The Game Plan

We’re faced with a Skyscrapers puzzle. Where do we start?

There is, of course, no mandatory strategy that you have to follow – whatever works, works! That being said, if you’re here you’re probably looking for more structured ways to approach Skyscrapers, so I’ll share some of what goes through my mind when tackling a puzzle.

Overview

Like many logic puzzles, Skyscrapers is a game of iterated deduction. We start by filling in what we ‘obviously’ know. Then we look for more obscure deductions we can make. When we do find one, we ‘chase it’ until we’ve exhausted all the things it affects.

We keep doing this, over and over, until we’ve solved the puzzle. The tough part is spotting a new deduction each time! The further on we go, generally the fewer ‘obvious’ deductions there’ll be available to us, and we may have to reach for more niche deductions.

Can’t talk loads about theory without showing how to apply it, so throughout this article I’ll demonstrate everything by solving this example puzzle:

Feel free to take a stab at it yourself, and compare how we approach it!

Pregame

At the start of a puzzle, there’ll often be many ‘obvious’ deductions that are freely available. You might be familiar with that initial rush to fill in everything we can.

However, this won’t always be the case! Some of the toughest puzzles are incredibly difficult to start, and might need an egregious amount of pencilmarking before even solving a third cell.

Fill out the obvious

There are two clues can be trivially solved immediately – the $1$-clue (Silhouette) and the $N$-clue (Stairs). In this puzzle, we’ve got both!

Easy cases

Blockade is a free and surprisingly common case to watch out for.

Look for lane peaks

Main article: Skylining

Lane peaks ($N$-skyscrapers) are a core part of the ‘structure’ of a Skyscrapers grid. They provide more information than any other skyscraper, and luckily for us are also often the easiest skyscrapers to deduce.

Since this is a 5x5 puzzle, the lane peaks are $5$-skyscrapers. We’ve already found two, and we can find two more by Ascendant.

With 4/5 lane peaks found, this pinpoints the last one.

Notice this means Blockade applies again in the 2nd column. These deductions aren’t once-and-done, they could apply at any moment!

Midgame

Pencilmark!

Often, like in this puzzle, you’ll find yourself unable to really make any more ‘obvious’ deductions. Don’t worry, this is common, especially in more difficult puzzles.

The solution? Pencilmarking – writing out candidates for unsolved cells. If you’re averse to this (I know I was for a while¹), unfortunately it really is the most powerful tool as your disposal, so you’re freezing yourself in the foot if you don’t make use of it!

The start of the puzzle is when there’s the least structure to the puzzle. Pencilmarking helps elucidate some of that structure to us.

Of course, it’s very possible to go overboard with pencilmarking, and then things get messy! Generally, I only pencilmark cells with two candidates (maybe three, for larger puzzles), or where the candidates are particularly notable.

In this row, we’ve already solved 3/5 cells, so the last two must contain $[12]$.

Always look for Sudoku-style deductions

The rules of Sudoku apply in Skyscrapers, and they’re pretty powerful rules. Always be on the lookout for them, because they’ll constantly come in crucial.

Here, we can eliminate $2$ as a candidate, because $2$ is already used in the column.

That leaves only $1$ as a candidate, so we can now solve the row.

And we can also solve this column, since we only have one unused skyscraper left.

Pencilmarking again:

We have a clash in the right column again, which allows us to solve the row.

Endgame

At this point, the puzzle is pretty much solved.

Can you see how we built a momentum? In fact, we’ve reached critical mass, where we have sufficient information to solve the entire puzzle