Twodoku – Easy

Solve Twodoku: Rules, Overlaps, and Strategies

Twodoku is a multi-Sudoku consisting of 2 classic 9×9 Sudoku grids. Two 9×9 Sudoku grids are placed diagonally offset and share a common 3×3 block.

This double form is also called Gattai-2.

The visible figure comprises 153 active cells within 15 rows and 15 columns. The overlapping block is the only direct connection: what is solved there is immediately an entry in both sub-grids.

The goal remains familiar: In each 9×9 sub-grid, the numbers 1 to 9 must appear exactly once in each row, each column, and each 3×3 block. A shared cell has the same entry in all corresponding sub-grids.

Rules

• Each active cell contains exactly one number from 1 to 9.
• Each contained 9×9 Sudoku satisfies the normal row, column, and 3×3 block rules individually.
• Overlapping cells belong to all intersecting sub-grids simultaneously.
• Given numbers are not altered.
• Areas without grid cells do not belong to the puzzle and are not to be filled.
• The puzzle is only solved when each sub-grid is complete and free of contradictions.

Orientation in the Diagram

For the examples, we count the rows of the entire diagram from top to bottom and the columns from left to right. Row 4, Column 7 refers to the cell at the intersection of these two main lines.

These overall coordinates do not yet specify which Sudoku units are valid. It is always necessary to check which 9×9 sub-grid the cell belongs to. An overlapping cell can thus have multiple relevant rows, columns, and blocks.

Basic Idea for Solving

Start with the known Sudoku techniques: complete houses, individual cell candidates, and hidden single candidates. After each safe entry in a shared cell, move to the adjacent sub-grid and immediately update candidates there.

If progress stalls, overlaps are not an obstacle but additional information. A candidate is only allowed if it fits in every affected row, column, and each affected 3×3 block.

1. Recognize Sub-Grids and Their Overlap

Do not start with individual numbers, but with the shape. The blue frame shows the sub-grid at the top left. The yellow area is also used with the sub-grid at the bottom right.

The shared area here is in the overall rows 7 to 9 and overall columns 7 to 9. Each of its 9 cells has only one value but belongs to the units of both sub-grids.

The thick lines help recognize the 3×3 blocks. For rows and columns, however, always consider the complete 9×9 sub-grid, not the entire visible width or height.

2. Complete a Nearly Full Unit

In the shown interim state, we consider row 8 of the top-left sub-grid. Only row 8, column 2 is open.

The eight visible entries include all numbers from 1 to 9 except 1. Therefore, the 1 must be in row 8, column 2. The other sub-grids are not needed for this first step.

Such full houses are the fastest entry. Check them in each sub-grid separately, as a long visible line might belong to several different Sudoku rows.

3. Find a Single Cell Candidate

Now consider row 1, column 5. The cell is not just the last gap of a unit; its row, column, and block neighbors must be checked together.

The numbers 1, 3, 4, 5, 6, 7, 8, and 9 are already visible in at least one related unit. They are excluded. The only candidate remaining is 2, which can be safely entered.

Blue cells show matching exclusion proofs. You do not need to mark them during your own solving: The key is to eliminate candidates from all units of the cell.

4. Use a Hidden Single Candidate

Next, we examine the 3×3 block of the top-left sub-grid within overall rows 1 to 3 and columns 4 to 6 for the number 3. Several cells in this unit are still empty.

The 3 appears in the displayed notes only at row 3, column 5. The cell has 5 as a candidate, but within the considered unit, the 3 has no other place.

Therefore, the 3 belongs to row 3, column 5. The other open cells have notes: row 1, column 5: 2; row 1, column 6: 6; row 2, column 6: 5.

5. Cut Candidates in the Overlap Cell

Row 9, column 8 belongs to multiple sub-grids. It is not enough to take its candidates from only one direction.

The individual tests yield candidates 1, 3, and 5 for the top-left sub-grid; 1 and 5 for the bottom-right sub-grid. Only the common intersection 1 and 5 satisfy all line, column, and block conditions simultaneously.

This smaller candidate list is already a real progress, even if no value is set yet. Always update shared cells as soon as something changes in one of the involved sub-grids.

6. Solve a Shared Cell Safely

Now comes the typical multi-Sudoku step. Row 7, column 7 lies in the top-left and bottom-right sub-grids at the same time.

After eliminating all options, only 5 remains in this cell. Therefore, 5 is entered there. For the final entry, all involved sub-grids are considered. The completed value affects all of them equally.

After such an entry, do not only check the unit where you found it. Its greatest impact often lies on the other side of the overlap.

7. Track the Effect in the Neighboring Grid

The 5 is now visible in row 7, column 7. Next, consider row 5, column 7. This cell shares a unit with the new entry in the adjacent sub-grid.

Before the entry, 4 and 5 were possible there. The 5 is now excluded. Only 4 remains; thus row 5, column 7 is solved.

This sequence is what makes multi-Sudoku solving effective: a safe step followed immediately by a control scan in the connected grid. A chain is formed without guessing.

8. Deduce From Block to Row or Column

We examine the 3×3 block of the bottom-right sub-grid in overall rows 10 to 12 and columns 7 to 9. There, the 6 can only be in row 10, column 8, or row 10, column 9.

All these options lie in the same overall row 10. The 6 must appear in this line within this block.

Outside the block, the 6 can be eliminated from the same sub-grid line, here in row 10, column 12. The red notes show these exclusions exactly.

9. Analyze a Naked Pair

We examine the 3×3 block in the bottom-right sub-grid within overall rows 7 to 9 and columns 10 to 12. There, row 7, column 11 and row 9, column 11 share exactly the same pair of candidates 5 and 6.

These two numbers must split the two blue cells below. Therefore, 5 and 6 cannot appear in any other cells of this unit.

In row 7, column 10 and row 9, column 10, the red notes are removed. A pair does not set either number yet but can prepare new single candidates within the same unit.

Typical Solution Workflow

1. Mentally mark the boundaries of all 9×9 sub-grids.
2. Look in each sub-grid for nearly full rows, columns, and blocks.
3. Note candidates as soon as a cell is not directly determined.
4. Check shared cells from all involved sub-grids' perspectives.
5. Immediately follow any new overlap entry into neighboring grids.
6. Next, use hidden single candidates, block-line interactions, and pairs.
7. Repeat until all sub-grids are complete.

Common Mistakes

• Treat the entire visible line as a single Sudoku row. Always valid are only the nine cells of a specific sub-grid.
• Check a shared cell only in the sub-grid where it was just found.
• Erroneously consider empty areas outside the drawn figure as fillable cells.
• Enforce a sub-grid in isolation. Some puzzles are only solvable with info from an overlap.
• Continue after a safe overlap entry without renewing candidates in the connected sub-grid.
• Guess when unsure, even though switching to another sub-grid can provide new hints.

Tips for Beginners

• Use different color border markings for sub-grids if the shape initially seems confusing.
• Start where many clues are given, then follow shared cells.
• Write only candidates allowed in all units of a cell.
• After each entry, first check row, column, and block, then the overlap.
• If a region stalls, deliberately switch to another sub-grid instead of guessing.

Conclusion

Twodoku does not require new calculation rules. The real challenge is to carefully apply familiar Sudoku logic to several overlapping 9×9 grids. By consciously tracking boundaries and shared cells, you turn the large figure into a sequence of small, verifiable steps.