How to solve Skyscrapers
Each number on the edge counts the buildings you can see from there. Start with the 1s and the biggest clues, then let each row and column fill in.
How it works
Skyscrapers is a square grid of building heights. In a 4×4, each row and each column holds the heights 1, 2, 3 and 4 once each, so the answer is a Latin square.
The numbers around the edge are visibility clues. Stand at that number and look along its row or column. A building is hidden if a taller one stands in front of it. The clue counts the buildings you can see.
Two clues give you cells straight away. A 1 means the first building hides all the rest, so it is the tallest. A clue equal to the size means you see every building, so they climb one step at a time.
Where to look first
Clues of 1 and clues equal to the size. Then the other clues: a clue of c means c − 1 taller buildings must stand behind the first one, so the first building is at most size − c + 1. That bound gets one step looser for each cell further in.
The tallest building is always visible, from both ends of its line. Find where it can go in each row and column and the rest follows.
When the edges run out
Pick a line with a clue and write the orders its cells can still take. Keep only the orders that show the right number of buildings. A height that none of them put in a cell is out. Our lesson on visibility shows how.
Worth memorizing
A 1 on the edge: the tallest building is right there.
It hides everything behind it.
A clue equal to the size: a staircase.
1, 2, 3 and up, from that edge.
A clue of c caps the first building at size − c + 1.
In a 4×4, a 3 means the first building is 1 or 2.
Practice
0 of 4 rightThe clue under column 2 is 1. What height is in the ringed cell?
The clue under column 3 is 4. What height is in the ringed cell?
Row 3 of this 5×5 shows 5 from the left. How many buildings do you see from the right?
Row 2 has 3 and 4 in its last two cells and shows 3 from the left. How does it read?