Skyscrapers
Place buildings using edge visibility clues
Skyscrapers is a visibility logic puzzle where you fill an NxN grid with building heights 1 through N. Each row and column contains every height exactly once. Numbers around the edges tell you how many buildings are visible from that direction — taller buildings block the view of shorter ones behind them. This creates an intuitive 3D reasoning challenge: you're essentially placing buildings on a city grid and figuring out the skyline from every angle.
History & Origins
Skyscrapers puzzles emerged from the broader family of Latin Square puzzles that have entertained mathematicians since Euler's work in the 1700s. The visibility mechanic — imagining looking at a skyline and counting visible buildings — was added by puzzle designers in the late 20th century. The puzzle has been a regular feature in the World Puzzle Championship since the 1990s and is considered one of the best introductions to constraint-based logical thinking because the 3D visualization element makes abstract logic feel tangible and intuitive.
How to Play Skyscrapers
Height Placement
Place buildings with heights 1 through N in each cell of the NxN grid.
Row Uniqueness
Each row contains every height exactly once, just like a row in Sudoku.
Column Uniqueness
Each column also contains every height exactly once.
Edge Visibility
Numbers on the edges tell you how many buildings are visible looking into the grid from that side. Taller buildings block shorter ones behind them.
Visibility Example
In a row [2,4,1,3], looking from the left you see 2 buildings (2, then 4). Looking from the right you see 2 (3, then... 1 is blocked, 4 is visible).
Use All Clues
Combine visibility clues with uniqueness constraints. A "1" means the tallest building (N) is first. An "N" means heights ascend from that edge.
Strategy & Solving Tips
Expert Skyscrapers solving connects edge clues with placement uniqueness. These techniques cover the key deduction patterns.
- A clue of "1" means the tallest building (height N) is in the first position from that edge
- A clue of "N" means buildings are in ascending order from that edge: 1, 2, 3, ..., N
- A clue of "2" means the second-tallest or tallest building is visible first, with the tallest nearby
- Height N can only appear where it doesn't violate any edge visibility clue
- Height 1 is never visible unless it's the first cell from an edge (taller buildings always block it)
- Combine opposing edge clues: if left says "2" and right says "3" in a 5x5 row, the height-5 building has limited valid positions
Common Mistakes to Avoid
- Confusing "visible" with "tallest" — a clue of 3 means you see three buildings of increasing height, not that the third is tallest
- Neglecting to use opposing edge clues together — the left and right clues for one row heavily constrain each other
- Placing the tallest building (N) without checking that it satisfies visibility clues from all four directions
- Forgetting that height 1 is invisible behind any other building — it can only be "seen" if it's the very first cell from an edge
Skyscrapers FAQ
How does visibility work?
Imagine standing at the edge of the grid and looking along a row or column. You can see a building only if no taller building is in front of it. A height-5 building always blocks 1, 2, 3, and 4 behind it.
Is Skyscrapers related to Sudoku?
Both are Latin square puzzles (unique values in rows and columns). Skyscrapers replaces Sudoku's box constraint with edge visibility clues, creating a fundamentally different reasoning experience.
Do all edges have clues?
Not necessarily. Some edge positions may be blank. You solve those rows/columns using uniqueness constraints and clues from the opposite or perpendicular edges.
What grid sizes are available?
Common sizes range from 4x4 (beginner-friendly) to 7x7 or larger. Larger grids have more heights and more complex visibility interactions.
Ready to Play Skyscrapers?
Build the skyline in Skyscrapers — the visibility puzzle where every edge clue reveals the city's profile. Place your buildings where the view makes sense.