How to play Skyscrapers
Skyscrapers is a logic puzzle played on a square N×N grid, for example 4×4 or 5×5. Each cell holds a building with a height from 1 to N, and every row and column must contain each height exactly once. The numbers around the edge tell you how many buildings you can see when you look along that row or column from that side; taller buildings hide shorter ones behind them.
The rules
- Fill every cell with a height from 1 to N.
- Each row and each column contains every height exactly once, like a small Sudoku without boxes.
- A clue outside the grid gives the number of buildings visible from that point, looking into the row or column.
- A building is visible only if it is taller than every building in front of it.
A worked example
Take a row of a 4×4 puzzle that reads 2, 4, 1, 3 from left to right. From the left you see the 2, then the 4, which is taller; the 1 and the 3 are hidden behind the 4. So the left clue is 2. From the right you see the 3, the 1 is hidden, then the 4 is visible and the 2 is hidden. The right clue is also 2.
Key deductions
- Clue 1: only one building is visible, so the tallest building (N) stands right next to that clue.
- Clue N: every building is visible, so the row or column reads 1, 2, 3 … N in order from that side.
- Any clue c: the first building from that side can be at most N − c + 1 tall. For example, with a clue of 3 in a 5×5 grid, the first building is 3 or lower.
- Opposite clues a and b: the tallest building is seen from both sides, so a + b can never be more than N + 1. When a + b equals N + 1, the tallest building's position is fixed.
How to solve
Begin with the clues of 1 and N, which place buildings immediately. Then use the maximum-height rule above to rule out heights near every clue, and write the remaining possibilities as notes. Because each height appears once per row and column, every placed building also removes options from its row and column, exactly as in Sudoku. Larger grids and fewer clues make the puzzle harder, because you must combine information from two or more sides before a cell is certain.
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