Sohei Sudoku – Medium

Sohei Sudoku

Sohei Sudoku is a Multidoku. This means: The puzzle is not made up of a single classic Sudoku, but of several interconnected 9x9 Sudokus. Each sub-Sudoku follows the normal Sudoku rules: In every row, every column, and each 3x3 block, the numbers 1 to 9 must appear exactly once.

Sohei Sudoku has a cross-shaped arrangement of four classic 9x9 Sudokus. The sub-Sudokus are positioned at the top, bottom, left, and right; with a characteristic free zone in the center.

In Sohei Sudoku, many progressions occur at the lateral connections, not in the empty center. It is crucial to carefully follow the actual boundaries of each sub-Sudoku. Like all Sudoku puzzles, no calculations are used. The numbers are symbols placed correctly through logical elimination.

Basic Rules

• The puzzle consists of multiple classic 9x9 Sudokus connected into a single figure.
• Exactly one number from 1 to 9 is entered in each active cell.
• Within each 9x9 Sudoku, each row must contain the numbers 1 to 9 exactly once.
• Within each 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 entered value must be the same for all involved sub-Sudokus.
<li-Given numbers may not be changed.
• Empty areas outside the visible grid are not part of the puzzle and are not filled.
• A Multidoku is solved when each contained 9x9 Sudoku is correctly solved and all shared cells match.
• Important: A long visible row is not automatically a Sudoku row. Always consider the boundaries of the respective 9x9 sub-Sudoku.

Strategies for solving

The basic techniques correspond to classic Sudoku. The difference is that certain entries in one sub-Sudoku can influence other sub-Sudokus. Shared cells and overlapping areas are particularly important.

1. Check a single sub-Sudoku like a normal Sudoku

Start with a sub-Sudoku that already has many numbers. Often, simple secure entries can be found there without considering the entire Multidoku structure at once.

In the considered 9x9 sub-Sudoku, one 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 in this sub-Sudoku row must be a 5.

This conclusion applies not to the entire visible width of the figure, but precisely to the nine cells of this one sub-Sudoku row.

2. Hidden single candidate in a 3x3 block

Not every secure number arises from an almost complete row. Often, a number can only be placed in one remaining cell in a 3x3 block. In the following complete Sohei Sudoku grid, we look at the top-left 3x3 block of a sub-Sudoku and search for the number 5.

In the considered sub-Sudoku, the 5 in the top-left 3x3 block is examined. In the second and third rows of this sub-Sudoku, a 5 already exists, so the 5 cannot be in those two rows within the 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. The only remaining cell in the first row is the third one, which must contain the 5.

This is a hidden single candidate. The cell may not seem obviously forced at first, but for the number 5, there is only this one permissible position in the examined block.

3. Use a shared cell as a bridge

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

In the first 9-row of the example, the sequence 276314.89 is present. Within this sub-Sudoku, only the 5 is missing. The open cell is also part of an adjacent sub-Sudoku. Once the 5 is entered, it also impacts the 9-row there.

The first entry is therefore not just a local progress. It also provides a hint for the neighboring sub-Sudoku because the same cell is part of a row, column, and 3x3 block there as well.

4. A consequence of an overlap

In the adjacent sub-Sudoku, the relevant 9-row is 58912346. Only the 7 is missing there, so this cell can also be filled securely.

This example illustrates the typical Multidoku effect: first, a cell in one sub-Sudoku is securely solved. Because this cell is shared, it immediately leads to another secure step in the neighboring sub-Sudoku.

5. Carefully check candidates in overlaps

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

Practically, this means: do not only check a shared cell from the perspective of the current sub-Sudoku. Deliberately switch to the other sub-Sudoku and verify the row, column, and block there as well. This approach often makes shared cells evident earlier as cells at the outer edge.

6. Follow the boundaries of sub-Sudokus carefully

Although Sohei Sudoku appears as a large interconnected puzzle, the logic arises from the individual 9x9 Sudokus. A visible row can contain parts of multiple different sub-Sudoku rows. Always clearly identify which 9x9 sub-Sudoku you are currently considering.

Typical solving process

1. Get an overview of the arrangement: four 9x9 Sudokus around a free center.
2. Select a sub-Sudoku with many givens and look for secure classic Sudoku steps there.
3. Check nearly complete rows, columns, and 3x3 blocks.
4. Look for hidden single candidates: numbers that can only appear in one position within a certain area.
5. Mentally mark shared cells and overlapping areas.
6. Immediately transfer each secure entry in a shared cell to all involved sub-Sudokus.
7. Check afterward for new hidden singles or eliminations in neighboring sub-Sudokus.
8. Alternate between sub-Sudokus regularly instead of solving areas in isolation.
9. For each entry, verify that it is allowed in all affected rows, columns, and 3x3 blocks.
10. Finish the puzzle only when every 9x9 Sudoku is fully and consistently solved.

Common mistakes

• Treating the entire figure as a single large Sudoku. The rules apply within each individual 9x9 Sudoku.
• Updating shared cells in only one sub-Sudoku. A shared cell affects all sub-Sudokus it belongs to.
• Incorrectly following boundaries. Not every visible row is part of the same Sudoku row in offset grids.
• Interpreting empty areas as cells. Areas without grid lines are not filled.
• Rushing too early. A wrong entry can damage multiple sub-Sudokus simultaneously.
• Not strictly checking candidates in overlaps. Candidates must be allowed in all involved rows, columns, and blocks.
• Not continuing after a secure entry. Shared cells often immediately create new eliminations.

Tips for beginners

• Start with a single sub-Sudoku and solve only secure steps there.
• Early on, identify shared areas. They often form the most important connections.
• Adhere strictly to the 9x9 boundaries of each Sudoku.
• Always check all involved sub-Sudokus for shared cells, not just the current area.
• Use candidate notes when multiple sub-Sudokus are involved.
• Switch perspectives: if stuck in one sub-Sudoku, examine neighboring shared cells.
• Ask yourself with each entry: In which sub-Sudoku is this number certain, and does it also affect another sub-Sudoku?
• View overlaps not just as difficulty but as additional hints.

Sohei Sudoku extends the classic Sudoku without changing the fundamental logic. Each number still follows the well-known Sudoku rules. The challenge lies in properly linking multiple sub-Sudokus. Those who diligently use shared cells can logically solve even complex Multidoku forms step by step.