Towers

Towers (also known as Skyscrapers) is an elegant logic puzzle. Played on an N×N grid, the goal is to place a tower of a unique height (from 1 to N) in every row and column—forming a Latin square—so that no height is repeated in any row or column.

The twist lies in the clues given around the grid’s edges: each number indicates how many towers are visible when looking into the grid from that direction. Since taller towers block the view of shorter ones behind them, a clue of “1” means the first tower must be the tallest (N), while a clue of “N” means the towers must be in strictly increasing order (e.g., 1-2-3-4).

For example, in a row with heights 2-1-4-3, a viewer from the left would see 2, then 4 (since 1 is hidden behind 2, and 3 is hidden behind 4)—so the left clue would be 2.

Using only these numerical hints and the Latin square constraint, you must deduce the exact height of every tower through pure logical reasoning—no guessing required. The puzzle is always uniquely solvable.

Towers is free and runs directly in your browser, with adjustable grid sizes for varying difficulty. It’s a perfect challenge for fans of Sudoku, Futoshiki, or other constraint-based number puzzles who enjoy spatial visualization and deductive logic.

Fill in the grid with towers whose heights range from 1 to the size of the grid, such that:

• Every height appears exactly once in each row and each column.
• Each clue around the edge indicates how many towers are visible when looking into the grid from that direction.

(Taller towers block the view of shorter ones behind them. For example, the sequence 2, 1, 4, 3, 5 would produce a clue of 3 from the left—because the 1 is hidden behind the 2, and the 3 is hidden behind the 4. From the right, the same sequence would yield a clue of 1, since the 5 hides all the others.)

Controls:

• To place a tower: click a square to select it, then type the desired height on your keyboard.
• To erase a tower: select the square and press Backspace.
• To add or remove a pencil mark (a possible candidate height): right-click the square, then type a number. Pencil marks help you keep track of heights that might belong in that cell.
• To mark a clue as satisfied: left-click the clue to grey it out. Click it again to unmark it.

Tip: On mobile devices, you can perform a "right-click" by using a long press.