Skyscraper

Skyscraper involves examining a column or row from the perspective of the skyscraper clue outside the grid and making eliminations and decisions based on several parameters: the clue outside the grid, digits in the row or column, candidates in cells, digit placement to achieve the Skyscraper, and the board variants.

Few Tips:

1. The number 1 outside the grid suggests that the digit next to the 1 must be 9, effectively concealing the rest of the skyscrapers.
2. The number 9 outside the grid implies that all the digits must be in order, from 1 to 9.
3. A large digit conceals all the lower skyscrapers after it from the viewpoint of the skyscraper number.
4. Unless the number outside the grid is 1, 9 cannot be in the first cell of the row or column.
5. When approaching the puzzle, start by focusing on tall skyscrapers, as they indicate that the higher numbers are likely close to the end of the row or column.
6. Consider using highlight markers to mark cells where 7, 8, and 9 cannot go, providing additional clarity in the solving process.
7. Using the drawing tool to depict ‘<’ and ‘>’ between cells can be beneficial, indicating the relationship and order between them.

Smart Eliminations

Level: Advanced

By analyzing all possible digit combinations in a row or column, you can eliminate digits that would violate the Skyscraper count if placed in that cell.

This strategy is best explained through examples.

Example 1:

We are examining the skyscraper number at the top of Column 6. The count of skyscrapers is 2, and the candidates for cell A6 are 4 and 8.

• If A6 = 4, the visible skyscrapers in Column 6 from the top would be: 4, 6, 7, & 9, totaling 4 skyscrapers. Therefore, A6 ≠ 4.
• If A6 = 8, the visible skyscrapers from the top are 8 and 9, which matches the clue.

Example 2:

In Row C, there must be only 2 skyscrapers visible from the left and 3 skyscrapers visible from the right.

• If C1 = 1, the skyscrapers in Row C from the left are: 1, 6, 9 (and if C3 is 7 or 8, an additional skyscraper appears).
• If C1 = 4, the skyscrapers from the left are: 4, 6, 9 (and if C3 is 7 or 8, an additional skyscraper appears).

Thus, C1 ≠ 1 and C1 ≠ 4, leaving 7 and 8 as the remaining candidates for C1.

Now, from the right side:

• If C6 = 1 or 4, only 2 skyscrapers (5 and 9) would be visible, but we need 3. Therefore, C6 ≠ 1 and C6 ≠ 4.

From this point, classic Sudoku logic dictates that both C1 and C6 have only 7 and 8 as candidates, meaning C3 and C8 must be 1 and 4.

Example 3:

Row G must have 4 skyscrapers from the left and 3 skyscrapers from the right.

Each candidate in G9 will result in 3 skyscrapers from the right. On the left side, if the candidates in G2, G3, & G4 are 1, 2, & 6, only 3 skyscrapers (3, 6, & 9) would be visible, but we need 4. Therefore, 4 must be a candidate in these cells, implying G9 ≠ 4.