Two conjugate pairs for a single digit that share one endpoint. The unshared endpoints drive eliminations.
A Skyscraper is a single-digit technique built from two conjugate pairs that share one endpoint. 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 two such pairs are connected at one cell, the unshared endpoints 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.
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