How to play Skyscrapers

What is a Skyscrapers?

Skyscrapers (also called Towers) is a logic puzzle in which you fill a grid with building heights so that every row and every column holds each height exactly once, and each number around the edge says how many buildings you would see looking along that line from that side, a building being visible only when nothing in front of it is as tall.

Also known as: Towers, Skyscraper Puzzle.

How do you solve a Skyscrapers?

1. 01

   Place the ones and the fives

   A clue of one means the tallest building stands nearest that edge, so the first square of that line is a five. A clue of five means the line climbs the whole way, so it reads one to five from that side. Do these first.

2. 02

   Keep the five away from a low clue

   A clue of c means the five cannot sit in any of the first c minus one squares, since each square before it would need to be visible. The same clue caps the nearest square at six minus c, because every taller building behind it has to fit in the count.

3. 03

   Read the two clues on one line together

   The clues at opposite ends of a line share one five. If they add up to six, the five sits exactly as many squares in as that side’s clue says: a two facing a four puts the five second from the two. Clues adding to more than six are impossible, a handy check that you are reading the edges the right way.

4. 04

   Work the Latin square with candidates

   Underneath the clues this is a Latin square, so every placed height rules itself out of its row and column. Pencil in candidates and look for a square with one left or a height with one home left. Lines with no clue at all, which this site allows, are solved entirely this way.

5. 05

   Count the view of a partly filled line

   Once a line has a few heights in it, count what is visible from the clued side and what the empty squares could add. A line whose count is already full must hide everything after its tallest placed building. The site checks a clue only when its line is complete, so this counting is yours.

6. 06

   Finish by testing the last orderings

   Near the end a line may have two or three orderings left; count the view for each and typically one survives. Every puzzle here has exactly one solution, so guessing is never required.

Common Skyscrapers mistakes

• Reading a clue from the wrong side. Clues on the right and bottom edges look into the board from there, so the first building they see is the last square of the row or column as you read it.
• Treating a clue as a statement about one square. Only a one and a five fix squares directly; everything in between rules out orderings and has to be combined with what is already placed.
• Expecting a clue on every line. Some lines carry no clue from one or both sides, and they are settled by the row-and-column rule rather than by anything you have missed.
• Ignoring the Latin rule while chasing clues. A placement that satisfies a clue but repeats a height in its column is wrong, and the site marks repeats the moment they appear.

Where does Skyscrapers come from?

The origin of Skyscrapers is less well documented than most grid puzzles: no single inventor or first publication is generally credited, so any precise date should be treated with caution.

Its standing is certain, though: it is a standard type in the World Puzzle Championship canon, typically set at five or six squares a side and often with only some edge clues given, as on this site. Some collections call it Towers.