Samurai Sudoku – Hard

Solving Samurai Sudoku: Rules, Overlaps, and Strategies

Samurai Sudoku is a multi-puzzle consisting of 5 classic 9×9 Sudoku grids. Four corner Sudokus and one central Sudoku form the well-known 21×21 arrangement of five 9×9 grids.

The visible figure comprises a total of 369 active cells within a frame of 21 rows and 21 columns. Each corner grid shares exactly one 3×3 block with the central Sudoku. These four blocks are the only transitions between the five partial puzzles.

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

Rules

• Exactly one number from 1 to 9 must be placed in each active cell.
• Each contained 9×9 Sudoku complies with the standard row, column, and 3×3 block rules.
• Overlapping cells belong to all the sub-grids that meet there.
• Pre-given numbers are not changed.
• Areas without grid cells are not part of the puzzle and are not filled in.
• The puzzle is solved only 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 columns from left to right. Row 4, Column 7 refers to the cell at the intersection of these two total lines.

These total coordinates do not yet specify which Sudoku units apply. You must always check in which 9×9 sub-grid the cell is located. An overlapping cell can therefore belong to multiple relevant rows, columns, and blocks.

Basic idea when solving

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

If progress stalls, overlaps are not obstacles but additional information. A candidate remains allowed only if it fits all affected rows, columns, and 3×3 blocks.

1. Recognize the sub-grids and their overlaps

Begin not with individual numbers but with the shape. The blue border shows the top-left sub-grid. The yellow area is used together with the center sub-grid.

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

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

2. Close an almost complete unit

In the shown intermediate state, we look at row 12 of the center sub-grid. Only row 12, column 12 is open there.

The eight visible entries contain all numbers from 1 to 9 except 5. Therefore, 5 must be in row 12, column 12. The other sub-grids are not needed for this first step.

Such complete houses are the fastest starting point. Check them in each sub-grid separately, since a long visible line can belong to multiple Sudoku rows.

3. Find a single cell candidate

Now consider row 1, column 13. 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, 5, 7, 8, and 9 are already visible in at least one related unit. They are therefore eliminated. The only candidate left is 6; it can be safely entered.

Blue cells show matching exclusion points. You don't need to mark them in your own solving; it’s crucial 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 total rows 4 to 6 and total columns 1 to 3, looking specifically for the number 4. Several cells in this unit are still empty.

The 4 appears in the notes only in row 4, column 2. The cell also has 2 as a candidate, but within this unit, 4 has no other place.

Thus, 4 belongs to row 4, column 2. The other open cells here note: row 5, column 2: 1; row 6, column 2: 2 and 7; row 6, column 3: 7.

5. Cut candidates in the overlap cell

Row 7, column 15 belongs to multiple sub-grids. Therefore, it is not enough to transfer its candidates from just one direction.

The individual checks show candidates 4 and 8 for the top-right sub-grid; candidates 4, 6, and 8 for the center sub-grid. Only the common intersection 4 and 8 satisfy all involved rows, columns, and blocks at once.

This smaller candidate list is already a significant progress, even if no value is set yet. Always update shared cells as soon as something changes in any involved sub-grid.

6. Solve a shared cell with certainty

Next comes the typical multi-puzzle step. Row 7, column 15 is also in the top-right and center sub-grids.

We check row 7 of the center sub-grid; here, 4 can only be at this position. Therefore, 4 is entered. The conclusion is found in one sub-grid; since it’s the same shared cell, the entry applies to all involved grids.

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

7. Track the effect into the neighboring grid

The 4 is now visible in row 7, column 15. Next, consider row 1, column 15. This cell is in the same unit of the adjacent sub-grid with the new entry.

Before the entry, both 4 and 7 were possible there. Now, 4 is eliminated. Only 7 remains; thus, row 1, column 15 is also solved.

This exact sequence makes multi-puzzles easier to solve: first a certain step, then immediate verification in the connected grid. This creates a chain without guessing.

8. Deduce from a block to a row or column

Consider the 3×3 block of the top-left sub-grid within total rows 1 to 3 and total columns 7 to 9. The 3 can only be in row 1, column 8 or row 3, column 8.

All these options lie in the same overall column 8. Therefore, 3 must appear within this block on this line.

Outside the block, the 3 can be eliminated from the same line of that sub-grid, here row 4, column 8. The red notes precisely show these exclusions.

9. Evaluate a naked pair

Consider row 4 of the top-left sub-grid. There, row 4, column 5 and row 4, column 8 have exactly the same two candidates, 3 and 8.

These two numbers must share the two blue cells below. Therefore, 3 and 8 cannot be in any other cell of this unit.

In row 4, column 6, the red notes are removed. A pair does not yet set either number but can prepare new single candidates in the same unit.

Typical solving sequence

1. Mentally mark the borders 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 immediately determined.
4. Check shared cells from all affected 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 cycle until all sub-grids are complete.

Common mistakes

• Treat the entire visible line as one Sudoku row. Valid are always the nine cells of a specific sub-grid.
• Check a shared cell only in the sub-grid where it was discovered.
• Erroneously see areas outside the drawn figure as fillable cells.
• Force a sub-grid in isolation. Some puzzles only become clear through overlap information.
• Work on a secure overlap entry without updating candidates in the connected sub-grid.
• Guess when uncertain, even though switching to another sub-grid can give new clues.

Tips for beginners

• Work with differently colored edge markings for sub-grids if the shape initially appears confusing.
• Start where many clues are present, then follow the shared cells.
• Only jot down candidates valid in all units of a cell.
• After each entry, first check row, column, and block, then the overlap.
• If a region gets stuck, deliberately switch to another sub-grid instead of guessing.

Conclusion

Samurai Sudoku requires no new calculation rules. The real challenge is to apply the familiar Sudoku logic carefully to multiple overlapping 9×9 grids. By consciously tracking borders and shared cells, you turn the large figure into a sequence of small, verifiable steps.