Skyscraper

Volodymyr Sakhan  ·  May 31, 2026

The Skyscraper is an advanced single-digit elimination technique. Once you have exhausted naked and hidden singles, pointing pairs, and naked pairs, the Skyscraper is one of the first patterns to look for. Our full solving guide covers where it fits in the overall solving order.

What Is the Skyscraper Technique?

A Skyscraper is a four-cell pattern built from a single digit. You need two rows (or two columns) where that digit appears exactly twice each, and the two rows share one column that contains one candidate from each row. Those two shared-column cells are the base. The remaining two cells — one from each row in different columns — are the roof.

The pattern has three named parts:

• Base pair — two cells in the same column (or row), one from each of the two rows. They form a strong link: exactly one of them is the target digit.
• Roof pair — the remaining two candidates, each in a different column. At least one of them must be the target digit.
• Elimination targets — any cell that can see both roof cells (shares a row, column, or box with both) cannot contain the digit.

The logic follows a short chain: if roof cell R1 is not the digit, then its base partner must be, which forces the other base cell to be false, which in turn forces roof cell R2 to be true. Either way, at least one roof cell is always true — so any cell seeing both is always false.

When to Use the Skyscraper

Look for a Skyscraper after simpler techniques have stopped working. The scan is straightforward:

1. Pick a digit and note every row (or column) where it appears exactly twice.
2. Check whether any two of those rows share exactly one column that contains one candidate from each row.
3. If so, the two shared-column cells are the base; the two remaining cells are the roof.
4. Look for any cell that sees both roof cells — that cell can be eliminated.

Step-by-Step Examples

Example 1 — Column-Based Skyscraper (Digit 1)

In this position, digit 1 is the target. Two columns each contain exactly two 1-candidates, and they share a row — the classic column-based Skyscraper.

1. Scan for digit 1: column A has exactly two candidates — A3 and A5.
2. Column D also has exactly two candidates — D1 and D5.
3. A5 and D5 share row 5 — this is the base pair (highlighted blue).
4. The roof pair is A3 and D1 (highlighted green) — they are in different rows and different columns.
5. Chain: if A3 ≠ 1 then A5 = 1, which forces D5 ≠ 1, which forces D1 = 1. So at least one of {A3, D1} is always 1.
6. B1 sees A3 (same box, top-left) and D1 (same row 1) → B1 ≠ 1.
7. C1 sees A3 (same box) and D1 (same row 1) → C1 ≠ 1.
8. E3 and F3 both see A3 (same row 3) and D1 (same top-middle box) → E3 ≠ 1, F3 ≠ 1.

Removing 1 from B1, C1, E3, and F3 breaks the deadlock and opens the path to further deductions.

Example 2 — Row-Based Skyscraper (Digit 7)

Here the same structure runs across rows instead of columns. Digit 7 appears exactly twice in each of two rows, and those rows share a column — giving a row-based Skyscraper.

1. Scan for digit 7: row 2 has exactly two candidates — A2 and D2.
2. Row 8 also has exactly two — A8 and E8.
3. A2 and A8 share column A — this is the base pair (highlighted blue). Column A has exactly these two 7-candidates, so exactly one of them is 7.
4. The roof pair is D2 and E8 (highlighted green) — different columns, different rows.
5. Chain: if D2 ≠ 7 then A2 = 7, which forces A8 ≠ 7, which forces E8 = 7. At least one of {D2, E8} is always 7.
6. D9 sees D2 (same column D) and E8 (same bottom-center box, rows 7–9, cols D–F) → D9 ≠ 7.

Eliminating 7 from D9 is the only deduction this board position needs to continue the solve.

Skyscraper vs. X-Wing and Simple Colouring

The Skyscraper is closely related to two other advanced techniques. Understanding the differences helps you see the bigger picture of single-digit elimination:

• X-Wing requires both conjugate pairs to align in the same two columns, forming a rectangle. Skyscraper relaxes this — the base column is shared, but the roof cells land in different columns. X-Wing eliminates candidates from entire columns; Skyscraper only eliminates from cells that see both roof tips.
• Simple Colouring assigns alternating colours along conjugate pairs. A Skyscraper is exactly a 3-link colour chain: one base-column link, one row weak link, one roof-column link. The two roof cells get opposite colours, and any cell seeing both colours is eliminated.
• Turbot Fish is the general family — the Skyscraper is its simplest member, an alternating-inference chain of length 3 (strong–weak–strong). Recognising this generalises naturally to the Two-String Kite and longer X-Cycle chains.

Mastering the Skyscraper is the first step towards understanding all Turbot Fish patterns and X-Cycle chains.

Practice Skyscraper Online

The Skyscraper typically appears in hard puzzles. Play hard sudoku on OnSudoku and keep an eye on digits that appear exactly twice in two rows or columns — that is where Skyscrapers hide.

Enable pencil marks, then scan digit by digit. When you find a Skyscraper, eliminate the candidates before placing any number — it often unlocks a chain of hidden singles.

Frequently Asked Questions