Skyscrapers puzzle online
Fill the grid with building heights so that each edge clue matches how many buildings you can see from that side.
Rules
- Fill each cell with a height from 1 to 4 (grid size). Every row and column contains each height exactly once.
- A clue outside the grid says how many buildings are visible looking along that row or column from that side.
- A taller building hides every shorter one behind it.
Example
Reading a clue
Take a row with the clue 3 on its left in a 5×5 grid. Reading from the left you must see exactly three buildings, so the sequence of record highs has length three. For example 2 4 1 5 3 shows 2, 4 and 5, which is three.
Techniques
Clue 1. The tallest building stands next to the clue.
Clue equal to n. The row is 1 2 3 … n in order away from the clue.
Clue 2. The cell next to the clue cannot be the second tallest if the tallest is last, and it cannot be the tallest.
Line sweep. For each cell, list the heights it could still be, given its row, column and the clues. When a height fits in only one cell of a line, place it. Pencilmark's “line sweep” hint does exactly this.
Opposite clues. Two clues that add up to n+1 on opposite ends of a line place the tallest building at the right spot in the middle.
FAQ
What are the rules of Skyscrapers?
Fill the grid so every row and column contains each height once. Clues around the edge tell how many buildings are visible from that side; taller buildings hide shorter ones behind them.
What does a clue of 1 mean?
Only one building is visible, so the tallest building stands right at that edge.
What does a clue equal to the grid size mean?
Every building is visible, so the heights rise in order from 1 to n.