Sudoku Solver

Expert

Skyscraper (Row)

Two horizontal rows linked by a base column, forming two "towers" lying on their sides.

The Skyscraper (Row) logic is identical to the Column version, but turned sideways.

Instead of looking for two tall towers standing up, imagine two long buildings lying on their sides.

Interactive Example

4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9

Click "Apply Logic" to see the strategy in action.

Real Example Explanation

In the interactive example above, look at the number 7:

  1. The Base: Look at Column 9 (the vertical street).
    • The candidate 7 appears only twice: at R1C9 and R9C9.
    • This is our pivot point. We know one of these base cells must be a 7.
  2. The Towers (Rows):
    • Building A (Top): Row 1 connects R1C9 to R1C4.
    • Building B (Bottom): Row 9 connects R9C9 to R9C6.
    • Because our "Top" candidates (R1C4 and R9C6) are in different columns, the rectangle is broken. It's a Skyscraper.
  3. The "At Least One" Rule:
    • Since our Base (Column 9) can only hold one 7, it forces a conflict.
    • If R1C9 is the 7, then Building A is "inactive", forcing Building B to be active (R9C6 is 7).
    • If R9C9 is the 7, then Building B is "inactive", forcing Building A to be active (R1C4 is 7).
    • Conclusion: At least one of the "tips" (R1C4 or R9C6) must be a 7.
  4. The "Kill Zone":
    • We look for any cell that sees BOTH tips.
    • We scan the intersection of Column 4 (Building A's tip) and Column 6 (Building B's tip).
    • The cells that align with both tips (e.g., R1C6, R9C4) are in the kill zone.

How to Spot It

  1. Pick a Number: Scan the grid for a number (like 7).
  2. Find Two Rows: Look for two rows where the number appears exactly twice.
  3. Check the Base: Verify that one candidate from each row aligns in the same column.
  4. Check the Tops: Verify the other two candidates are "misaligned" (different columns).
  5. Eliminate: Clear candidates from the cells that see both Tops.

Quick Comparison

  • X-Wing: Perfect Rectangle. 2 Rows, 2 Columns.
  • Skyscraper (Row): Broken Rectangle. 2 Rows, 3 Columns.