Skyscrapers

How to play Skyscrapers

Skyscrapers is a number-placement logic puzzle played on a square grid, where every filled number represents the height of a building. Unlike Sudoku, there are no boxes to fill — the entire challenge comes from a Latin square (each height appears exactly once in every row and every column) combined with a ring of "visibility" clues printed around the four edges of the grid. Those clues tell you how many buildings you would actually be able to see if you stood at that edge and looked straight down the row or column, since taller buildings in front block your view of shorter ones behind them. Reasoning out where each height must go, purely from those visibility counts and the Latin-square rule, is the whole game — there is no guessing required, and no arithmetic beyond counting.

The goal

Fill every cell of the N×N grid with a building height from 1 to N so that each row and each column contains every height exactly once, and so that every visibility clue shown around the edges matches the number of buildings actually visible from that direction on the finished grid. Not every edge line necessarily shows a clue — some are left blank on purpose — but every clue that IS shown must be satisfied exactly. When the whole grid is filled in correctly, you win.

The rules

• Each row must contain every height from 1 to N exactly once, and each column must contain every height from 1 to N exactly once — just like a Sudoku row or column, but with no smaller boxes to worry about.
• A clue printed on the LEFT of a row tells you how many buildings are visible when looking along that row from left to right. A clue on the RIGHT tells you the same thing looking from right to left. A clue above a column is looking top-to-bottom; a clue below is looking bottom-to-top.
• A building is "visible" from a given direction if it is taller than every single building that direction has already looked past. The very first building in any line of sight is always visible (there is nothing in front of it yet); after that, only a NEW tallest-so-far counts.
• Because every height in a row or column is different (the Latin-square rule guarantees no ties), visibility is never ambiguous — a building is either strictly taller than everything before it, or it is hidden behind something taller.
• Worked example: reading the heights [2, 1, 4, 3] from left to right, the count of visible buildings is 2. The 2 is visible first (nothing taller has come before it). The 1 is shorter than the 2 already seen, so it is hidden. The 4 is taller than everything seen so far (the 2), so it becomes newly visible — that is the 2nd visible building. The 3 is shorter than the 4 just seen, so it stays hidden. Total: 2 visible.

Controls

• Tap an empty cell inside the grid to select it — locked given cells (if any) cannot be selected or changed.
• Tap a height button from the number pad below the board to drop that height into the selected cell. On a keyboard, just press the matching number key (1 to N).
• Made a mistake? Tap Erase (or press Backspace/Delete) to clear the selected cell and try a different height.
• The clue numbers around the outside of the grid are shown in a smaller, amber colour so you can always tell them apart from the bold white puzzle digits inside the grid.

Difficulty levels

• Easy uses a compact 4×4 grid. There are only 4 heights to juggle and just 16 cells to fill, making it the friendliest way to learn how the visibility clues work.
• Medium steps up to a 5×5 grid. You will need to track five different heights across five rows and columns at once, so the deductions take a little more bookkeeping.
• Hard uses the full 6×6 grid. Every puzzle is still proven to have exactly one solution before you ever see it, but with six heights in play you will need to combine several clues and cross-check rows against columns to crack it.

Solving tips

• A clue equal to N (the size of the grid) means that entire line must be arranged in strictly ascending order away from that edge — every building is taller than the last, so every single one is visible.
• A clue of 1 means the very first building in that line of sight must be the tallest possible height (N) — nothing else in the line can ever be seen past it, since it is already the maximum.
• Cross-reference clues on the same row or column from both directions (left and right, or top and bottom) — together they often narrow down exactly where the tallest and shortest buildings in that line must sit.
• Work on the most restrictive clues first — small clues (like 1 or 2) and clues equal to N are the most powerful, since they force specific heights into specific positions immediately, and those placements then help you deduce the rest of the row or column via the ordinary Latin-square rule.

Scoring and the leaderboard

Each solved puzzle earns a score of max(1, min(99999, 10000 − seconds × 5 − mistakes × 200)). You start from 10000 points; every second that passes costs 5 points, and every wrong height you place costs 200 points. So the faster and cleaner your solve, the higher your score, always kept between 1 and 99,999. Scores are recorded separately for each grid size — sign in to save your best result to the leaderboard, and try the Daily puzzle for a fresh, identical-for-everyone challenge each day.

Frequently asked questions