With a clue of c, c − 1 more buildings have to come into view after the first, each taller than the last. So the building d squares in from the clue (counting the first as 0) can be at most n − c + 1 + d tall. In practice: the tallest building can’t stand within c − 1 squares of a clue of c.
This is one of the Skyscrapers techniques. Each page shows its technique on the same 7×7 from the game, Hard level 1.
The rule
- For each clue of 2 or more, take the squares nearest it.
- The first square can be at most n − c + 1 tall, the next at most one more, and so on, until the limit reaches n.
- Cross out of the notes every height over the limit.
In a real puzzle
On the 7×7, it’s first needed at step 3. Row 7 needs its 7, and the clues around the grid keep a 7 out of every open square in row 7 but one: row 7, column 4.
How often you’ll need it
On every one of the game’s 150 levels: 3.5 times per Easy level on average, 4.1 on Medium and 3.2 on Hard. It’s 3 of the 47 moves on the 7×7 here.