Skyscrapers solving techniques
Skyscrapers techniques start at the edge and move inward. Here are the steps our solver uses, with a real example of each and how often our puzzles need it.
- Clues 1 and N
- Naked single
- Hidden single
- Distance from the clue
- Naked pair
- Line permutations
- Contradiction
Clues 1 and Ntier 1
When: A 1 sees only the tallest tower, so it stands next to the clue; an N sees every tower, so they rise 1, 2, 3... from the clue.
A clue of 1 sees only the first tower, so the tallest stands there. A clue equal to the size sees every tower: the line rises 1, 2, 3 and on from that side.
From one of our puzzles (4x4): The 1 after row 3 sees only the first tower, so D3 is the tallest, 4.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Clues 1 and N | 100% | 74% | 67% | 58% |
Naked singletier 1
When: A cell with one possible height takes it; the height leaves its row and column.
A cell with one possible height takes it; the height leaves its row and column.
From one of our puzzles (4x4): A1 can only be 3, so no other cell of its row or column is 3.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Naked single | 100% | 100% | 100% | 100% |
Distance from the cluetier 2
When: A clue of c rules out tall towers near it: the cell d steps in can be at most N - c + 1 + d.
A clue of c needs c - 1 shorter towers in front of the tallest it sees, so tall towers cannot stand close to it: the cell d steps in holds at most N - c + 1 + d.
From one of our puzzles (4x4): The 3 at the bottom of column B needs 2 shorter towers in front of the tallest it sees, so the first cells cannot be too tall: B4 at most 2.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Distance from the clue | 0% | 100% | 99% | 100% |
Naked pairtier 2
When: Two cells of a line with the same two candidates own those heights.
Two cells of a line with the same two candidates own those heights; the rest of the line loses them.
From one of our puzzles (5x5): E3 and E5 can only be 1 or 2, so the rest of column E cannot.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Naked pair | 0% | 1% | 44% | 57% |
Line permutationstier 3
When: List the orders of a line that fit its candidates and both clues; heights that never appear in a cell are out.
List the orders a whole line can take with the candidates it has and both its clues. A height that no order puts in a cell is out. On a 6x6 there are at most 720 orders, and usually only a few survive.
From one of our puzzles (4x4): Only 3 orders of column B fit its candidates and clues; B3 loses the heights no order puts there.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Line permutations | 0% | 0% | 100% | 100% |
Contradictiontier 4
When: If a height in a cell leads to a broken clue a few steps later, that height is out.
Assume a height, follow the clues and the singles, and see whether some clue can no longer be met. If so, the height is out.
From one of our puzzles (6x6): Suppose B2 were 4: following the rules from there, the left clue of row 6 would see 3, not 4. So B2 is not 4.
| Share of puzzles that need it | Easy (662) | Medium (662) | Hard (662) | Expert (612) |
|---|---|---|---|---|
| Contradiction | 0% | 0% | 0% | 100% |
Source: the Gridaday bank, 2,598 puzzles of Skyscrapers graded by our solver; data as of 2026-10-17.