Medium Skyscraper Sudoku

Clues outside the grid count how many buildings are visible when looking in from that side (taller buildings block shorter ones).

Easy Medium Hard Expert

Skyscraper Sudoku at medium difficulty. Permutation analysis from both sides of each row and column narrows the board quickly.

3
2
2
3
3
5
4
4
1
4
2
3
3
2
4
1
3
5
7
3
2
5
1
9
9
6
1
3
4
9
8
6
1
4
7
6
8
4
3
5
7
9
3
5
6
8
9
5
1
8
1
4
4
2
2
2
3
2
3
3
3
4
4
2
2
1
3
4
Mistakes
0/3
Score
-
Time
00:00
Try Hard Skyscraper Sudoku →
Progress0%

What is Skyscraper Sudoku?

Difficulty
★★★★☆
4/5
Constraint Type
Outside Clues
Typical Givens
4–10 clue values
Avg. Solve (Medium)
25 min

Solving Techniques for Medium Level

Technique Description Level
Clue 1 Forces 9 First A visibility clue of 1 means the first building from that edge must be a 9. All shorter buildings behind it are hidden. Beginner
Clue 9 Forces Ascending Order A clue of 9 means all buildings are visible, so digits are in strictly ascending order from that edge: 1, 2, 3, 4, 5, 6, 7, 8, 9. Beginner
Permutation Enumeration For each clue value V, enumerate all permutations of 1–9 that give exactly V visible buildings. Cross-reference opposite-edge clues. Intermediate
9 Always Visible The digit 9 is always visible from either edge. The digit 8 is visible only if it appears before any 9 from that edge. Intermediate

Master these, then take on Hard Skyscraper Sudoku to learn Advanced techniques.

Techniques to Master at Medium

  • Hidden Singles technique — Count where 9 can stand in each line — as the tallest building it is always the last one visible, so a clue of V puts it no earlier than position V — and 9's hidden singles fall out of pure counting.
  • Obvious Pairs technique — Cells just inside a clue-2 edge often reduce to two tall options like {7,8}; these visibility pairs eliminate through the boxes the edge rows cross.

Average Solve Time by Difficulty

Easy
12 min
Medium
25 min
Hard
50 min
Expert
80 min
Want a full walkthrough of rules, strategies, and solving steps? How to Play Skyscraper Sudoku →

Related Variants

Outside Sudoku

Both decode digits written around the border — placement windows here, visibility counts there.

Sandwich Sudoku

Another grid solved from the margins, swapping visibility logic for sums between the 1 and the 9.

Little Killer Sudoku

Outside clues turned diagonal: arrows fire sum totals across the grid instead of counting buildings down a line.

Frequently Asked Questions — Medium Skyscraper Sudoku

What techniques help most in medium Skyscraper Sudoku?
Permutation analysis: for each row or column, list all arrangements of digits 1–9 that produce the given visibility count from each side. Then use the intersection of valid arrangements to find digits that are fixed in specific positions regardless of arrangement. This is the core medium-level technique.
How do opposite-side clues interact?
A row has both a left clue and a right clue. Together they constrain the same arrangement from two directions. Many arrangements that satisfy the left clue fail the right clue, and vice versa. Using both clues simultaneously greatly reduces the number of valid permutations.
What does a skyscraper clue of 2 tell me?
A clue of 2 means exactly two buildings are visible. This means the 9 is not in the first position (otherwise only 1 would be visible), but the second visible building must be 9 or must be higher than everything before it. Several arrangement patterns are consistent, but clue 2 is still quite restrictive.
How long does medium Skyscraper Sudoku take?
Most players finish medium Skyscraper Sudoku in 15–30 minutes. The solving rhythm alternates between listing valid permutations for uncertain rows and using standard Sudoku constraints to eliminate specific digits from cells.
Does a 0 ever appear as a Skyscraper clue?
No. From any direction, the first digit in the row or column is always visible, so the minimum visibility count is 1. A 0 clue would be impossible and does not appear in valid puzzles.

More questions? See the full Skyscraper Sudoku guide.