Gattai-3 – Hard

Gattai-3

Gattai-3 is a multi-sudoku. This means: The puzzle does not consist of a single classic Sudoku, but of multiple interconnected 9x9 Sudokus. Each sub-sudoku follows the standard Sudoku rules: Each row, column, and 3x3 box must contain the numbers 1 to 9 exactly once.

Gattai-3 is a merged arrangement of three classic 9x9 Sudokus. The sub-Sudokus are not simply next to each other but form a common shape with overlapping areas.

Gattai-3 relies on switching between the three sub-Sudokus and using shared areas consistently as connection points. Like all Sudokus, there is no calculation involved. The numbers are symbols placed correctly through logical elimination.

Basic Rules

• The puzzle consists of several classic 9x9 Sudokus connected into a common shape.
• Exactly one number from 1 to 9 is written in each active cell.
• Within each individual 9x9 Sudoku, each row must contain the numbers 1 to 9 exactly once.
• Within each individual 9x9 Sudoku, each column must contain the numbers 1 to 9 exactly once.
• Within each 9x9 Sudoku, each 3x3 block must contain the numbers 1 to 9 exactly once.
• Shared cells belong to multiple sub-Sudokus. The value entered there must be the same for all involved sub-Sudokus.
• Pre-given numbers must not be changed.
• Unseen areas outside the visible grid do not belong to the puzzle and are not filled in.
• A multi-sudoku is solved when all contained 9x9 Sudokus are correctly solved and all shared cells match.
• Important: A long visible row is not automatically a Sudoku row. Always consider the boundaries of the 9x9 sub-sudoku being viewed.

Solving Strategies

The basic techniques correspond to classic Sudoku. The difference is that certain entries in one sub-sudoku can influence others, especially in shared cells and overlapping areas.

1. Check a single sub-sudoku as a normal Sudoku

Start with a sub-sudoku where many numbers are already given. Often, simple safe entries can be found there without considering the entire multi-sudoku form at once.

In the considered 9x9 part-sudoku, a row reads 43172689. The numbers 1, 2, 3, 4, 6, 7, 8, and 9 are already present. The only missing number is 5. Therefore, the last open cell of this part-sudoku row must be a 5.

This conclusion applies only to the nine cells of this specific part-sudoku row, not the entire visible width of the shape.

2. Hidden single candidate in a 3x3 block

Not every safe number results from an almost complete row. Often, a number can only go in one position within a 3x3 block. In the following complete Gattai-3 grid, we look at the top-left 3x3 block of a sub-sudoku to find the number 5.

In the examined sub-sudoku, the 5 is checked in the top-left 3x3 block. The second and third rows already contain a 5, so it cannot be in those rows within that block. Additionally, the first and second columns of this sub-sudoku already contain a 5. This excludes the first two cells in the first row of the block, leaving only the third cell. That cell must contain the 5.

This is a hidden single candidate. The cell may not seem immediately obvious, but for the number 5, only this position within the block is allowed.

3. Use a shared cell as a bridge

Shared cells are the most important feature of Gattai-3. A shared cell belongs to multiple sub-Sudokus. When a number is confidently determined there, it must be immediately reflected in all involved sub-Sudokus.

In the left 9-row of the example, the sequence 123456.78 is present. The only remaining number in this sub-sudoku is 9. The open cell also lies in the neighboring sub-sudoku. Once 9 is entered, it also affects the 9 in that adjacent sub-sudoku's line.

This first entry is therefore not just a local progress step but also an indication for the neighboring sub-sudoku, as the same cell belongs to a line, column, and 3x3 block in that area as well.

4. Overlap leads to a follow-up step

The relevant 9-line in the neighboring sub-sudoku is 45697812. Only the 3 is missing, so this cell can also be confidently filled.

This example shows the typical multi-sudoku effect: First, a cell is confidently solved in one sub-sudoku. Because this cell is shared, it immediately causes a further confident deduction in the adjacent sub-sudoku.

5. Check candidates in overlaps rigorously

A normal Sudoku cell is restricted by a row, column, and 3x3 block. A shared cell may also belong to additional rows, columns, and blocks of other sub-sudokus. Therefore, a candidate in a shared cell is only valid if it is allowed in all involved sub-Sudokus.

Practically, this means: do not evaluate a shared cell only from the perspective of the sub-Sudoku you're working on. Switch deliberately to the other sub-sudoku and check its row, column, and block as well. This often helps to identify shared cells as border cells earlier.

6. Carefully track the boundaries of sub-Sudokus

While Gattai-3 looks like a large connected puzzle, its logic stems from the individual 9x9 Sudokus. A visible row may contain multiple different sub-sudoku rows. Always clearly specify which 9x9 sub-sudoku is being considered.

Typical solving process

1. First, get an overview of the arrangement: three merged 9x9 Sudokus.
2. Select a sub-sudoku with many clues and find safe classical Sudoku steps.
3. Check nearly complete rows, columns, and 3x3 blocks.
4. Search for hidden single candidates: numbers that can only go in one position within a region.
5. Mentally mark shared cells and overlapping areas.
6. Immediately transfer each certain entry in a shared cell to all involved sub-sudokus.
7. Afterwards, verify whether new candidates or eliminations arise in neighboring sub-sudokus.
8. Regularly switch between the sub-sudokus instead of solving a region in isolation.
9. At each entry, verify that it is allowed in all affected rows, columns, and 3x3 blocks.
10. Stop when every single 9x9 Sudoku is fully and consistently solved.

Common mistakes

• Treating the entire shape as a single large Sudoku. But rules apply within each individual 9x9 Sudoku.
• Updating shared cells in only one sub-Sudoku. A shared cell always affects all sub-sudokus it belongs to.
• Falsely tracking boundaries. Not every visible row is part of the same Sudoku row in offset grids.
• Interpreting areas without grids as cells. Areas without a grid are not filled in.
• Relying on guessing too early. A wrong entry can damage multiple sub-sudokus simultaneously.
• Not checking candidates in overlaps carefully enough. A candidate must be allowed in all involved rows, columns, and blocks.
• Not proceeding after a safe entry. Shared cells often lead to immediate new eliminations.

Tips for beginners

• Start with a single sub-sudoku and only make safe moves.
• Early on, look for shared areas. These often form the most important connections.
• Strictly observe the 9x9 boundaries of individual Sudokus.
• Always check all involved sub-sudokus for shared cells, not just the area you're working on.
• Use candidate notes as soon as multiple sub-sudokus are involved.
• Switch perspective: if a sub-sudoku cannot progress, check the neighboring shared cells.
• Ask yourself with each entry: In which sub-sudoku is this number surely? Does it also affect another sub-sudoku?
• View overlaps not just as a difficulty but as additional clues.

Gattai-3 extends the classic Sudoku without changing its fundamental logic. Each number still follows the known Sudoku rules. The challenge is to properly link several sub-sudokus. By consistently using shared cells, even complex multi-sudoku shapes can be logically solved step by step.