Skyscrapers — The Visibility Puzzle
Place buildings of different heights in the grid. Border clues tell you how many you can see from each direction. A skyscraper game that mixes Latin-square logic with spatial reasoning.
Play Skyscrapers
4×4 grid, generous clues and given cells
Standard play. Timer runs. Hints available.
What is the skyscrapers puzzle?
Skyscrapers is a logic puzzle played on an N×N grid. Each cell represents a building with a height from 1 to N. You fill the grid so that every row and column contains each height exactly once, same as a Latin square. Numbers along the grid's border, called visibility clues, tell you how many buildings are visible when you look into the grid from that direction. A taller building blocks everything shorter behind it.
The concept maps directly to a city skyline. Imagine standing at the edge of a row of buildings and counting how many rooftops you can see. A row with heights [2, 4, 1, 3] shows 2 buildings from the left (the 2 and the 4), because the 4 hides both the 1 and the 3. From the right you also see 2 (the 3 and the 4). That counting mechanic is the whole puzzle.
You might also see this called a “towers puzzle.” Some puzzle books and math education sites use “towers” or “skyscraper logic puzzle” interchangeably. The rules are the same regardless of the name.
Skyscrapers shares DNA with Sudoku: both demand unique numbers in every row and column. But where Sudoku uses 3×3 box constraints and given cells, Skyscrapers replaces all of that with border visibility clues. The reasoning shifts from “which numbers fit this group” to “where must the tall buildings go for this line of sight to work.” If you have played Sudoku, Futoshiki, or KenKen, the Latin-square elimination will feel familiar, but the spatial-visibility layer is a genuinely different kind of thinking.
The puzzle shows up in math classrooms too. Teachers use 4×4 Skyscrapers grids to introduce logical reasoning and spatial thinking without needing arithmetic. Three of the top ten Google results for “skyscraper puzzle” come from education sites, which says something about how approachable the core mechanic is even for younger students.
We have 1,500 skyscrapers puzzles across five difficulty levels, from 4×4 grids that take a couple of minutes to 7×7 grids that can keep you busy for half an hour. Play skyscrapers online free, or print them for offline solving. For a daily skyscrapers puzzle challenge, check the daily experiment page.
How to play
Place heights 1 to N in every cell. Each row and column must contain every height exactly once. Border clues tell you how many buildings you can see from that edge.
A clue of 1 means the tallest building is right at the edge, blocking everything behind it. A clue equal to the grid size means all buildings are in ascending order and every one is visible. A blank border position means no clue is given; you figure it out from other constraints.
Select a cell by clicking or tapping it, then type a number or use the on-screen pad. Toggle pencil mode (N key) to track candidate heights in empty cells. The buildings mode (B key) renders bars proportional to each height, which makes the visibility relationships easier to spot. If you get stuck, three hints are available per puzzle in classic and timed modes.
For the full rules with a step-by-step walkthrough, see the rules page with worked examples.
Play modes
Classic
Timer counts up. Up to 3 hints. Undo available. The default way to play.
Timed Trial
Beat the countdown. Time limits scale with difficulty: 3 min for easy up to 30 min for einstein.
Challenge
No hints. No undo. Every placement is permanent.
Skyscrapers tips and strategies
Technique by technique, from the first cell you fill to the last.
Clue-1 and clue-N shortcuts
A border clue of 1 means only one building is visible from that edge. The only way that happens is if the tallest building (height N) sits in the first position, blocking everything behind it. Fill that cell immediately. A clue equal to N means every building is visible, which requires ascending order: 1, 2, 3, through N. The entire line is solved in one step. Always start with these because they give you free placements with zero ambiguity.
Clue = N-1 deduction
If the clue is one less than the grid size, the tallest building must be in the second position. The first cell gets a shorter building whose height is constrained by what still needs to go in the row. On a 4×4 grid with a left clue of 3, height 4 goes in position 2, and position 1 must be shorter than whatever ends up in position 3. Combined with column constraints, this usually narrows things to one possibility.
Opposing clue pairs
When you know both clues for a row or column (left and right, or top and bottom), you can pin down where the tallest building sits. If left=2 and right=1, the tallest building is last. If left=2 and right=2, it is somewhere in the middle. When the two clues sum to N+1, things get especially constrained. These pairs give more information than either clue alone, so prioritize lines where both clues are visible.
Latin-square elimination
Once you place a height in a cell, remove it as a candidate from every other cell in that row and column. When a cell has only one candidate left, fill it. This is the same elimination logic used in Sudoku and Futoshiki, and it drives most of the cascade after your initial clue-based placements.
Working from the extremes
Heights N and 1 are the most constrained values. N determines visibility because it blocks everything behind it. Height 1 never blocks anything and is invisible unless nothing taller stands between it and the edge. Place the tallest buildings first when clues force their position, then use the shortest to fill gaps that remain.
Scanning for naked singles
After each placement, re-scan the grid for cells where only one height is still possible. Constraint propagation from multiple clues often creates chains of forced placements: fill one cell, eliminate its value from its row and column, and another cell drops to a single candidate. On larger grids this cascade can solve a dozen cells from a single starting deduction.
These six techniques cover everything you need for 4×4 through 6×6 puzzles. On 7×7 grids at expert and einstein difficulty, you will combine them simultaneously across intersecting rows and columns. Pencil marks help track possibilities when the grid gets crowded.
Difficulty levels
Five levels scale the grid size and the number of visible border clues. Larger grids with fewer clues demand deeper chains of reasoning.
| Level | Grid | Clues | Techniques | Time |
|---|---|---|---|---|
| Easy | 4×4 | 12-16 of 16 | Direct deductions, given cells | 3 min |
| Medium | 5×5 | 14-20 of 20 | Clue pairing, elimination | 5 min |
| Hard | 6×6 | 14-20 of 24 | Multi-clue reasoning | 10 min |
| Expert | 7×7 | 14-20 of 28 | Constraint chains | 18 min |
| Einstein | 7×7 | 10-16 of 28 | Full propagation, logic only | 30 min |