Skyscraper Sudoku – Easy

Skyscraper Sudoku

Skyscraper Sudoku combines the usual Sudoku rules with visibility clues at the edges. Each number in the grid represents the height of a building: 1 is the shortest and 9 the tallest.

A edge number indicates how many buildings are visible when looking from that side into the respective row or column. A building is visible if all buildings in front are shorter. A taller building blocks the view of all shorter buildings behind it.

Basic Rules

• The playing field consists of 9 rows and 9 columns.
• Each row must contain the numbers 1 to 9 exactly once.
• Each column must contain the numbers 1 to 9 exactly once.
• Each 3x3 block must contain the numbers 1 to 9 exactly once.
• Each number corresponds to the height of a building.
• An edge number indicates how many buildings are visible from that perspective.
• The first building at the edge is always visible.
• After that, a building is only visible if it is taller than all previous buildings.
• 9 is the tallest building. Once it is reached, no further buildings can be visible behind it.
• All edge clues and standard Sudoku rules must be satisfied simultaneously.

Strategies for Solving

1. Correctly count visible buildings

In the following fully solved example grid, we focus on the first row. The clues on the left and right sides of this row are both 4.

From the left, the first row reads as:

1 5 3 4 7 9 8 6 2

• The 1 is visible.
• The 5 is taller than the 1 and visible.
• The 3 and 4 are blocked by the 5.
• The 7 is taller than the 5 and visible.
• The 9 is taller than all previous buildings and visible.
• After the 9, no further buildings can be seen.

Hence, from the left, exactly four buildings are visible: 1, 5, 7, and 9.

From the right, reading the same row gives: 2, 6, 8, 9, 7, 4, 3, 5, 1. Visible are 2, 6, 8, and 9, also exactly four buildings.

2. A clue of 1 places the 9 directly at the edge

If only one building should be visible from a side, that building must be the 9. A smaller number would be visible and the 9 behind it would also be visible from the opposite side, resulting in at least two buildings.

In the following puzzle, there are four clues with value 1:

• Above the sixth column is 1. The top cell of this column must be 9.
• To the right of the fourth row is 1. The rightmost cell of this row must be 9.
• To the left of the seventh row is 1. The leftmost cell of this row must be 9.
• Below the fifth column is 1. The bottom cell of this column must be 9.

All four clues directly follow from the edge hints and require no further assumptions.

3. A clue of 2 can determine the order of a pair of numbers

Looking at the second row, which is fully filled, the clue on the left is 2. Only the numbers 2 and 8 are missing in this row.

There are initially two possible sequences for the empty cells.

Option A:

289635417

From the left, three buildings are visible: 2, 8, and 9. This contradicts the clue 2.

Option B:

829635417

From the left, 8 is visible first. The 2 is blocked by 8. Then 9 is visible and blocks all subsequent buildings. This results in exactly two buildings visible.

Thus, the clue of 2 clearly indicates that the 8 must come before the 2.

4. Using clues from both sides together

In the following grid, the first row has clues of 4 on both sides. Only 2 and 5 are missing in the row.

If 2 is placed in the second position and 5 at the right edge, it looks like:

123479865

From the left, six buildings are visible: 1, 2, 3, 4, 7, and 9. Too many for the clue 4.

Reversing the order gives:

153479862

From the left, visible are 1, 5, 7, 9. From the right, visible are 2, 6, 8, 9. Both clues of 4 are satisfied.

The edge clues together decisively determine the order of the missing numbers.

5. A clue can exclude candidates without placing a number immediately

If the number 9 is already in the third cell of a row and the left clue is 2, then only one building can be visible before the 9.

This means: the second cell must be smaller than the first. If it were larger, there would be at least three visible buildings, which is impossible.

Such order information is also useful when the exact numbers are not yet known.

6. High clues require many new height records

A high clue like 5 or 6 indicates that many buildings in the row or column must increase in height consecutively. Very high numbers should not appear too early, or they would block many buildings behind.

A clue of 6 does not automatically establish a complete order. However, it excludes many arrangements. It’s better to combine possible number sequences with known Sudoku candidates rather than guessing.

Typical solving process

1. Enter all 9s directly fixed by a edge clue 1.
2. Check rows and columns where many numbers are already given.
3. Count visible buildings exactly from the perspective of the relevant hint.
4. Compare edge clues from both sides of the same row or column.
5. Test all possible sequences for missing numbers and eliminate arrangements with incorrect visibility.
6. Combine the visibility logic with standard Sudoku rules for rows, columns, and 3x3 blocks.
7. Finally, verify a completely solved row or column from both ends.

Common mistakes

• Interpreting the edge number as the sum of building heights. It counts only visible buildings.
• Counting every taller building without checking if a taller one is already in front.
• Reading the clue from the wrong side.
• Forgetting that the first building at the edge is always visible.
• Counting beyond 9 as visible after encountering the 9.
• Accepting a sequence that satisfies the edge clue but violates standard Sudoku rules.
• Prematurely deducing a single number from a middle-edge clue when multiple sequences are still possible.

Tips for beginners

• Start with clues of 1 because they immediately fix a 9 at the edge.
• Visualize a running maximum height when counting: only a number taller than the current maximum is visible.
• Write down both possible sequences for two options and count the visible buildings.
• Use clues from both sides together.
• Always verify conclusions against the row, column, and 3x3 block.

Skyscraper Sudoku becomes intuitive once you see visibility as a consequence of height records. The first building is always visible; subsequent buildings are only visible if taller than previous ones. The edge clues thus determine possible sequences and augment the normal Sudoku rules with a clear, logically checkable additional condition.