Sudoku skyscraper: the cousin of X-wing for short-strong patterns
The skyscraper sits in the middle of the advanced sudoku-technique progression: easier than swordfish, less restrictive than X-wing, and useful in puzzles where the X-wing pattern almost-but-doesn’t exist. Once you can see it, it cracks half of the expert puzzles X-wing fails on.
Background: strong links
A strong link on a digit is when that digit has exactly two candidate positions in a row, column, or 3×3 box. The digit MUST go in one of those two cells.
Strong links are the building blocks of every advanced fish pattern. X-wing uses four strong links across two units; swordfish uses six across three units. The skyscraper is the minimal interesting structure: two strong links sharing one column.
The skyscraper shape
Pick a digit. Find two rows where the digit can only go in two cells each (i.e. two strong links on that digit within rows). Both strong links share one common column— that column contains a candidate in both rows. The other ends of the strong links — the “tops” of the skyscraper — are in different columns.
Why the elimination works
Here’s the case-split. In row 3, the 4 goes in col 2 or col 5. In row 7, the 4 goes in col 2 or col 7.
Suppose the 4 in row 3 is in col 2. Then the 4 in row 7 CAN’T also be in col 2 (column constraint), so row 7’s 4 is at col 7. Now consider any cell that sees both col 5 and col 7 (i.e. shares a row with either col 5 or col 7, but isn’t the actual top of the skyscraper). Hmm wait, that’s not quite the right framing.
Here’s the cleaner statement: if the digit at the base (col 2) of either row is FALSE, then the digit at the top of THAT row is TRUE. Since at least one base must be FALSE (they share a column and can’t both be the row’s 4), at least one of the two tops is TRUE. So: any cell that sees BOTH tops cannot be the digit 4— one of the two tops will be 4, and a cell that sees both can’t conflict with whichever it turns out to be.
In the example above, cells that see both col 5 and col 7 (e.g. cells in rows that include both columns as peers) get 4 eliminated as a candidate.
Two-string kite — the column-version sibling
The skyscraper has a 90°-rotated sibling called the two-string kite: two strong links in COLUMNS that share a common ROW. The reasoning is identical, just flipped axes. Most sudoku engines treat skyscrapers and kites as the same family (“turbot fish”) and the elimination logic is the same.
If you’re scanning for a skyscraper and finding nothing, scan for the kite next.
How to hunt
- Pick a digit you suspect (often one you’ve made no recent progress on).
- List every row where that digit appears in exactly two cells — these are your strong-link candidates.
- For each pair of rows, check whether their strong links share a common column.
- If yes, identify the “top” cells (the non-shared ends).
- Find any cell that sees BOTH top cells. Erase the digit as a candidate.
The check repeats for columns (swap rows for columns → you’re hunting kites).
When the skyscraper beats X-wing
X-wing requires both strong links to share BOTH columns. Skyscraper only requires one shared column. That’s a strictly weaker condition, so any X-wing you find is also “technically” a degenerate skyscraper — but the interesting case is when an X-wing fails because only ONE column is shared. The skyscraper still produces an elimination there; X-wing can’t.
In practice on expert puzzles, skyscrapers come up about twice as often as X-wings. Worth having both tools.