Skyscraper
Two strong links on the same digit, sharing a column on one end and not the other — eliminates the digit from any cell that sees both 'roof' cells of the pattern.
A skyscraper is one of three single-digit patterns that share a common underlying logic. Pick a digit. Find two rows where the digit has exactly two candidate cells in each, and where one of the columns matches between the two rows but the other doesn't. The two matching cells form the "base" of the skyscraper; the two non-matching cells form the "roof." The digit can be eliminated from any cell that sees both roof cells.
The argument
Each row has a strong link on the digit between exactly two cells. Whichever cell in row 1 holds the digit, it forces the placement in row 2's strong link to be the opposite cell of the matching column. So either the digit is in the base (the matching column), or it's split across the two roof cells — one in each row.
In both cases, the roof cells together cover the digit's placement in the two rows. Any cell that sees both roof cells must avoid the digit, because one of them is going to be the digit, and a third cell sharing units with both can't repeat it.
The pattern works rotated 90°: two columns, each with the digit having exactly two candidate cells, sharing a row on one end. The eliminations happen in cells visible from both "roof" cells of the columnar variant.
Why it sits between X-wing and chains
A skyscraper is the simplest case of the two-strong-links family. An X-wing is two strong links that share both columns; a skyscraper shares only one. The shared column is the part of the pattern that lets the eliminations fire — it forces the strong links to align, even though they don't quite form an X-wing's grid.
Skyscrapers are also a special case of the chain techniques. An Alternating Inference Chain of length two — strong link, weak link, strong link — produces the same eliminations a skyscraper does. The skyscraper label is just the named pattern most solvers learn before drilling AIC fluency.
When you'll see it
Skyscrapers turn up regularly on hard and expert puzzles. They're one of the patterns that the Sudoku Mountain solver detects and emits a deduction step for, alongside 2-string kite and empty rectangle — all three share the same underlying detector and produce identical kinds of eliminations under different visual shapes.
See also
- 2-string kite— A digit's strong link in a row meets a strong link in a column, with the two cells sharing a box at the corner. Eliminates the digit from cells seeing both far ends.
- Empty rectangle— A box where a digit's candidates sit in one row and one column intersecting inside the box. Combined with a strong link, eliminates the digit elsewhere on the matching axis.
- Strong link— A relationship between two cells in a unit where a digit must occupy exactly one of them — the basic primitive that hidden singles, X-wings, and chain reasoning all rest on.
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
Read more
- Which technique is this puzzle asking for
How to read a fresh hard Sudoku and predict which intermediate technique will break it open before you've placed a single digit.