Skylining
Peaking the Grid
The most important skyscrapers in an NxN Skyscrapers puzzle are the -skyscrapers. For instance, in a 5x5 Skyscrapers they’re the five -skyscrapers:
| 3 | 1 | 5 | 4 | 2 | ||
| 2 | 3 | 4 | 5 | 1 | ||
| 4 | 5 | 1 | 2 | 3 | ||
| 1 | 4 | 2 | 3 | 5 | ||
| 5 | 2 | 3 | 1 | 4 | ||
I call these lane peaks. Following the namesake of the puzzle, if we were to visualise the skyscrapers in the grid we’d have an urban city skyline of buildings. The -skyscrapers would be the tallest buildings, visible from any of the four sides.
Solving the lane peaks is central to solving a Skyscrapers puzzle. Abstractly, they’re the heart of the structure of the puzzle which everything else centers around. Concretely, most logical deductions we could make require the lane peak to be solved.
We can still make some general deductions in a lane even without a lane peak, and these can even assist in finding the lane peak. But we really just want to find the lane peak. In short, specificity beats generality.
There’s not much else to really say here. To really feel the importance of lane peaks, you just need to solve a lot of Skyscrapers. So, from here we’ll just look at many example scenarios where finding the lane peak is helpful.