How to play the skyscrapers puzzle
The rules, the visibility mechanic, solving strategies, and a step-by-step example. Also known as a towers puzzle.
What is a Skyscrapers puzzle?
Skyscrapers is a logic puzzle on an N×N grid. Each cell represents a building with a height from 1 to N. The grid must be filled so that every row and column contains each height exactly once (a Latin square). Border clues along all four sides tell you how many buildings are visible when you look into the grid from that edge.
Taller buildings block shorter ones behind them. If you look along a row and see heights [2, 4, 1, 3], the visibility count from the left is 2 (heights 2 and 4 are visible; 1 and 3 are hidden behind the 4).
The three rules
- Latin square: Fill every cell with a height from 1 to N. Each row and each column must contain every height exactly once.
- Visibility clues: Numbers along the grid border indicate how many buildings are visible when looking into the grid from that position. Taller buildings block shorter ones behind them.
- Hidden clues: Some border positions have no clue shown. These positions still have a valid visibility count — you just need to deduce it from other constraints.
Worked example (4×4)
Consider the row [2, 4, 1, 3] on a 4×4 grid:
- From the left: 2 is visible (first building), 4 is visible (taller than 2), 1 is hidden (behind 4), 3 is hidden (behind 4). Visibility = 2.
- From the right: 3 is visible (first from right), 1 is hidden (behind 3), 4 is visible (taller than 3), 2 is hidden (behind 4). Visibility = 2.
If the left clue is 2 and the right clue is 2, the row [2, 4, 1, 3] satisfies both. Your job is to find the arrangement that satisfies all clues simultaneously.
Solving strategies
1. Clue = 1 placement
A clue of 1 means only one building is visible from that edge — the tallest (height N). Place N in the first cell from that edge. This is the simplest and most common starting deduction.
2. Clue = N placement
A clue equal to the grid size N means every building is visible, which is only possible if they appear in ascending order: 1, 2, 3, …, N. This fills the entire line immediately.
3. Clue = N-1 deduction
A clue of N-1 means all but one building is visible. The tallest (N) cannot be in position 1 (that would give visibility 1) and must be in position 2. The first cell must be less than all buildings behind position 2 except N.
4. Opposite clue pairing
If a line has clues L (left/top) and R (right/bottom), and L + R = N + 1, the tallest building N is at one of the two edges. For example, on a 4×4 grid with left clue 3 and right clue 2 (3+2=5=4+1), height 4 must be in position 2 or 3.
5. Latin-square elimination
Whenever you place a height, eliminate it from all other cells in that row and column. This often cascades — reducing a cell to one candidate triggers another placement, and so on.
6. Partial visibility reasoning
Even before a line is complete, count the minimum visibility so far. If placing a tall building in an empty cell would exceed the clue, that building cannot go there. Similarly, if the remaining empty cells cannot generate enough new visibility to reach the clue, something is wrong.
Skyscrapers vs other puzzles
| Aspect | Sudoku | KenKen | Skyscrapers |
|---|---|---|---|
| Grid | 9×9 | 3×3 to 9×9 | 4×4 to 7×7 |
| Extra constraint | 3×3 boxes | Caged arithmetic | Border visibility clues |
| Reasoning style | Elimination in groups | Arithmetic + elimination | Spatial line-of-sight |
Common mistakes
- Forgetting Latin-square uniqueness: Each height appears exactly once per row and column. Placing a duplicate is the most common error.
- Miscounting visibility: Remember that visibility is counted from the edge inward. A building is visible only if no taller building stands between it and the edge.
- Ignoring hidden clues: A missing clue does not mean “no constraint” — it means the constraint exists but you must deduce it. Other clues plus the Latin-square rule constrain hidden-clue lines too.
- Not using pencil marks: On 6×6 and larger grids, tracking candidates manually is error-prone. Use our pencil marks feature (N key).
Frequently asked questions
What is a skyscraper puzzle?
A logic puzzle where you place buildings of different heights in a grid. Border clues tell you how many buildings are visible from each direction. The tallest buildings block the view of shorter ones behind them. The puzzle is also called a “towers puzzle” in some books and education sites.
How do you solve a skyscraper puzzle?
Start with clues of 1 (tallest building goes first) and clues equal to the grid size (ascending order). Then cross-reference opposing clues on the same row or column to narrow down where the tall buildings go. Use Latin-square elimination (no repeated heights in any row or column) to fill the rest.
What is the difference between skyscrapers and Sudoku?
Both are Latin-square puzzles where each number appears once per row and column. Sudoku adds 3×3 box constraints and gives you pre-filled cells. Skyscrapers uses border visibility clues instead, which adds a spatial reasoning element. The thinking style is quite different.
Is a skyscraper puzzle hard?
On a 4×4 grid with most clues shown, the puzzle is approachable for beginners. On a 7×7 grid with hidden clues, it requires multi-step deductions that challenge experienced solvers. The difficulty range is wider than most people expect.
Do I need to guess?
No. Every puzzle on The Puzzle Labs has a unique solution reachable through logic. Our Einstein level is certified to require no guessing or trial-and-error. If you feel stuck, step back and look for constraints you missed.