How to Solve a 4×4 Skyscraper Puzzle, Step by Step

The fastest way to learn skyscraper puzzles isn't to read the rules again — it's to watch one get solved, deduction by deduction, with nothing skipped. So that's what this is: a complete walkthrough of a single 4×4 skyscraper puzzle, from the very first forced move to the finished grid. The 4×4 is the perfect size to learn on, small enough to follow every step but big enough to use every core technique. Grab a pencil and follow along, and afterwards you can play a 4×4 skyscraper puzzle of your own. New to the idea entirely? Skim the rules first.

The puzzle

We have a 4×4 grid. We'll fill it with building heights 1, 2, 3, and 4, so that each height appears once in every row and column. The clues around the border tell us how many buildings are visible from that direction — remember, a taller building hides every shorter building behind it.

Here are our clues, reading along each edge:

• Top clues (over columns 1–4, left to right): 3, 2, 1, 2
• Bottom clues (under columns 1–4): 1, 2, 3, 2
• Left clues (beside rows 1–4, top to bottom): 2, 2, 4, 1
• Right clues (beside rows 1–4): 2, 2, 1, 4

We'll refer to cells as Row and Column — so R2C3 is row 2, column 3.

Step 1: The clue of 4 fills a whole row

The left clue on row 3 is 4. In a 4×4 grid, seeing all four buildings is only possible if they climb in perfect order from that side. So row 3 must be, left to right:

Row 3 = 1, 2, 3, 4.

That's four cells placed from a single clue. Extreme clues are gifts — always look for them first.

Step 2: The clue of 4 on the right fills another row

The right clue on row 4 is 4. Same logic, but viewed from the right: all four buildings visible means they ascend from the right side, so they descend left to right:

Row 4 = 4, 3, 2, 1.

Two rows down already, and we've barely started.

Step 3: A clue of 1 places the tallest building

The top clue on column 3 is 1. Seeing only one building from the top means the tallest (4) sits in the first cell of that column:

R1C3 = 4.

Now look at column 3. We have R1C3 = 4, R3C3 = 3 (from step 1), and R4C3 = 2 (from step 2). The only missing height is 1, which must go in the remaining cell:

R2C3 = 1. Column 3 is now 4, 1, 3, 2.

Step 4: Crack row 1 using a top clue

Row 1 has a 4 sitting in column 3, and a left clue of 2. Let's also use the top clue of column 1, which is 3.

Look at column 1. From steps 1 and 2 we know R3C1 = 1 and R4C1 = 4. The two empty cells, R1C1 and R2C1, must hold the missing heights 2 and 3.

The top clue of column 1 is 3, meaning three buildings are visible looking down. Going down the column we'd see R1C1, then R2C1, then 1, then 4. For exactly three to be visible, R2C1 must be taller than R1C1 (so both are visible before the 4 caps it off). That forces:

R1C1 = 2 and R2C1 = 3.

Now finish row 1. It has 2 in column 1 and 4 in column 3, so it still needs 1 and 3 in columns 2 and 4. The left clue of 2 means after the first building we should see only one more — the 4 — so R1C2 must be shorter than the 2 beside it. That makes R1C2 = 1, leaving:

Row 1 = 2, 1, 4, 3.

Step 5: Elimination finishes the grid

Only row 2 is left, and it already has R2C1 = 3 and R2C3 = 1. It needs 2 and 4 in columns 2 and 4.

Look at column 2: it now holds 1 (R1), 2 (R3), and 3 (R4), so the missing height 4 must go in R2C2. That leaves 2 for R2C4:

Row 2 = 3, 4, 1, 2.

The finished puzzle

Every cell is placed, with no guessing anywhere:

	C1	C2	C3	C4
R1	2	1	4	3
R2	3	4	1	2
R3	1	2	3	4
R4	4	3	2	1

Take a moment to check a clue or two against it. Row 1 from the left: you see the 2, then the 4 hides the rest — two buildings, matching the left clue of 2. Column 1 from the top: 2, then 3, then 4 caps it — three buildings, matching the top clue of 3. Every clue checks out.

What you just learned

Notice the order we solved in: extreme clues first (the 4s and the 1), then a clue pair plus column logic to break open row 1, then plain Latin-square elimination to mop up. That's the exact priority you'll use on every skyscraper puzzle, at any size. The bigger grids just have more steps, not different ones.

The only way to make it stick is to do it yourself. Play a 4×4 skyscraper puzzle now, start by hunting for the 1s and 4s, and when you're ready for more techniques, our full solving strategy guide covers every clue type.