Skyscraper Sudoku is a 9x9 Sudoku variant in which each digit is the height of a building and the numbers printed outside the grid count how many buildings are visible looking along that row or column from that side. A taller building hides every shorter building behind it, so the same nine digits produce a different clue depending on the order you place them in. The usual row, column, and 3x3 box rules apply throughout — the edge clues are an extra layer, not a replacement.
What is Skyscraper Sudoku?
Skyscraper Sudoku takes a complete, unique-solution Sudoku and reinterprets its digits as a city skyline. Every cell holds a building whose height is the digit in it: a 1 is a single storey, a 9 towers over everything else. The numbers around the outside of the grid are viewpoints. Standing at one and looking inward, you count the rooftops you can actually see, and that count is the clue.
What makes the variant interesting is that the clue is a statement about order, not about content. Every row of a Sudoku contains the same nine digits, so a sum-based clue like Sandwich or Killer tells you something about which digits sit where. A Skyscraper clue instead tells you how those nine digits are arranged relative to each other, which is information no ordinary Sudoku technique produces. That is why the clues can carry so much weight: they see a dimension of the puzzle the standard rules are blind to.
Skyscraper Sudoku Rules
- Standard Sudoku rules: Each row, each column, and each 3x3 box must contain the digits 1 through 9 exactly once.
- Digits are heights: The digit in a cell is the height of the building standing there, from 1 (shortest) to 9 (tallest).
- Taller hides shorter: Looking along a row or column, a building is visible only if every building in front of it is strictly shorter. A taller building hides all shorter buildings behind it.
- Edge clues count what you can see: The number outside the grid is exactly how many buildings are visible from that viewpoint, looking inward along that row or column.
- The clues are required: Puzzles are generated to be unique under the visibility constraint, so the given digits on their own are not enough. Every printed clue is load-bearing.
How the Visibility Constraint Works
Counting visible buildings is a running-maximum scan. Walk the line from the clue inward, keeping track of the tallest building you have seen so far. The first building is always visible. Every later building is visible if and only if it is taller than that running maximum, at which point it becomes the new maximum.
Take the row 4 1 6 2 9 3 5 7 8 and look at it from the left. You see the 4. The 1 is hidden behind it, and so is the 2. The 6 is taller than 4, so it is visible. The 9 is taller still, so it is visible — and because nothing can exceed a 9, the 3, 5, 7 and 8 behind it are all hidden. Three rooftops in total, so the left clue for that row is 3. Read the same row from the right and you see 8, then 9, and nothing more: the right clue is 2.
Three consequences follow directly, and they are the backbone of every Skyscraper solve:
A clue of 1 places the 9
Only one building can be visible when the tallest one stands in front. A clue of 1 puts the 9 in the cell nearest that clue, with no further deduction needed. It is the single most valuable clue on the board, and a good place to start every puzzle.
A clue of 9 fills the whole line
Seeing all nine buildings means every one of them is taller than the one in front, so the line reads 1, 2, 3, 4, 5, 6, 7, 8, 9 in order moving away from the clue. A clue of 9 solves an entire row or column in one step.
A clue of k caps the nearest cell at 10 − k
If k buildings are visible, then k − 1 of them stand behind the first one and each is taller than the last. That leaves at most 9 − (k − 1) = 10 − k for the nearest cell. A clue of 4 means the cell touching it holds at most 6; a clue of 7 means at most 3. This bound applies to every clue on the board and quietly removes candidates everywhere.
Solving Strategies
1. Sweep for 1s and 9s first
Before anything else, scan every clue on all four sides for the value 1 and the value 9. Each 1 gives you a placed 9 for free, and each 9 gives you a completely solved line. On a typical Skyscraper puzzle these two clue values do more work than the next ten deductions combined.
2. Apply the 10 − k cap everywhere
Go around the border once and write the cap on every edge cell: clue 2 means at most 8, clue 3 at most 7, clue 5 at most 5. These caps are cheap to derive and they stack with normal Sudoku elimination, often knocking a candidate list down to one entry on a cell you would otherwise have ignored.
3. Work the corners
A corner cell sits at the head of two clued lines at once, so it inherits both caps. If the row clue is 4 and the column clue is 5, the corner is capped at 6 by one and 5 by the other, so it is at most 5. Corners are the most over-constrained cells on a Skyscraper board and are usually the first to resolve.
4. Test the placement of the 9
The 9 is the pivot of every line, because it truncates the view from both sides. Once you know where a row's 9 is, the left clue is entirely determined by the cells in front of it, and the cells behind it become irrelevant to that clue. If you are stuck on a line, try each legal position for its 9 and check the clue against it — most positions fail immediately.
5. Fall back on ordinary technique
Underneath the skyline this is still Sudoku. Naked singles, hidden singles, pointing pairs, and the rest of the toolkit from our solving techniques library apply exactly as they always do. The edge clues are there to break open lines that plain elimination cannot touch, not to replace it.
Mini Skyscraper Sudoku (6x6)
Mini Skyscraper brings the visibility rule to a compact 6x6 grid using the digits 1 through 6 with 2x3 boxes. Everything works the same way, just smaller: clues run from 1 to 6, a clue of 1 places the 6 next to it, a clue of 6 fills the line 1, 2, 3, 4, 5, 6 in order, and the cap on the nearest cell becomes 7 − k. Opposite clues on a line sum to at most 7.
Because a 6x6 line has only six positions, the whole space of arrangements is small enough to reason about in your head, which makes it the right place to build the visibility instinct. Mini Skyscraper is free to play; the 9x9 version is part of the premium collection.
Tips for Beginners
- Read the clue as a sentence. "From here I can see four rooftops" is much easier to reason about than a bare number in a margin.
- The first cell is always visible. Every clue is at least 1, and the cell touching a clue always counts toward it. That is often the deduction people miss.
- Height order matters, not height values. A clue never tells you which digits are in the line — a Sudoku row always holds all nine. It only tells you about their arrangement.
- Small clues mean tall buildings up front. A clue of 2 or 3 means something very tall is near that edge. A clue of 7 or 8 means the line climbs gently.
- Cross-check both ends of a line. Before committing to an arrangement, count it from both directions and confirm both clues. It catches most mistakes on the spot.
- Start on Mini Skyscraper. The free 6x6 grid teaches the running-maximum scan on a line short enough to check at a glance.
Skyscraper Sudoku rewards a kind of thinking that ordinary Sudoku never asks for: reasoning about sequence rather than about sets. Once the running-maximum scan becomes automatic, the clues around the border stop looking like decoration and start reading as sentences about the shape of each line — and a board that seemed impossibly thin on givens opens up from the outside in.