Reading skyscraper clues

Most of a Skyscrapers grid is solved by a handful of ideas about what an edge clue allows. Here they are, from the obvious to the useful.

A clue counts the towers you can see from the edge, looking into the grid. A tower is visible if it is taller than all towers in front of it. That one rule produces every technique below. The examples use a 5 × 5 grid, so the heights are 1 to 5.

Clues of 1 and of the full size

A clue of 1 means the first tower already hides all the others: it must be the tallest, 5. A clue of 5 means you see every tower, so the line must be 1, 2, 3, 4, 5 in order from that side. Both give certain cells at once, and they are the first things to look for.

Distance limits

A large clue cannot start with a tall tower. With a clue of c, the tower at distance d from the edge can be at most 5 − c + d. A clue of 4 therefore limits the first cell to 2 at most and the second to 3 at most. A clue of 2 rules out a 5 in the first cell. Writing these limits as notes along the edges turns many empty cells into short lists.

Opposite clues

The tallest tower is visible from both ends of its line, and it divides the line into the part seen from the left and the part seen from the right. So two opposite clues add up to at most 6 on a 5 × 5 grid. A pair of 2 and 4, adding up to exactly 6, pins the 5 down: it must stand where both views end, at the fourth cell from the side of the 4.

Find the tallest towers first

Every row and every column has exactly one 5. Clues of 2 or more keep it out of the first cell, distance limits keep it further away from large clues, and a 5 already placed rules out the rest of its row and column. Often only one cell is left. Then do the same with 4: after the 5s, the 4s fall quickly, and the small heights usually finish themselves.

When to start using notes

On 4 × 4 grids notes are rarely needed. From 5 × 5 on, write candidates once the certain moves are done, and look for a height that can go in only one cell of a row or column — a hidden single, as in sudoku. On a 6 × 6 strong-day grid this is the usual way through the middle of the puzzle.

A quick check before you finish

When a line is full, count the visible towers from both ends and compare them with the clues. The game marks clashes in rows and columns, but a wrong count of visible towers only shows when the grid is complete. Checking each line as you finish it saves a long search at the end.

Try it on a free grid, or on the grid in today's set.