How to play Rooftops
Rooftops is a daily skyscraper logic puzzle. You fill a small city grid with buildings of different heights, using the clues around the edge, which count the rooftops you can see from each side. A puzzle takes two to ten minutes.
The rules
- Fill every tile with a building. On a 5×5 board the heights go from 1, the lowest, to 5, the tallest.
- Each row and each column has every height exactly once, like a small sudoku without boxes.
- A clue on the edge counts the rooftops you see when you look into that row or column from there.
- Taller buildings hide shorter ones. A building is visible only if it is taller than every building in front of it. A row of 2, 1, 4, 3 shows two rooftops from the left (the 2 and the 4) and two from the right (the 3 and the 4).
Every puzzle has exactly one answer, and you can always reach it by logic alone. Some harder boards start with a few buildings already in place; they carry a small corner stamp.
Controls
- Tap a tile to select it, then tap a height on the pad below the board. Tap the same height again to take it off.
- Notes switches the pad to pencil marks, so you can write the heights a tile could still have.
- Erase clears the selected tile. Undo steps back one move.
- On a keyboard: arrow keys move, a digit places a height, Shift plus a digit writes a note, N switches notes on and off, and Backspace clears the tile.
- Hint highlights the next step you can prove and explains why.
- A clue that is met gets a tick and fades. A clue that can't be met any more gets a red ring and a wavy underline, and so does a height that appears twice in a row or column.
Five techniques that solve every board
Every Rooftops puzzle can be finished with the moves below. Easy puzzles need only the first three. Medium puzzles ask you to count arrangements in a row or column. Hard puzzles need the what-if check at least once.
1. The 1 and the full clue
A 1 means you see only one rooftop, so the tallest building must stand right next to the clue, hiding everything behind it. A clue equal to the board size, such as a 4 on a 4×4 board, means you see every rooftop. That only happens when the buildings rise one step at a time: 1, 2, 3, 4.
2. Edge limits
A tall building close to a clue hides too much. With a clue of 3 on a 4×4 board, the first tile can't be a 4 (you would see one rooftop) or a 3 (you would see at most two), so it is a 1 or a 2. The second tile can be at most 3. In general, the tile next to clue c on a board of size N is at most N - c + 1, and each tile further in may be one taller. A 2 always rules out the tallest building next to it.
3. The last place, the last height
Two quick checks, as in sudoku. If a height can go in only one tile of a row or column, it goes there. If a tile has only one height left that its row, its column and the clues allow, that is its height. The pad helps here: a height that is on the board in every row gets a tick.
4. Count the arrangements
When a row or column with a clue has only a few tiles left, list the orders the missing heights can take and count the rooftops each one shows. Throw away the orders that don't match the clue. A height that never shows up on a tile in the orders that remain can't go there. With both ends clued, check each order against both clues. Start with the tallest building: where it stands decides most of what you can see.
5. What if
On hard boards, pick a tile with two options in your notes. Imagine one of them, and play the simple moves above from there in your head. If some row or column soon can't be finished, or a clue can't be met, the guess was wrong and the other option is right. Tiles next to a clue are the best place to start, because the chain stays short.
Questions
When does a new puzzle come out?
At midnight in your own time zone. The board grows through the week, from 4×4 on Monday to a hard 6×6 at the weekend.
Do I need an account?
No. Your streak, times and progress are saved in this browser. Clearing browser data removes them.
Does using a hint break my streak?
No. Your result just shows how many hints you used.
Is Rooftops the same as Skyscrapers?
The rules come from a classic pencil puzzle known as Skyscrapers or Towers. Rooftops has its own boards made by our own generator, a new puzzle every day, 300 practice puzzles and step-by-step hints.
Why do some puzzles start with buildings already placed?
On some boards the clues alone would leave more than one answer, or would need a guess. A few starting buildings keep the puzzle to one answer you can reach by logic.
Can a puzzle need a guess?
No. Before a puzzle is published, a solver works through it with the five techniques above, step by step. If it ever has to guess, the puzzle is thrown away.