Skyscraper Sudoku Strategy

Skyscraper is a short single-digit chain that looks like an almost X-Wing. Two strong links stand in parallel rows or columns. One side lines up, and the other side is offset. The offset endpoints are the "roofs", and any cell that sees both roofs can lose the target candidate.

This is a Hard-level pattern that fits naturally after X-Wing. If an X-Wing fails because the second side does not line up, check whether the offset endpoints still create a Skyscraper elimination.

The Pattern

• Target digit: choose one candidate, such as 4.
• Two strong links: find two rows or two columns where 4 appears exactly twice.
• Base side: one endpoint from each link aligns in the same column or row.
• Roof cells: the two other endpoints do not align with each other.
• Elimination: any cell that sees both roof cells cannot be 4.

Why It Works

Each strong link says one of its two endpoints must contain the target digit. If the aligned base cells were both false, both roof cells would be true. If one base cell is true, it removes the target from peers on the base line and still leaves the opposite strong link forcing its roof. Either way, at least one roof cell must be true.

That means a cell that sees both roofs cannot hold the same candidate. It would be eliminated no matter which roof becomes true.

Step-by-Step Example

Imagine candidate 4 appears only at r2c3 and r2c8 in row 2, and only at r7c3 and r7c6 in row 7. The base cells are r2c3 and r7c3 because they share column 3. The roof cells are r2c8 and r7c6.

Now look for any cell containing candidate 4 that sees both roof cells. A cell at r2c6 would see r2c8 by row and r7c6 by column, so you can remove 4 from r2c6.

Skyscraper vs X-Wing

In an X-Wing, both sides align. If row 2 and row 7 both had candidates in columns 3 and 8, you could remove the candidate from the rest of columns 3 and 8. In a Skyscraper, only one side aligns. The elimination is narrower, but it often appears in puzzles where a clean X-Wing is absent.

Common Mistakes

• Starting from rows with extra candidates: each strong link line must have exactly two placements for the target digit.
• Eliminating across the whole base line: Skyscraper removes only from cells that see both roof cells.
• Using different candidates: every endpoint and elimination must involve the same digit.
• Removing from a roof: roofs are endpoints of the logic. Do not eliminate from them.

What to Learn Next

If Skyscraper makes sense, continue with Two-String Kite for another short strong-link pattern, then Simple Coloring for longer chains. For row-column pattern logic, move on to Swordfish and Finned X-Wing.

Practice

Try scanning for Skyscraper after failed X-Wing checks in Hard printable Sudoku puzzles or today's daily Sudoku. Focus on one candidate at a time and look for two-position rows or columns.

← Back to all strategies