Skyscraper
A Skyscraper is a single-digit pattern built on two rows in which a digit has exactly two candidate cells. One cell of each row lies in the same column; these two cells are the base, and they cannot both hold the digit. The other two cells, the tops, lie in different columns. Because at least one base cell is not the digit, at least one top must be, so the digit can be removed from every cell that sees both tops. The same works with columns instead of rows. The Skyscraper is a form of Turbot Fish, like the 2-String Kite, and it is an Expert technique in Bare Sudoku.
When to use it
When X-Wing and Swordfish find nothing. The Skyscraper is one of the most common Expert patterns in Bare Sudoku, and it often appears where an X-Wing almost works: two rows with two candidates each for a digit, sharing only one column instead of two. It needs complete notes for the digit you examine.
How to spot it
Pick a digit and list the rows in which it has exactly two candidate cells. Compare those rows in pairs: if exactly one candidate cell of each row sits in the same column, those two cells are the base and the other two are the tops. Then look for cells that see both tops and still contain the digit; usually they sit in the box of one top and the column of the other. Repeat with columns instead of rows. In the game, tap the digit key to highlight its candidates and look for two rows that show exactly two each.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 6 | 23 | 125 | 35 | 7 | 4 | 9 | 158 | 18 |
| r2 | 8 | 49 | 457 | 59 | 6 | 1 | 3 | 2 | 47 |
| r3 | 59 | 349 | 1457 | 359 | 8 | 2 | 457 | 6 | 147 |
| r4 | 59 | 289 | 258 | 4 | 3 | 58 | 1 | 7 | 6 |
| r5 | 4 | 6 | 58 | 1 | 9 | 7 | 58 | 3 | 2 |
| r6 | 1 | 7 | 3 | 6 | 2 | 58 | 458 | 45 | 9 |
| r7 | 2 | 5 | 48 | 7 | 1 | 9 | 6 | 48 | 3 |
| r8 | 7 | 1 | 6 | 8 | 4 | 3 | 2 | 9 | 5 |
| r9 | 3 | 48 | 9 | 2 | 5 | 6 | 47 | 148 | 1478 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- Digit 8 has exactly two candidate cells in row 5, r5c3 and r5c7, and exactly two in row 7, r7c3 and r7c8.
- r5c3 and r7c3 are both in column 3, so at most one of them can be 8. They form the base; r5c7 and r7c8 are the tops.
- If r5c3 is not 8, row 5 must put its 8 in r5c7. If r7c3 is not 8, row 7 must put its 8 in r7c8. At least one base cell is not 8, so at least one top is 8.
- A cell that sees both tops can never be 8. Remove 8 from r6c8, r9c7.
Common mistakes
- Using a row that has three candidate cells for the digit. Each of the two rows must have exactly two, or the row could place the digit somewhere else.
- Taking two rows whose candidates line up in both columns. That is an X-Wing, which removes the digit from the rest of the two columns instead.
- Removing the digit from cells that see only one top. The eliminated cell must see both tops.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: Skyscraper
Frequently asked questions
What is a Skyscraper in Sudoku?
A pattern of one digit in two rows, or two columns, where the digit has exactly two candidate cells each. One cell of each row lines up in a shared column; the other two, the tops, do not. At least one top holds the digit, so it is removed from every cell that sees both tops.
Why is it called a Skyscraper?
Because of its shape in the column version: two columns rise from a shared base row like two towers, and their tops end at different heights. The row version is the same pattern turned on its side.
Is a Skyscraper a Turbot Fish?
Yes. A Turbot Fish joins two units in which a digit has exactly two candidates through two cells that see each other. In a Skyscraper the two units are parallel rows or parallel columns, and the joined cells share a column or a row; in a 2-String Kite they are a row and a column joined in a box.
How is a Skyscraper different from an X-Wing?
An X-Wing needs both pairs of candidates to line up in the same two columns, and it removes the digit from the rest of those columns. A Skyscraper lines up only one pair; the tops are free, and only cells that see both tops lose the digit.
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