To solve Skyscrapers, use the clues to work out where the tall buildings can’t be, then count rows and columns as in Sudoku. A clue of 1 puts the tallest building next to it; a clue as big as the grid makes the line climb one step at a time. Any other clue keeps the tall buildings away from its end. When a line has only a few ways left to match its clues, list them. Six techniques cover every puzzle in the game.
New to Skyscrapers? Read the Skyscrapers rules first. This page assumes you know the two rules: each height once in every row and column, and the clues count the buildings you can see.
1. Clues of 1 and n
A clue of 1 sees only the first building, so it’s the tallest.
A clue as big as the grid sees every building, so the line climbs 1, 2, 3 and so on from that end.
2. One height left
Look at what a square’s row and column already hold, and at its notes. When only one height is left, that’s its height.
3. One place left
Turn it round: pick a height a row or column still needs, and find where it can go. When there’s only one place left, it goes there. The tallest building is a good one to look for: the clues often rule it out of all but one square.
4. Distance from a clue
With a clue of c, c − 1 more buildings have to come into view after the first, each taller than the last. So the building d squares in from the clue (counting the first as 0) can be at most n − c + 1 + d tall. In practice: the tallest building can’t stand within c − 1 squares of a clue of c.
5. Every arrangement
When a line has clues and only a few heights left to place, list every ordering that matches its clues and notes. A height no ordering puts in a square is ruled out there; a height every ordering puts there is placed.
6. What if
When nothing else works, pick a square with two heights left and suppose it’s one of them. Follow what that forces through the clues and the lines. If something runs out of options, cross that height out. The what-if page follows one through a real puzzle.
How often each technique is needed
We solved every one of the game’s 150 levels by following the hints, which always use the simplest technique that works. This is how many times each technique was used, on average, per level:
| Technique | Easy 5×5 | Medium 6×6 | Hard 7×7 |
|---|---|---|---|
| Clues of 1 and n | 1.6 | 1.1 | 0.8 |
| One height left | 12.4 | 16.4 | 26.8 |
| One place left | 2.6 | 4.1 | 7.2 |
| Distance from a clue | 3.5 | 4.1 | 3.2 |
| Every arrangement | 5.2 | 9.1 | 11.5 |
| What if | 0 | 0 | 4.9 |
Every level needs distance and every arrangement; one height left does the most work. What-if is only for Hard, where every level needs it.
A 6×6, solved in stages
This is Medium level 20 from the game.
Stage 1: a clue of 1
Row 5 has a clue of 1 on the right, so its last square is the tallest building, 6.
Stage 2: row 2 from its clue of 5
Row 2 has a clue of 5 on the right. Reading from the right, five buildings must come into view, so the squares can be at most 2, 3, 4, 5 and 6 tall. The 2 is already given at the far end, so from the right the row is 1, 3, 4, 5, 6.
Stage 3: every arrangement
Two more steps from distance, and then column 3. It has a clue of 2 at the bottom, and of the orderings its clue and notes still allow, every one puts the 6 in row 4.
From there it’s counting and arrangements to the end. In all, the level takes 34 steps: 1 from a clue of 1, 6 from distance, 8 arrangements, 14 squares with one height left and 5 heights with one place left.
When you get stuck
- Check every clue of 1 and n, and every clue’s distance limits.
- Count rows and columns as in Sudoku: one height left, one place left.
- Fill in notes on the bigger grids; arrangements are much easier to see with them.
- List the orderings for a line with clues and only a few squares left.
- Don’t guess. Every puzzle here can be finished by logic.