Skyscraper Puzzles are a challenging logic puzzle.
How to Play Skyscraper
A Skyscraper puzzle is made of a grid. Every square in the grid must be filled with a number from one to the grid size so that every row and column contains one of each number.
Visualize each number inside the grid as a skyscraper. The number represents how many storeys tall the skyscraper is.
Around the outside of the grid is a street with hints that tell you how many skyscrapers you could see if you were standing there looking at it. Every skyscraper will block the view of any shorter skyscrapers, while taller skyscrapers will still be visible.
Skyscraper Tips & Example
When you read the description for how to play skyscraper, it sounds a bit confusing, right?!
This is definitely a puzzle that’s hard for beginners.
I’m going to teach you some tips and tricks by using a Skyscraper Example (5×5, very easy).
1 is “in view”
The number one rule of Skyscraper is how many towers you can see. When the number is one, you can only see one skyscraper. This means the tallest tower (or biggest number) will be right up beside the one.
In the example, we have four 1’s which allow us to write in three 5’s.
1 is “hidden”
The second-largest number around the outside (in our example, 4) means that every tower except one will be visible. This means that the tallest tower (the 5 for us) must be one of the last 2 squares (highlighted green).
For our example, this doesn’t help us because we’ve already filled in the 5 in both those blocks. But it’s a good thing to know!
2 are “in view”
When you can only view 2 skyscrapers AND you know the tallest skyscraper is at the end (like our first row), there’s only one place the second tallest skyscraper can be.
At the start.
Why? Because if you put the second-tallest skyscraper further in, you’ll be able to see shorter skyscrapers in front of it.
2 are “in view”
This is just like the last tip except we already know that the second highest is hidden. The tallest skyscraper is at the ‘end’ and we need the 3 to hide the shorter towers. Therefore, the 3 must go at the beginning.
Track Your Progress
Keep track of how many “visible” skyscrapers you have in each row and column.
This makes it easier to see at a glance where you need tall and short skyscrapers.
Cannot be Second-Highest
When there are 2 skyscrapers visible, the second skyscraper cannot be the second-highest.
For our example, when there are 2 skyscrapers visible, the second one cannot be a 4.
All of the green squares are 2nd’s of 2 visible. When we look at the second column, that leaves us only one spot for a 4.
I’ve also put a small 4 in the 4th column to indicate that we cannot have a 4 there in the future. Why didn’t I put one in the other green squares? Because there’s already a 4 in each of those columns so we know a 4 can’t go in any of them anyways.
A number must appear once (and only once) in each row and column.
We have 3 out of 5 fives filled in. There are only 4 spaces we can potentially put the other two. I’ve marked them in small font.
3 are “in view”
Let’s look at the third column.
We’ve already figured out that the 5 has to be the third or fourth tower from the top. We also know that there must be 3 skyscrapers visible from the bottom.
The 5 cannot be the second from the bottom because then we’d only be able to see 2 skyscrapers.
This means we can fill in the 5 directly in the middle AND we can fill out the opposite 5 in the second column.
Cannot be 1
Looking at column 1, we’re only missing 1 and 2.
If we look at row 3, we should only be able to see 2 skyscrapers. We already have the 5 in place. If we make the first square a 1, then 3 skyscrapers would be visible. So we know that the first square must be 2.
This means the 4th square in column 1, must be 1.
Let’s take a look at row 3. We have the 2 and 5 in place.
We know that the four cannot be in the second square (because there’s already a 4 in that row) and it cannot be in the fourth square (because we determined that earlier and marked it down).
This means the 5th square in row 3 must be a 4!
Another easy set of possibilities to mark down is in row 5. We have the 3, 4, and 5 so the remaining two squares have to be 1 and 2.
It’s that 2 and 5 again!
Remember earlier when we learned about having 2 visible skyscrapers and a 5 at the end of the row/column? Here it is again!
We must put the 3 at the beginning otherwise we’d have more than 2 skyscrapers visible.
What are the options?
Back to row 3 we go. We have the 2, 5, and 4 marked in which leaves us only the 1 and 3.
We need to be able to see 2 skyscrapers (which we already can) so our 3-story skyscraper must go behind the 5.
Once we put the 1 into the second square of row 3, we can also finish column 2 (by putting a 2).
Let’s look to row 1 first. We know where the 3, 4, and 5 are so we can mark the remaining two squares as potentials for 1 and 2.
Now let’s look at column 3. We know where the 5 is. This is where potentials can be helfpul. We also know where the 1 and 2 will go (there are 2 squares that can only contain 1 or 2). So all that’s left is the possibility for 3 and 4.
Can you finish the puzzle?
Those are all my tips and tricks for completing this skyscraper example. Can you finish the puzzle now?
If you want the solution it’s at the bottom of the post!