🏙️ Skyscrapers
🧩 Logic · 0 playsSkyscrapers
Arrange buildings by height to match how many are visible from each edge.
About Skyscrapers
The grid holds buildings whose heights run from 1 up to its width, each height appearing once in every row and once in every column. The numbers printed around the outside say how many buildings are visible looking down that line, given that a taller building hides every shorter one behind it. A clue of 1 puts the tallest building in the nearest cell; a clue equal to the grid's width forces a strict ascent from the edge inwards. Good solvers read the edge numbers for what they forbid rather than what they permit — that is usually the shorter route.
How to Play
Tap a cell and enter a height. Every row and column contains each height exactly once. An edge clue counts the buildings visible from that side, with taller buildings concealing shorter ones behind them.
💡 Tips & Strategy
The edge clues at the two extremes are gifts. A clue of 1 means the tallest building stands nearest you and hides everything behind it, so that cell is immediately N. A clue of N means you can see every building, which forces a strict staircase 1, 2, 3 up to N reading inward. Fill both kinds before anything else.
Clues in between constrain by ceiling rather than by certainty. From a clue of c, the cell at position i counting from the edge can be no taller than N minus c plus i. A clue of 2 on a five-grid therefore bars the 5 from the first cell, and a clue of 3 bars both 5 and 4. Applying this rule along every clued line removes a great many candidates cheaply.
Opposite clues talk to each other. For any line, the clue from one end plus the clue from the other cannot exceed N plus 1 — and when they sum to exactly N plus 1, the tallest building's position is fixed. It is a quick check that often decides a stubborn line.
Finally, track where N can live. It blocks everything behind it, so it must sit in a position consistent with every clue on its row and column at once. Placing the tallest buildings usually collapses the rest of the grid quickly.