Rascacielos

Skyscrapers is a logic puzzle played on an NxN grid where each cell represents a building of a certain height (1 to N stories). Like Sudoku, each row and column must contain every height exactly once. The twist: clue numbers around the edges of the grid indicate how many buildings are visible when looking into the grid from that direction. Taller buildings block the view of shorter ones behind them, just like real skyscrapers on a city skyline.

Rules

1. Fill each cell with a number from 1 to N, representing building height.
2. Each row must contain every number from 1 to N exactly once.
3. Each column must contain every number from 1 to N exactly once.
4. Clue numbers on the edges indicate how many buildings are visible from that position, looking into the row or column. A building is visible if no taller building stands between it and the viewer.

Visibility Example (N=4)

Row: [2, 4, 1, 3] viewed from the left:

• Building 2 is visible (first).
• Building 4 is visible (taller than 2).
• Building 1 is hidden (behind 4).
• Building 3 is hidden (behind 4).
• Clue from left = 2.

Strategies

• Clue = 1: The tallest building (N) must be in the first position from that edge, since only it can block everything else.
• Clue = N: The buildings must be in ascending order (1, 2, 3, ..., N) from that edge, since every building must be visible.
• Clue = 2: The tallest building (N) cannot be in the first position (that would give clue 1) but must be somewhere after the first cell. The first cell must be tall enough that only one additional building is visible.
• Large Clue Near-edge Logic: For clue = N−1, the first cell must be 1, and the remaining cells are in ascending order except for one swap.
• Cross-referencing Clues: Where a row and column intersect, both sets of clues must be satisfied simultaneously, narrowing candidates.
• Elimination by Simulation: For difficult puzzles, mentally test what visibility a partial row would produce and eliminate placements that violate the clue.

Skyscrapers belongs to the family of Latin square puzzles — grids where each symbol appears exactly once in every row and column. The addition of visibility clues transforms the abstract Latin square into a concrete, visual puzzle with an intuitive real-world metaphor.

The puzzle appears to have originated in the puzzle competition community in the late 1990s or early 2000s. It became a staple of the World Puzzle Championship (WPC), where it has appeared in various forms since at least 2002. The WPC community, organized by the World Puzzle Federation, was instrumental in developing and popularizing the format.

Skyscrapers gained broader public awareness when it appeared in puzzle books and newspapers during the Sudoku wave of the mid-2000s. Publishers looking for puzzles with the same "Latin square" foundation as Sudoku but with a distinct flavor found Skyscrapers to be an ideal candidate. Its intuitive theme — imagining buildings and skylines — makes it immediately engaging for new solvers.

The puzzle has been widely adopted in education as a tool for spatial reasoning and logical deduction. It appears in math competition training materials, puzzle apps, and classroom resources. Variations include grids with missing clues (increasing difficulty), grids with internal clue cells, and multi-layer 3D versions. The puzzle is sometimes combined with other constraint types — for example, Skyscrapers with inequality signs or Skyscrapers with cages — creating hybrid puzzles for advanced solvers.