Sohei Sudoku – Hard

Solving Sohei Sudoku: Rules, Overlaps, and Strategies

Sohei Sudoku is a multi-doku composed of 4 classical 9×9 Sudoku puzzles. Four 9×9 Sudokus are positioned above, left, right, and below each other around an open center.

In total, the visible figure includes 288 active cells within a grid of 21 rows and 21 columns. Adjacent sub-grids overlap each other in a 3×3 block. Each of the four Sudokus thus has two transitions to its neighbors.

The goal remains familiar: in each individual 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 sub-grid references.

Rules

• Exactly one number from 1 to 9 is placed in each active cell.
• Each contained 9×9 Sudoku satisfies the normal rules for rows, columns, and 3×3 blocks.
• Overlapping cells belong to all the sub-grids they meet simultaneously.
• Given numbers are not changed.
• Areas without grid cells do not belong to the puzzle and are not filled in.
• The puzzle is only solved when each sub-grid is complete and conflict-free.

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 overall lines.

These overall coordinates do not yet specify which Sudoku units are valid. It must always be checked which 9×9 sub-grid the cell belongs to. An overlap cell can therefore 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 secure entry in a shared cell, switch immediately to the adjacent sub-grid and update the candidates there.

When progress stalls, overlaps are not an obstacle but additional information. A candidate is only allowed there if it fits in all affected rows, columns, and 3×3 blocks.

1. Recognize the sub-grids and their overlaps

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

The shared area lies here in 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 identify the 3×3 blocks. For rows and columns, however, always the complete 9×9 sub-grid counts, not the entire visible width or height.

2. Complete a nearly full unit

In the shown intermediate state, consider the row in overall row 1 of the top sub-grid. Only row 1, column 14 is open there.

The eight visible entries contain all numbers from 1 to 9 except 7. Therefore, 7 must be in row 1, column 14. The other sub-grids are not needed for this first step.

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

3. Find a single cell candidate

Now consider row 1, column 9. The cell is not just the last gap of a single unit; its row, column, and block neighbors must be checked together.

The numbers 1, 2, 3, 4, 6, 7, 8, and 9 are already visible in at least one associated unit. They are therefore eliminated. Only 5 remains as a candidate; it can be confidently entered.

Blue cells indicate matching exclusion witnesses. For your own solving, you don't need to mark them: the crucial point is to eliminate candidates from all units of the cell.

4. Use a hidden single candidate

Next, check the 3×3 block of the top sub-grid in overall rows 4 to 6 and overall columns 13 to 15 specifically for the number 7. Several cells of this unit are still empty.

The 7 appears in the notes only at row 4, column 15. The cell also has 5 as a candidate, but within the considered unit, the 7 has no other place.

Therefore, the 7 belongs to row 4, column 15. The other open cells have notes: row 4, column 13: 5; row 5, column 14: 1; row 6, column 13: 1 and 6.

5. Cut candidates in the overlap field

Row 7, column 15 belongs to several sub-grids. So, its candidates must be taken from all directions, not just one.

The individual checks yield candidates 1, 4, and 5 for the top sub-grid; candidates 1 and 4 for the right sub-grid. Only the common intersection 1 and 4 satisfy all involved row, 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 either of the involved sub-grids.

6. Solve a shared cell confidently

This is a typical multi-doku step. Row 7, column 7 lies within the top and left sub-grids.

After all exclusions, only 5 remains in this cell. It is entered there. To finalize, consider all involved sub-grids. The completed entry affects each of them equally.

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

7. Track the effect into the neighboring grid

The 5 is now visible in row 7, column 7. Next, consider row 1, column 7. This cell is in the same unit of the adjacent sub-grid as the new entry.

Before the entry, both 5 and 8 were possible there. The 5 is now eliminated. Only 8 remains; thus, row 1, column 7 is also solved.

This exact sequence makes multi-doku puzzles quite solvable: a secure step followed immediately by a check in the connected grid. This creates a chain without guesswork.

Typical solving process

1. Mentally mark the boundaries of all 9×9 sub-grids.
2. Look for nearly complete rows, columns, and blocks in each sub-grid.
3. Note candidates as soon as a cell is not determined directly.
4. Check shared cells from the perspective of all involved sub-grids.
5. Immediately follow each new overlap entry into neighboring grids.
6. Subsequently use hidden single candidates, block-line interactions, and pairs.
7. Repeat the process 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 in which it just appeared.
• Erroneously see empty areas outside the drawn figure as fillable cells.
• Isolate a sub-grid. Some puzzles become clear only through information from an overlap.
• Continue working after a secure overlap entry without updating candidates in the connected sub-grid.
• Guess when unsure, although switching to another sub-grid can provide new clues.

Tips for Beginners

• Use different colored edge markings for sub-grids if the shape initially seems confusing.
• Start where many clues are present, then follow the shared cells.
• Write down only candidates allowed in all units of the cell.
• Check rows, columns, and blocks after each entry, then verify the overlap.
• If a region is stuck, consciously switch to another sub-grid instead of guessing.

Conclusion

Sohei Sudoku does not require new rules. The real task is to carefully apply the familiar Sudoku logic to multiple overlapping 9×9 grids. Those who consciously follow boundaries and shared cells turn the large figure into a series of smaller, verifiable steps.