Skyscrapers - Visibility Logic
How to play: Each row and column must contain numbers 1 through N exactly once (Latin square). The numbers around the EDGES tell you how many SKYSCRAPERS you would see looking from that direction. Taller skyscrapers HIDE shorter ones behind them. So a 4 means you can see all 4 in increasing order; a 1 means the tallest is right at the edge. Click a cell, then press a number key (1-N) to enter. Press 0 or backspace to clear.
About Skyscrapers
Skyscrapers is a Latin square logic puzzle with a clever spatial twist: each cell represents a building of a given height, and the numbers around the edges tell you HOW MANY buildings you’d see if you were standing on that side looking in. Taller buildings hide shorter ones behind them, so a 1 means the tallest is right at the edge (hiding everything), and an N means the buildings are arranged in strict ascending order from that side.
Our online version ships with 4 puzzles ranging from 4×4 (introductory) to 5×5 (challenging).
How to Play
- Each row and each column must contain numbers 1 through N exactly once (Latin square rule).
- The numbers around the OUTSIDE of the grid indicate how many skyscrapers are visible from that direction.
- Click a cell to select it, then press a number key (1, 2, 3…) to enter that height. Press 0 or Backspace to clear.
- Use arrow keys to move the selection.
- Solve by filling the grid so all clues match: each row/col is a permutation of 1..N AND each edge-clue equals the visibility count from that side.
Strategy Tips
- Clue 1 means the tallest is at that edge. If a column has clue 1 from the top, the tallest building (N) goes in row 0 of that column.
- Clue N means strict ascending order. If a row has clue N from the left, the row must be 1, 2, 3, …, N in order.
- Sum of opposite clues. If row clues are L from left and R from right, the leftmost cell can’t be too tall (L cells must be visible from left).
- Tallest building blocks all. Once you place N, every visibility line through it is determined past that point.
- Use Latin square logic. If a row needs 1-N once each, use elimination as in Sudoku.
- Cross-reference rows and columns. A cell that’s forced by both row and column constraints is a guaranteed entry.
A Brief History
Skyscrapers (also called Towers, High & Low, or Visibility Puzzles) emerged in the late 1990s as part of the broader “Sudoku family” of Latin square puzzles. The visibility constraint adds a geometric reasoning element absent in classic Sudoku, making the puzzles feel more spatial. They’re a regular fixture in puzzle magazines like Logic Pride and online puzzle sites like Cracking the Cryptic.
Frequently Asked Questions
How does visibility work?
You’re at the edge looking down a row or column. Taller buildings hide shorter ones behind them. So if a row is 2,3,1,4 from your viewpoint, you see 2 (it’s first), then 3 (taller than 2), then 1 (hidden by 3), then 4 (taller than 3). Total visible: 3.
What’s the minimum and maximum visibility clue?
Min is 1 (tallest building is right at the edge, hiding everything else). Max is N (buildings in strictly ascending order, all visible).
Are all clues required?
Some Skyscraper variants omit clues to make the puzzle harder. Our puzzles include all clues to make them solvable with pure deduction.
Why is my Check showing errors when I haven’t filled everything?
Check counts duplicate numbers in any row or column. Even partial grids with duplicates will show errors. Visibility constraints are only checked when the line is fully filled.
How is this different from Sudoku?
Sudoku has 9×9 grids with 3×3 box constraints AND row/column constraints. Skyscrapers uses smaller grids (4×4 to 7×7), no box constraints, but adds the visibility-from-edge constraint. The deduction style feels more spatial.
Can I play on mobile?
Yes – tap a cell, then a number keypad will appear (or use the on-screen keyboard).
Does each puzzle have a unique solution?
Yes. Every puzzle in the pack has exactly one solution that can be deduced from the clues.
What if I get stuck?
Use Check to count duplicate-number errors (it doesn’t tell you which cells). Most stuck states are due to a single mistake earlier – work backward.