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Puzzle Quarry

Skyscrapers Puzzle

Choose a side and a level and a fresh skyline is cut, checked and put on screen. No limit, no account, and nothing leaves the machine you are reading this on.

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A medium 5×5 board with 8 numbers round the rim. Pick a cell, then a height — or press the pencil to write candidates.

Check this before you rely on it. This skyscrapers puzzle generator is provided free and without warranty, and its results are not professional advice.

A city block seen from four pavements

Picture the grid as a plot of land divided into square lots, with a tower standing on every one of them. On a side of five the towers are five storeys, four storeys, three, two and one, and each height is used exactly once along every street and exactly once along every avenue. That much is a Latin square and it is thousands of years old.

What makes it a puzzle is that you are told nothing about any individual lot. Instead you are given the view. A number printed outside the grid says how many rooftops would be in sight if you stood at that spot on the pavement and looked straight down the street — and a taller tower hides every shorter one standing behind it, completely, however many there are.

So a 1 means the very first building blocks the whole street, which can only happen if it is the tallest there is. A 5 on a side of five means every roof is in sight, which can only happen if they climb one storey at a time from where you are standing. Every number between those two is a statement about the order the heights come in, and the whole game is turning those statements into a filled grid.

The rim is the whole of the clue set

Nothing is ever printed inside the grid. There are no starting heights to copy in, no shaded lots, no second rule layered on top — the board arrives completely blank and everything you are given is standing outside it. That is unusual among grid puzzles and it changes how the opening feels: instead of writing digits in, you spend the first minute crossing them out.

An edge with no number against it carries no clue at all. It is not a view of nought, because there is no such thing — stand anywhere and you can always see at least the building nearest you. A blank means the setter rubbed that number out and checked that the board still had exactly one answer without it, which is a different and much more interesting fact than a zero would be.

Both ends of every street are worth reading, and beginners routinely read only one. The row that is a staircase from the left is a view of 1 from the right, because from that side the tallest tower is the nearest one and it hides the lot. Any pair of numbers facing each other across a line is really a single statement about that line, and the pages here treat it as one.

What side and level actually change

Side and difficulty are separate choices and they do genuinely different things. A wider board means more lots, longer streets and a longer sitting; it does not by itself mean a harder argument. A gentle 6×6 is twenty minutes of pleasant sweeping, and a 5×5 with two awkward corners can stop an experienced solver for a quarter of an hour.

The four levels name the reasoning a board forces instead. Easy is finished by reading the printed numbers once and then crossing out. Medium adds the moment where you have to try a height in a lot and reject it because of what the view would become. Hard makes you write out the orderings of a whole street. Expert is where the numbers at both ends of one street have to be held in mind together before anything at all will move.

The grade is measured rather than estimated. Every published board goes through a program that always takes the cheapest argument available to it, and the hardest argument it was ever forced onto is the level printed beside the board. Ask for an expert 4×4 and you will usually be handed a hard one, because sixteen lots rarely leave room for the argument that expert means here.

Common questions

What do the numbers around a skyscrapers grid mean?

Each one is how many buildings you would see looking in from that spot, with a taller tower hiding every shorter one behind it. An edge with no number printed against it is not a clue at all.

Can a rim number ever be a zero?

No. You can always see the building nearest you, so the smallest legal view is one. A blank edge means the number was rubbed out because the board stayed unique without it.

Is a towers puzzle the same thing?

Yes — same Latin rows, same views from the edges. Towers is simply the other English name, and collections that use it are printing this puzzle under a different cover.

More Skyscrapers pages