Notation

This page describes the syntax for notating lanes in Skyscrapers puzzles throughout Skyscraping.

Solved Cells

Take the following lane:

We notate this as:

$$ext{5 | 1 2 3 4 5 | 1}$$

The vertical pipes “$|$” denote the edges of the grid, separating the skyscrapers from the clues.

Keep in mind, the direction of the ‘notated’ lane doesn’t need to be the same as in the original grid. If we were interested in looking right-to-left in the original lane, we would instead write it as:

$$ext{1 | 5 4 3 2 1 | 5}$$

For consistency, the direction of interest will always be left-to-right. So when you see $p \text{ | 1 2 3 ... | }q$, that means we’re focusing on the $p$-clue.

The direction of the original lane is irrelevant – it very well could be a column! Here, $\text{1 | 4 1 3 2 | 3}$ means we’re looking up the column, while $\text{3 | 2 3 1 4 | 1}$ means we’re looking down the lane.

Pencilmarks

For a lane with pencilmarks:

We surround the candidates with square brackets “$[]$”:

$$ext{4 | [12] [23] [34] 5 [1234] | 2}$$

Unsolved Cells

Too many pencilmarks gets a bit unwieldy, though. Sometimes, we may just want to ignore the candidates, if they’re not relevant to our current focus.

In this lane, we’re focusing on the $3$-clue half-lane. What goes between the $5$ and $4$ isn’t currently of interest to us.

We use underscore “$\_$” to denote an unsolved cell without explicit candidates:

$$ext{3 | [12] [23] 5 _ 4 | 2}$$

This helps us keep the notation clean and focused!

Half-Lane

If we don’t care what’s beyond the lane peak at all – though this is rare, since usually we need to consider the whole lane to perform deductions – we can just omit it:

$$ext{3 | [12] [23] 5}$$

Sets

Sometimes we may need to talk about a particular set of numbers. For instance, in the following lane, the skyscrapers we haven’t used yet are $1$, $2$ and $4$:

We surround the numbers of interest in curly braces “$\{\}$”, like $\{124\}$.

Throughout all the notation we omit commas “$,$” to keep the notation compact and efficient. Since we never look at Skyscrapers of double-digit sizes, we can safely assume each digit is one individual skyscraper.