What do the numbers around a skyscraper puzzle mean?
Each number outside the grid says how many buildings you can see from that spot, looking along its row or column. A taller building hides every shorter one behind it. So a clue of 1 means the tallest building stands right next to it, and a clue as large as the grid means the heights rise one by one, smallest first. A row with no clue can be in any order the other clues allow.
The grid itself is a city of 4 × 4 up to 6 × 6 blocks. Every row and every column holds one building of each height, from 1 to the size of the grid. Select a block and tap a height, or type it. Each filled block is drawn as a tower as tall as its number, so you can check a view by eye.
How is your Skyscrapers Puzzle time calculated?
Your result is the time from Start until every block is filled and every clue is met. Next to it are the times you pressed Check, which marks any building that disagrees with the answer, and Hint, which places one (or fixes a wrong one). A height used twice in a line, or a finished line whose view doesn't match its clue, is outlined in red as you go; that comes from the clues, never from the answer.
There is no rating, because no published typical time exists for puzzles built like these. The size of the city matters most: each step up adds a row, a column and a height to place.
How do you solve a skyscraper puzzle?
- Clue 1: the tallest building is in the block next to the clue.
- Clue equal to the size: the whole line runs 1, 2, 3 and so on, away from the clue.
- Where the tallest can't be: a clue of k means at least k − 1 shorter buildings stand in front of the tallest one, so it can't be in the first k − 1 blocks.
- Opposite clues: the clues at the two ends of a line add up to at most the size of the grid plus one. In a 4 × 4, a 4 and a 2 can't face each other. The site's tests check this over every possible line.
- One height per line: as in Sudoku, once a height is placed in a row or column, it can't appear there again.
Does every Skyscrapers puzzle have exactly one answer?
Yes. Each puzzle starts as a random city with all four sides of clues. Clues are then removed in random order, and a removal is kept only if a solver that never guesses can still work out the whole city. It looks at one line at a time, keeping only the orders of heights that fit that line's clues and what is already known. At least 8 clues stay on a 4 × 4, so the puzzle stays quick. The site's tests count the answers of hundreds of puzzles by trying them all: always exactly one.
Is a skyscraper puzzle a Latin square?
Its answer is one. A Latin square is a grid where every row and column holds each symbol once, like a Sudoku without the boxes. Without clues there would be far too many cities to choose from: the site's code counts 576 different 4 × 4 Latin squares and 161,280 of size 5 × 5. The clues cut that down to one.
For another number grid with clues around it, try Kakuro; for counting cubes in 3D, the Block Counting Test.