Sudoku Skyscraper Rules: Learn This Towering Strategy for Solving

As you become an experienced Sudoku player, it's only natural that you'll look to develop strategies that help you solve puzzles with greater speed and success. The Skyscraper tactic is one the best you can learn.

Understanding Skyscraper Basics

The Skyscraper tactic is one that works on the idea of visualizing two skyscrapers of varying heights. If you imagine a skyscraper building, it involves several floors and moves up vertically. In Sudoku, a skyscraper is built when a specific number (candidate) can only be placed in one of two cells within a column. A skyscraper could potentially have any number of floors between 2 and 9, for example;

• Column 1 has two cells (row 1 and row 9) where a 7 could be used. This skyscraper building is 9 floors tall.
• Column 3 has two cells (row 4 and row 7) where a 7 could be used. This skyscraper building is 4 floors tall.
• Column 7 has two cells (row 5 and row 9) where a 7 could be used. This skyscraper building is 5 floors tall.
• Column 8 has two cells (row 6 and row 9) where a 4 could be used. This skyscraper building is 4 floors tall.

For a skyscraper pattern to be formed, though, the two skyscrapers should have the same bottom row as if they were built on a level ground. So column 3 can't be one in the above situation. Two skyscrapers also have to apply for the same candidate, meaning column 8 is irrelevant here.

So, column 1 and column 7 can form the skyscraper pattern. Just remember that had they both been up to either row 1 or row 5, this would be an X-Wing due to the rectangular nature.

Applying The Skyscraper Rules

The best way to understand how Skyscraper tactics can work is to use an example. Let's imagine a scenario where a Skyscraper pattern involves;

• Two cells where a 2 is a candidate in column 1 (rows 6 and 8).
• Two cells where a 2 is a candidate in column 8 (rows 5 and 8).

It's not quite an X-wing because two of the candidate cells are spread across rows 5 and 6. So, the Skyscraper technique should be used instead. While there are only two possibilities for a 2 in column 1 and column 8, you may also have other candidates in rows 5, 6, and 8 as well as the four 3x3 grids.

Due to the fact that there are only two possible candidates in the columns, there is an 'either or' situation. If a 2 is placed in row 8 of column 1, then a 2 can now be used in row 6 of column 1 or row 8 of column 8. Similarly, if a 2 is placed in row 8 of column 8, there cannot be a 2 in either row 8 of column 1 or row 5 of column 8.

As a result of this, it is guaranteed that a 2 will be placed in either the cell at column 1 row 6 or column 8 row 5. Now, using the Skyscraper method means we can eliminate any other 2s that can be seen by both of these cells. For example;

• If a 2 is placed in row 6 of column 9, it is visible by the column 1 cell (row) and column 8 cell (3x3 grid). So, the 2 candidate can be removed from this cell.
• If a 2 is found in row 5 of column 7, it is visible by the column 8 cell but not the column 1 cell. Therefore, we cannot remove the 2 candidate from this cell.
• If a 2 is found at row 5 of column 3, it is visible by the column 1 cell (3x3 grid) and column 8 cell (row). So, the 2 candidate can be removed from this cell.

By removing the 2 candidate from 2 cells, it is possible that we will reveal a cell. So, if removing the 2 means that only a 4 is available in row 6 of column 9, we can fill this in. From here, we can remove any 4s from the row, column, and 3x3 grid too. So, it's not hard to see how this could help us navigate the puzzle and potentially start a chain where several cells are filled.

Integrating with Other Strategies

The Skyscraper strategy is one that can be used in conjunction with other techniques within the same game. For example, you may find an X-Wing or a Y-Wing elsewhere on the board. Likewise, when using this tactic, you can still use the magic number to confirm that adding a candidate to one of the cells in the column wouldn't see the row or 3x3 grid fall short or surpass a total of 45.

Arguably the best tactic to combine with the Skyscraper, though, is forcing chains. Even when a Skyscraper does not leave a naked solution after eliminating a candidate, it will open the door to testing out two options in two cells to see if this reveals any naked numbers. And once one is revealed, it could spark a situation where several cells can be filled.

Common Mistakes to Avoid

The Skyscraper technique is considered an advanced strategy but is one you can learn fairly easily if you already know how to X-Wing. Nevertheless, there are some common mistakes that players should avoid. They are;

• Not confirming that the 2 highlighted cells are the only two possibilities within a column. If a third exists and it ends up being the correct solution, every step made during the Skyscraper technique will be an error.
• Removing additional candidates found on the same rows as the skyscrapers without first confirming that the cells can be seen by both of the skyscraper cells. If only one skyscraper interacts with the cell, leave it.
• Using the Skyscraper technique on two skyscrapers of the same size. In this instance, you should opt for the X-Wing instead. Not only is it quicker, but it also aids in the confirmation of candidate placements.

When the pattern exists, the Skyscraper method can be used to tackle some very challenging Sudoku puzzles. Once you've used it a few times, it will allow you to get faster times and avoid guessing.

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