A Guide to Skyscrapers
Introduction
Skyscrapers are fascinating puzzles done on various-sized grids surrounded by row clues and column clues.
The goal is to fill in the puzzle cells with values ranging from 1 to N, where N is the size of the grid.
For example, in a 4×4 grid you'll work with the values 1, 2, 3 and 4, whereas in a 7×7 grid you get to play with the full range of 1, 2, 3, 4, 5, 6 and 7.
Each cell value represents a skyscraper's height. Just like in a real city, taller buildings block the visibility of the shorter buildings behind them.
Rules
- No value can be repeated within the same row
- No value can be repeated within the same column
- Filled rows and columns must meet all outer edge clue requirements.
Clues
Skyscraper puzzles offer two different types of clues:
- Edge clues that surround the grid
- Known values inside of the grid
Edge clues tell you exactly how many skyscrapers can be seen when looking at that row or column from the perspective of that clue. Remember, taller buildings hide shorter ones behind them. This visual thinking is what makes these puzzles so uniquely engaging!
Example Row
In this example we see a completed 4x4 puzzle row:
The edge clue on the left indicates that 2 skyscrapers can be seen from its perspective. The edge clue on the right also sees 2 skyscrapers from its perspective.
Consider the following diagram as a visual representation of the row as a city skyline, with each building having a unique height.
From the left we can only see two skyscrapers. The first visible skyscraper has a height of 3 and becomes the tallest visible skyscraper. The next skyscraper has a height of 1 and is hidden because it is shorter than the tallest visible skyscraper (3). The next skyscraper that can be seen is 4, which becomes the new tallest visible skyscraper. The last skyscraper, 2 is also hidden because it is shorter than 4.
Using the same method we find that we can only see two skyscrapers from the right, 2 and 4 (which hides the 1 and 3). Column clues work the same way, from the top or bottom.
Note that the skyscraper with the same height as the grid size will always be visible since it is the tallest possible skyscraper.
Strategies
Let's dive into some strategies that transform daunting puzzles into conquerable challenges.
To illustrate, we'll tackle this 4x4 puzzle together.
The values that must appear in each row and column are 1, 2, 3 and 4. No more, no less, and no value is repeated in the same row or column.
Strategy 1.
Edge Clue – 1
An edge clue of 1 always means this: The tallest skyscraper must be standing right next to that edge!
Only the tallest skyscraper can block every other building.
In our example, let's start by placing a 4 next to all edge clues of 1.
Strategy 2.
Edge Clue – N
An edge clue equal to the grid size always means this: Every skyscraper must be visible from that clue's perspective!
When you spot this clue, you can confidently fill in an entire row or column.
Buildings must be placed in ascending order for each building to be visible.
Let's fill in two columns using this rule.
Strategy 3.
Single Cell Deduction
Sometimes you'll find yourself with just one empty cell in a row or column, which always means this: The value has to be the missing unique number in the grid size sequence.
In our example, the third row is missing a 1, so let's fill it in.
Strategy 4.
Single Value Deduction
When the same value exists in every row and column except for one, it means this: The missing value must live at the intersection of both the row and column missing that value.
In our example, only the second row and the second column do not contain a 4. So, we can deduce that the value where those two rows intersect must be a 4. Let's fill that in.
We can use Strategy 3: Single Cell Deduction to figure out that a 1 belongs in the second row.
Strategy 5.
Pencil Marks
When things get tricky, we can fill in possible values using pencil marks. All remaining cells can either contain a 2 or a 3.
Pencil marks are usually placed in the top-right corner of a puzzle cell.
Strategy 6.
Visible Height Deduction
Don't worry, we're not stuck! See the edge clue on the right of the first row? If we place a 3 next to it, then both the 1 and 2 are blocked so we can't meet the edge clue rule.
Instead, let's place a 2 in that cell and remove any conflicting pencil marks in its row and column.
Pencil marks are removed once the value is found.
Based on the remaining pencil marks, we only have the option to place 3s in column 2 and 4.
Let's finish off the puzzle with Strategy 3: Single Cell Deduction and place a 2 in the final cell.
🎉 All done! Use these strategies and tips to solve the rest of the puzzles in this book. Fun challenges await you!
Have Any Questions?
Have questions about a product? Want to suggest something? Just want to chat about puzzles and games? Random Box welcomes your thoughts. Remember to add Random Box to your allowed sender list so you don't miss a response!