The Skyscraper is an advanced Sudoku technique that can be understood as a special case of both Turbot Fish and X-Chains. It involves a single candidate digit that forms two conjugate pairs in two different rows (or columns), where one end of each pair shares the same column (or row), creating a linked chain. The pattern resembles two parallel towers of different heights sharing a common base, which gives the technique its name.
To construct a Skyscraper, find two rows where a candidate digit appears in exactly two cells each (forming conjugate pairs within each row). If one cell from each row is in the same column, those cells create a strong link that connects the two conjugate pairs. The key insight is that the two unlinked endpoints (the cells not sharing a column) cannot both be empty of the candidate. At least one of those endpoints must contain the digit, because if one endpoint is eliminated, its conjugate partner in the same row is forced, which forces the linked cell, which forces the other conjugate pair, ultimately placing the digit at the other endpoint.
This means any cell that can see both unlinked endpoints can have the candidate eliminated, since the digit must be in at least one of those endpoints. The Skyscraper is easier to spot than a full X-Chain and provides a gentle introduction to chain-based reasoning. It appears frequently in hard Sudoku puzzles and often unlocks progress when X-Wing patterns are not available. Understanding Skyscrapers bridges the gap between fish techniques and the more complex coloring and chain strategies.
Try It Yourself
Walk through each step of the skyscraper technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
We are looking for a Skyscraper on candidate 5. In row 4, candidate 5 appears in exactly two cells: (3,0) and (3,5). In row 6, it appears in (5,0) and (5,5). Both rows have conjugate pairs for digit 5.
Step-by-Step Guide
Choose a candidate digit and find rows where it appears in exactly two cells (conjugate pairs).
Look for two such rows where one cell in each row shares the same column — these form the linked base.
Identify the two unlinked endpoints: the cells in the two rows that do not share a column.
Recognize that the candidate must appear in at least one of the two unlinked endpoints.
Eliminate the candidate from any cell that can see both unlinked endpoints simultaneously.
The technique also works with columns as the base and rows providing the shared link.
Imagine two seesaws sharing one support post — when one side goes up, the other must come down, so anything standing between both far ends will always get bumped.
Each row's conjugate pair is a binary constraint guaranteeing the digit occupies exactly one of its two cells. The shared column cell creates a logical implication chain: if one unlinked endpoint is false, its conjugate partner (the shared cell) is forced true, which forces the other shared-column cell false via the column constraint, which in turn forces the second endpoint true. This means at least one endpoint must always hold the digit, so any cell visible to both endpoints cannot contain it without creating a duplicate.
When to use: Use Skyscraper when you find two rows (or columns) each with a candidate in exactly two cells, and one cell from each row shares the same column. It is ideal when X-Wing fails because the cells do not form a perfect rectangle.
Common Mistakes to Avoid
Confusing a Skyscraper with an X-Wing when both endpoints share the same column.
If all four cells form a rectangle (both pairs share both columns), it is an X-Wing, not a Skyscraper. A Skyscraper has only one shared column between the two pairs.
Eliminating from cells that can only see one of the two unlinked endpoints.
Eliminations only apply to cells that see BOTH unlinked endpoints. A cell seeing just one endpoint has no guarantee.
Forgetting that the pattern works with columns as the base just as well as rows.
Always check both orientations. Column-based Skyscrapers have shared rows and eliminate from cells seeing both unlinked endpoints.
More Examples
See skyscraper applied in different puzzle configurations to strengthen your pattern recognition.
Skyscraper on Digit 6
Highlighted cells show the skyscraper pattern
Practice Puzzles
Apply the skyscraper technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Two conjugate pairs of a candidate share one endpoint in the same row/column
- Action:
- Eliminate the candidate from cells that see both unlinked endpoints
- Look for:
- Two linked conjugate pairs forming a skyscraper shape