Two conjugate pairs for a single digit whose base cells share a unit. The unshared endpoints (roofs) drive eliminations.
Look for one digit with exactly two candidate cells in each of two rows, where one cell from each pair falls in the same column. That shared column forces the digit into one of the two ends outside it — the roofs. Eliminate the digit from any cell that sees both roofs; rows and columns can be swapped throughout.
A Skyscraper is a single-digit technique built from two conjugate pairs whose base cells share a unit. A conjugate pair means a digit has exactly two candidate cells in a row or column, if it's not in one, it must be in the other. When the two pairs share one column (for row pairs) or one row (for column pairs) — so their base cells lie in the same unit and see each other — the two unshared endpoints (the roofs) create a powerful elimination zone.
The name "Skyscraper" comes from the visual shape: two vertical (or horizontal) lines of different heights connected at one end, resembling a city skyline. Despite the evocative name, the logic is straightforward, it's a short chain of strong links.
Skyscrapers appear in Hard and Extreme puzzles and are one of the most accessible advanced single-digit techniques. They're easier to spot than X-Wings because you're looking for just two conjugate pairs rather than a full rectangle.
Choose a digit and find two rows (or columns) where that digit appears as a candidate in exactly two cells each. These are your two conjugate pairs. Now check: do the pairs share one column (or row)? If so, you have a Skyscraper.
The logic works because the digit must be in one cell of each pair. At the shared endpoint, both pairs "compete" for the same column. This forces the digit to appear at one of the two unshared endpoints. Any cell that can see both unshared endpoints (shares a row, column, or box with both) cannot contain the digit.
In practice: find the two unshared endpoints, then look for cells that share a unit with both. Eliminate the digit from those cells.
Example 1: Skyscraper in Rows
Step 1: Scanning digit 1, we find two rows where it appears in exactly two cells. In row 2, digit 1 is in R2C2 and R2C9. In row 4, digit 1 is in R4C3 and R4C9. The pairs share column 9, that's the connection point.
Step 2: The unshared endpoints are R2C2 and R4C3. The digit must end up in at least one of these two cells. Any cell that sees both R2C2 and R4C3 cannot contain digit 1.
Step 3: R3C3 shares column 3 with R4C3 and box 1 with R2C2, but actually it shares the column with R4C3 and the row... Let's check: R3C3 sees R4C3 via column 3. R3C3 sees R2C2 via box 1. So R3C3 sees both unshared endpoints. Eliminate 1 from R3C3, R5C2, and R6C2.
Example 2: Skyscraper in Columns
Step 1: Now consider digit 3 in columns 5 and 9. In column 5, digit 3 appears in R2C5 and R5C5. In column 9, digit 3 appears in R1C9 and R5C9. The pairs share row 5, that's the connection point.
Step 2: The unshared endpoints are R2C5 and R1C9. The digit must end up in at least one of these two cells.
Step 3: Cells seeing both unshared endpoints: R1C6 sees R1C9 (same row) and R2C5 (same box). R2C8 sees R2C5 (same row) and R1C9 (same box). Eliminate 3 from R1C6 and R2C8.
A conjugate pair is a row or column in which a digit has exactly two remaining candidate cells, so if the digit is not in one it must be in the other. A Skyscraper uses two of them, linked by base cells in a shared unit, so the digit is forced onto one of the two roofs.
Only cells that can see both roofs — the two endpoints outside the shared base unit. Seeing a cell means sharing a row, column or box with it, so a target typically lies in the same box as one roof and on the same line as the other. Check every cell in that overlap and remove the digit.
An X-Wing needs both conjugate pairs to occupy the same two columns, forming a rectangle. A Skyscraper needs them to share only one column, so the shape is lopsided. The elimination zone differs too: instead of clearing every other cell in two columns, you clear only the cells that see both roofs.
Both use two conjugate pairs of one digit, but the link between them differs. A Skyscraper joins two pairs of the same orientation — two rows or two columns — whose base cells share a line. A Two-String Kite joins a row pair to a column pair through a shared box. Both then eliminate from cells seeing the two free endpoints.
The name comes from the shape. Draw the two conjugate pairs as lines and you get two towers of different heights standing on a shared base, like a city skyline. The naming is purely visual — underneath it is a short chain of two strong links, sometimes classed as a Turbot Fish.
Yes. Two columns in which the digit has exactly two candidate cells, with one cell from each pair in the same row, work identically. The shared row becomes the base and the two remaining endpoints become the roofs. Scan both orientations, since a puzzle may hide the pattern in only one of them.
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