Skyscrapers
Puzzle · 9 playsSkyscrapers
Build a city block where the clues around the edge count the towers you can see.
About Skyscrapers
A city grid viewed from all four sides at once. Each cell holds a building, one of every height in each row and each column, and the numbers around the border tell you how many buildings are visible looking along that line — a taller tower hides every shorter one standing behind it. Turning a handful of sightlines into a complete skyline is an unusually elegant piece of reasoning, and the grid tends to resolve all at once near the end. Free to play in your browser — no download, no sign-up.
How to Play
Fill the grid so every row and column holds each height from 1 to N exactly once. An edge clue counts the buildings visible from that side; taller ones hide shorter ones behind them. A clue of 1 means the tallest building stands nearest you; a clue of N means the line climbs steadily away.
Tips & Strategy
Start with the extreme clues, because they place buildings without any deduction at all. A clue of 1 means the tallest building sits immediately in front of you — nothing else could hide it. A clue of N means the line ascends strictly: 1, 2, 3 … N reading inward. A clue of N−1 is almost as good, with only two arrangements to check in most sizes.
A clue of 2 is more useful than it looks. It bars the tallest building from the nearest cell — put N first and you would only see one. On a 5-grid, a clue of 2 also means the second cell is either 5 or the eventual second-visible tower, so start by writing 5 out of the front cell and see what that forces in the column.
Use the height-position bound: a cell at distance d from an edge with clue c can hold at most height N − c + 1 + d. The front cell of a clue-3 line in a 5-grid can therefore be no taller than 3, the second no taller than 4. Writing these ceilings across every clued line thins the candidates dramatically before you place anything.
Pair opposite clues on the same line. In a 5-grid, clues of 2 and 4 facing each other sum to 6, which is N+1 — the tightest such pairing, meaning the 5 sits in exactly one place. More generally, two clues on one line can never sum to more than N+1, so if they do, you have misread the board. Finally, treat it as a Latin square throughout: once visibility narrows the candidates, ordinary row-and-column elimination finishes the job.