Skyscraper
A single-digit chain on two lines with one shared cross-line, eliminating the digit where the far ends see common cells.
A skyscraper is a single-digit technique built from two strong links. Take a digit that appears exactly twice in each of two rows. If one end of each pair shares the same column (the "base"), the two far ends (the "roof") are connected: one of them must hold the digit, so any cell seeing both roof cells can have the digit removed.
It is often easier to spot than an XY-Wing and resolves many expert puzzles.
How to spot it
Find a digit with exactly two candidate cells in each of two rows. If those pairs share a column at one end, focus on the two cells at the other end. Any cell that sees both of those far cells cannot contain the digit.
- Digit appears twice in two rows (or columns).
- One end of each pair shares a line — the base.
- Eliminate the digit from cells seeing both roof ends.
Worked example
- Digit 1 sits in only two cells of row 3 and two of row 7.
- In both rows one of those cells is in column 5 (the base).
- The other ends are in columns 2 and 8 (the roof).
- A cell that sees both roof cells must therefore not be 1.
- Remove 1 from it.
Try it yourself
Tap a cell, then a number, to practise.
Frequently asked questions
- Is the skyscraper a fish?
- It is closely related; it is effectively a degenerate fish / single-digit chain that is quicker to see by eye.
- Rows or columns?
- Either. Build it on two rows and eliminate via columns, or the other way round.
Related techniques
Further reading
- Single Digit Patterns (Skyscraper, Empty Rectangle) — HoDoKu
- Introducing Chains and Links — SudokuWiki.org
Practice: Skyscraper
Put the Skyscraper to work on a live board — free puzzles with notes, hints and four difficulty levels.
Try it on a live board