Skyscraper

Two Lines, One Shared Column

By Minimal Sudoku Team•Last updated: January 28, 2025

The Skyscraper is a single-digit technique that uses two rows (or columns) where a candidate appears exactly twice. When one cell from each row shares a column, the "rooftops" of the skyscraper create eliminations.

Quick Summary

Pattern: Two rows with candidate in exactly 2 cells each
Requirement: One cell from each row shares the same column
Result: Eliminate from cells seeing both "rooftop" cells
Difficulty: Advanced — related to X-Wing and Turbot Fish

The Concept

A Skyscraper looks like two buildings of different heights sharing one column. The candidate appears exactly twice in each of two rows, with one "base" cell from each row aligned in the same column.

The two non-aligned cells are the "rooftops" — and cells that see both rooftops can have the candidate eliminated.

The Golden Rule

🏙️ Skyscraper Rule

When a candidate appears exactly twice in each of two rows, and one cell from each row shares a column (the "base"), eliminate the candidate from cells that see both "rooftop" cells (the non-base cells).

Pattern Structure

Skyscraper structure:

The shared column forms the base; the two off-column cells are the rooftops.

→ Eliminate X from any cell that sees both rooftops.

How to Find Skyscrapers

Choose a candidate

Pick a digit to analyze.

Find rows with exactly 2 positions

Look for rows where your candidate appears in exactly 2 cells.

Find a pair sharing one column

Find two such rows where one cell from each is in the same column.

Identify the rooftops

The cells NOT in the shared column are the rooftops.

Find elimination targets

Eliminate the candidate from any cell that sees both rooftops.

Why It Works

Consider the shared column (the "base"):

At least one of the two base cells must contain the candidate
If Base 1 has it → Rooftop 1 doesn't → Rooftop 2 might
If Base 2 has it → Rooftop 2 doesn't → Rooftop 1 might

In all scenarios, at least one rooftop contains the candidate. Any cell seeing both rooftops will always "see" the candidate.

Like a Broken X-Wing

A Skyscraper is essentially an X-Wing where the cells don't quite align — they share only one column instead of two.

Detection Tips

Start from X-Wing Failures

When hunting for X-Wings, if you find two rows with exactly 2 candidates but they don't share both columns, check if they could form a Skyscraper.

Works Both Ways

The pattern works with rows (eliminate from columns) or columns (eliminate from rows). Check both orientations.

Focus on the Rooftops

The eliminations happen from cells seeing both rooftops. Often these are in the same box or on the same row/column as both rooftops.

Single-Digit Patterns

✈️X-Wing ⬜Empty Rectangle 🎨Simple Coloring

Advanced

X-Wing

The perfectly aligned version of the pattern — when both columns match.