Tripledoku – Easy

Tripledoku

Tripledoku is a Multidoku. This means: The puzzle isn't just a single classic Sudoku, but several interconnected 9x9 Sudokus. Each sub-Sudoku follows the normal Sudoku rules: in each row, column, and 3x3 block, the numbers 1 to 9 must appear exactly once.

Tripledoku consists of three classic 9x9 Sudokus that are merged in a stepped or diagonal manner. The top, middle, and bottom sub-Sudoku partially overlap.

In Tripledoku, it is especially important to pass on information along the chain: progress in the upper part can influence the middle Sudoku, which in turn can affect the lower Sudoku. As with all Sudokus, no calculations are made. The numbers are symbols that are correctly placed through logical elimination.

Basic Rules

• The puzzle consists of several classic 9x9 Sudokus connected into 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. The value entered there is 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 in.
• 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 the each 9x9 Sub-Sudoku always determine the relevant segment.

Solving Strategies

The basic techniques are the same as in classic Sudoku. The difference is that secure entries in one sub-Sudoku can influence other sub-Sudokus. Shared cells and overlapping areas are especially important.

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

Start with a sub-Sudoku that already has many numbers filled in. Easy secure entries can often be identified there without considering the entire Multidoku at once.

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

This conclusion is valid only for the nine cells of this specific sub-Sudoku row, not for the entire visible width of the figure.

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 position within a 3x3 block. In the following complete Tripledoku 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 in the top-left 3x3 block is checked. In the second and third rows of this sub-Sudoku, a 5 is already present, so it cannot be in these rows within 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, leaving only the third cell in the first row as the possible position for the 5. That cell must contain the 5.

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

3. Using a shared cell as a bridge

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

In the left 9-row of the example, the sequence 123456.78 is displayed. Within this sub-Sudoku, only the 9 is missing. This open cell also lies in an adjacent sub-Sudoku. Once the 9 is entered, it immediately affects the 9 in that neighboring sub-Sudoku's row.

This first entry is not just a local progress. It also serves as a hint for the adjacent sub-Sudoku, since the same cell is part of a row, a column, and a 3x3 block there as well.

4. A consequence from an overlap

In the adjacent sub-Sudoku, the relevant 9-row is 45697812. Only the 3 is missing, so this cell can also be confidently filled.

This example illustrates the typical Multidoku effect: First, a cell in one sub-Sudoku is securely resolved. As this cell is shared, it immediately results in another secure move in the neighboring sub-Sudoku.

5. Carefully examine candidates in overlaps

A normal Sudoku cell is limited 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 in a shared cell may only remain if it is allowed in all involved sub-Sudokus.

In practice: do not evaluate a shared cell only from the perspective of the sub-Sudoku you're working on. Openly switch to the other sub-Sudoku and check the corresponding row, column, and block there as well. This approach often clarifies shared cells as early as the outer edge cells.

6. Clearly track the borders of sub-Sudokus

Tripledoku looks like a large connected puzzle. Still, the logic arises from the individual 9x9 Sudokus. A visible row can contain multiple different sub-Sudoku rows. Therefore, always clearly specify which 9x9 Sudoku is currently being considered during solving.

Typical solving process

1. Get an overview of the arrangement: three stepped 9x9 Sudokus with shared areas.
2. Select a sub-Sudoku with many givens and look for secure classical Sudoku steps there.
3. Check almost complete rows, columns, and 3x3 blocks.
4. Look for hidden singles: numbers possible in only one position in a region.
5. Mentally mark shared cells and overlapping areas.
6. Immediately transfer each secure entry in a shared cell to all involved sub-Sudokus.
7. After that, check if new candidates or eliminations arise in neighboring sub-Sudokus.
8. Regularly switch between sub-Sudokus rather than solving a region 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 each individual 9x9 Sudoku is fully and consistently solved.

Common mistakes

• Treating the entire figure as one large Sudoku. The rules apply within each individual 9x9 Sudoku.
• Updating shared cells in only one sub-Sudoku. A shared cell applies to all sub-Sudokus it belongs to.
• Falsely tracking the borders. With displaced grids, not every visible row is part of the same Sudoku row.
• Interpreting regions without grid as cells. Areas without grids are not filled in.
• Rushing too early. A wrong entry can damage several sub-Sudokus simultaneously.
• Not strictly checking candidates in overlaps. A candidate must be allowed in all involved rows, columns, and blocks.
• Not continuing after a secure entry. Shared cells often create new eliminations immediately.

Tips for beginners

• Start with a single sub-Sudoku and only use secure steps there.
• Early on, look for shared regions. They often form the main connections.
• Hold strictly to the 9x9 boundaries of individual Sudokus.
• Always check all involved sub-Sudokus for shared cells, not just the region you're working on.
• Use candidate notes once multiple sub-Sudokus are in play.
• Switch perspective: if one sub-Sudoku stalls, check the neighboring shared cells.
• Ask yourself with every entry: In which sub-Sudoku is this number secure, and does it also act in another sub-Sudoku?
• View overlaps not only as a difficulty but also as additional clues.

Tripledoku extends classic Sudoku without changing its fundamental logic. Each number still follows the known Sudoku rules. The challenge is to cleanly connect multiple sub-Sudokus. Those who consistently use shared cells can also solve complex Multidoku shapes step-by-step logically.