If a digit fits in exactly two cells in each of two rows, and one cell from each row sits in the same column, those two can't both hold the digit. So at least one of the other two cells (the tops) does, and no cell that sees both tops can be that digit. It works the same with rows and columns swapped.
A Skyscraper is an X-Wing that doesn't quite line up: one end of each row matches, the other doesn't. Draw the two rows as columns and they look like two towers of different heights, hence the name.
It is one of the first patterns hard puzzles ask for once the pairs and X-Wings run out.
A Skyscraper
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In columns 4 and 9, the 4 fits in just two cells each. R7C4 and R7C9 share row 7, so they can't both be the 4, which means R6C4 or R5C9 is. So the 4 can be removed from every cell that sees both of them: R6C7. That leaves R6C7 with only one candidate: 2.
Only the 4s are shown, so the pattern stands out.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Pick a digit and look only at its candidates.
2Find two rows where the digit has exactly two possible cells each.
3Check whether one cell from each row is in the same column. Those two are the base.
4The other two cells are the tops. They must be in different columns (if they line up too, it's an X-Wing).
5Remove the digit from every cell that sees both tops, that is, shares a row, column or box with each of them.
6Try the same with columns: two columns with two spots each, one end of each in the same row.
Why it works
The two base cells share a column, so at most one of them can hold the digit.
Each row needs the digit in one of its two cells. Wherever a base cell isn't the digit, the top of its row is. Since at least one base is empty of it, at least one top holds it.
A cell that sees both tops would clash with whichever top holds the digit, so it can never be that digit.
Common mistakes
Using a row where the digit has three or more spots. Each of the two rows must have exactly two.
Removing the digit from cells that see only one of the tops. A cell must see both.
Mixing up base and tops: the base cells are the ones that line up; the eliminations come from the other two.
Questions
How is a Skyscraper different from an X-Wing?
In an X-Wing both ends line up, so the digit is locked into two columns. In a Skyscraper only one end lines up, so you only learn that one of the two tops holds the digit.
Does the base have to be at the bottom?
No. The shared end can be on either side, and the rows can be anywhere on the board. It works the same for two columns whose shared end is in one row.
What should I learn next?
The 2-String Kite uses the same idea with one row and one column instead of two rows.
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