Twodoku – Medium

Twodoku

Twodoku is a MultiDoku. This means: The puzzle does not consist of a single classic Sudoku, but of several interconnected 9x9 Sudokus. Each sub-Sudoku follows the normal Sudoku rules: The numbers 1 to 9 must appear exactly once in each row, each column, and each 3x3 block.

Twodoku connects two classic 9x9 Sudokus. One Sudoku is located in the top-left, the second offset downward and to the right. Both grids share a common area. This results in some cells being used by both sub-Sudokus simultaneously.

Twodoku is a good introduction to MultiDoku because only two sub-Sudokus need to be coordinated. Like all Sudokus, no arithmetic is involved. The numbers are symbols correctly placed through logical elimination.

Basic Rules

• The puzzle consists of several classic 9x9 Sudokus connected to form a common figure.
• Exactly one number from 1 to 9 is entered into 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 individual 9x9 Sudoku, each 3x3 block must contain the numbers 1 to 9 exactly once.
• Shared cells belong to multiple sub-Sudokus at once. The value entered there must be the same in all involved sub-Sudokus.
• Given numbers cannot 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 completed and all shared cells match.
• Important: A long visible row is not automatically a Sudoku row. The boundaries of each 9x9 sub-Sudoku always determine the relevant segment.

Strategies for Solving

The basic techniques correspond to those of classic Sudoku. The difference is that safe entries in one sub-Sudoku can influence others. Shared cells and overlapping areas are especially important.

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

Start with a sub-Sudoku that already has many numbers filled in. Often, simple safe entries can be found there without considering the entire MultiDoku form 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 specifically to the nine cells of this one sub-Sudoku row, not to the entire visible width of the figure.

2. Hidden single candidate in a 3x3 block

Not every safe number arises from a nearly complete row. Often, a number can only logically fit in one remaining position within a 3x3 block. In the following complete Twodoku grid, we look at the top-left 3x3 block of a sub-Sudoku and search for the number 5.

In the examined sub-Sudoku, the 5 in the top-left 3x3 block is checked. In the second and third rows of this sub-Sudoku, there is already a 5 in each, so the 5 cannot be in those two rows of the block. Additionally, the first and second columns of this sub-Sudoku already contain a 5 each. This excludes the first two cells of the first row in the block. The only remaining cell is the third cell in the first row, which must contain the 5.

This is a hidden single candidate. It may not be immediately obvious, but for the number 5, there is only this one allowed position within the examined block.

3. Use a shared cell as a bridge

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

In the first 9-cell row of the example, the sequence 276314.89 appears. Within this sub-Sudoku, only the 5 is missing. The open cell also lies in the adjacent sub-Sudoku. Once the 5 is entered, it also affects that 9-cell row.

The first entry is not just a local advance; it is also a hint for the neighboring sub-Sudoku because the same cell there is part of a row, a column, and a 3x3 block.

4. Derive a next step from an overlapping area

In the adjacent sub-Sudoku, the relevant 9-cell row is 58912346. Only the 7th cell in that row is missing, so it can also be safely filled.

This example demonstrates the typical MultiDoku effect: first, a cell in one sub-Sudoku is safely solved. Since this cell is shared, it immediately leads to another safe step in the neighboring sub-Sudoku.

5. Strictly check candidates in overlaps

A normal Sudoku cell is restricted by a row, a column, and a 3x3 block. A shared cell can additionally belong to other rows, columns, and blocks of different sub-Sudokus. Therefore, a candidate must be permissible in all involved sub-Sudokus to remain a viable option.

Practically, this means: do not only check a shared cell from the perspective of the sub-Sudoku you are currently working on. Deliberately switch to the other sub-Sudoku and verify its row, column, and block as well. This often makes shared cells easier to identify as boundary or core cells early on.

6. Continually track the boundaries of sub-Sudokus

Twodoku appears like a large connected puzzle. Still, its logic is derived from the individual 9x9 Sudokus. A visible row can include parts of different sub-Sudoku rows. Always clearly identify which 9x9 Sudoku is currently being considered during solving.

Typical solving sequence

1. Get an overview of the arrangement: an upper-left and a lower-right 9x9 Sudoku with a shared overlap.
2. Select a sub-Sudoku with many clues and look for safe classic Sudoku steps.
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 safe entry in a shared cell across all involved sub-Sudokus.
7. Afterward, check if new candidates or eliminations emerge in the neighboring sub-Sudoku.
8. Regularly switch between sub-Sudokus instead of solving a region in isolation.
9. At each entry, verify it is allowed in all affected rows, columns, and 3x3 blocks.
10. Stop only when all individual 9x9 Sudokus are fully and consistently solved.

Common mistakes

• Treat the entire figure as one big Sudoku. However, rules apply within each 9x9 Sudoku.
• Update shared cells only in one sub-Sudoku. They always belong to all relevant Sudokus.
• Misjudge boundaries. In offset grids, not every visible row is part of the same Sudoku row.
• Interpret empty areas without grids as cells. Areas without grids are not filled.
• Rely on guesswork too early. Incorrect entries can damage multiple sub-Sudokus simultaneously.
• Fail to rigorously check candidates in overlaps. A candidate must be valid in all involved rows, columns, and blocks.
• Proceed with a safe entry without further verification, as shared cells often produce immediate new eliminations.

Tips for beginners

• Start with one sub-Sudoku and solve only safe steps there.
• Early identify shared areas; they often form the key connections.
• Strictly respect the 9x9 boundaries of individual Sudokus.
• Always verify shared cells in all involved sub-Sudokus, not only the current one.
• Use candidate notes once multiple sub-Sudokus are in play.
• Change perspective: if one sub-Sudoku stalls, check the neighboring shared cells.
• Ask yourself with each entry: in which sub-Sudoku is this number safe, and does it influence another?
• View overlaps not just as difficulty but as additional clues.

Twodoku extends the classic Sudoku without changing its core logic. Each number still follows the known Sudoku rules. The challenge is to connect multiple sub-Sudokus cleanly. Those who use shared cells consistently can solve complex MultiDoku forms step by step through logical deduction.