A skyscraper is two rows that each have exactly two cells left for one digit, where one cell from each row lines up in a single shared column. The aligned pair is the base; the two cells sticking out at different heights are the roofs — the two towers the technique is named for.
The base column can hold the digit only once, so the two base cells cannot both be true: at least one of the two rows must place its digit at the roof instead. You never learn which — and it does not matter. Any cell that sees both roofs would clash with either outcome, so the digit is struck from it.
To spot one, hunt for rows (or columns — the pattern transposes) reduced to two candidates for a digit, then look for two of them sharing one column. The skyscraper is the first of the single-digit link patterns, and the doorway to the two-string kite and the empty rectangle on the rungs above.
On the board
Follow the digit 8. Row 4 has exactly two cells for it — columns 6 and 7 — and row 8 also has exactly two: columns 4 and 7. The column-7 pair is the base; R4C6 and R8C4 are the roofs. If neither roof held the 8, both rows would push it into column 7 — two 8s in one column. So at least one roof is an 8, and the two cells that see both roofs give it up: R5C4, which shares column 4 with one roof and the centre box with the other, and R9C6, which shares column 6 with one and the bottom-middle box with the other.
This is the exact board the app's interactive Skyscraper demo uses — step 21 of its 64-step walkthrough, drawn here with its live pencil marks.
