through a Skyscraper for the candidate 3.
After filling in pencil marks, you find:
| Col 2 | Col 5 | Col 8 | |
|---|---|---|---|
| Row 1 | 3 | 3 | |
| Row 7 | 3 | 5 |
Wait — Row 7 has 3 in columns 2 and… let’s correct this:
| Col 2 | Col 6 | Col 8 | |
|---|---|---|---|
| Row 1 | 3 | 3 | |
| Row 7 | 3 | 3 |
- Row 1 has candidate 3 in columns 2 and 8 (exactly two positions)
- Row 7 has candidate 3 in columns 2 and 6 (exactly two positions)
- Shared column: 2 (the base)
- Tops: R1C8 and R7C6
Logic: Either R1C2 or R1C8 contains 3. Either R7C2 or R7C6 contains 3. But R1C2 and R7C2 are in the same column — they can’t both be 3. So:
- If R1C2 = 3, then R7C2 ≠ 3, so R7C6 = 3
- If R1C2 ≠ 3, then R1C8 = 3
Either way, at least one of R1C8 or R7C6 must be 3. Therefore, any cell that sees both R1C8 and R7C6 cannot contain 3.
Eliminations: Remove 3 from any cell that shares a house with both R1C8 and R7C6.
Column-Based Skyscraper
Everything above describes a row-based Skyscraper. The pattern works identically with columns:
- Find two columns where a candidate appears in exactly two cells each
- One cell from each column shares the same row (the base)
- Eliminate the candidate from cells that see both non-shared endpoints (the tops)
Always check both orientations if you’re stuck.
Common Mistakes to Avoid
Confusing Skyscraper with X-Wing. If both columns match (not just one), you have an X-Wing. A Skyscraper requires exactly one shared column/row.
Rows/columns with more than two positions. A Skyscraper requires the candidate to appear in exactly two cells per row (or column). If there are three or more positions, the pattern doesn’t apply.
Eliminating from the wrong cells. Only eliminate from cells that can see both tops (non-shared endpoints). Don’t eliminate from cells that only see one.
Incomplete pencil marks. Without accurate and complete candidates, Skyscrapers are impossible to spot.
Forgetting the column-based version. If you only check rows, you’ll miss half the Skyscrapers. Always scan columns too.
When to Look for a Skyscraper
The Skyscraper is an advanced technique — use it after exhausting:
- All naked singles and hidden singles
- Naked pairs and hidden pairs
- Pointing pairs and pointing triples
- Naked triples and hidden triples
- X-Wings
The Skyscraper is particularly useful on Expert difficulty puzzles, where it appears on average twice per solve on SudokuPulse.
Skyscraper vs. Related Techniques
| Feature | X-Wing | Skyscraper | Two-String Kite |
|---|---|---|---|
| Structure | 2 rows × 2 cols aligned | 2 rows share 1 col | Row + column linked via box |
| Shared elements | Both columns | One column (base) | One box (intersection) |
| Difficulty | Advanced | Advanced | Advanced |
| Eliminations | From entire columns | From cells seeing both tops | From one cell seeing both endpoints |
Frequently Asked Questions
What is the difference between a Skyscraper and a Turbot Fish?
The Skyscraper is a specific type of Turbot Fish. A Turbot Fish is any pattern involving two strong links connected end-to-end. The Skyscraper occurs when both strong links are in rows (or both in columns). When one link is in a row and the other in a column (connected through a box), it’s called a Two-String Kite instead.
How common are Skyscrapers?
Skyscrapers appear regularly in Expert and Evil difficulty puzzles. They’re more common than Swordfish but less common than X-Wings. On SudokuPulse, Expert puzzles average about 2 Skyscraper applications per solve.
Can a Skyscraper solve the whole puzzle?
Not by itself, but the eliminations often trigger naked or hidden singles that can cascade through much of the remaining puzzle.
What if I can’t find any Skyscrapers?
Try scanning each digit individually. If no Skyscrapers exist, the puzzle may need other advanced techniques like Two-String Kites, Swordfish, XY-Wings, or chains.
Practice the Skyscraper
Ready to test this technique? Try our Expert or Evil difficulty puzzles where Skyscrapers appear frequently.