Cross Sudoku – Hard

Solving Cross Sudoku: Rules, Overlaps, and Strategies

Cross Sudoku is a multi-doku consisting of 5 classic 9×9 Sudoku puzzles. Five 9×9 Sudokus form a cross: a central sub-grid and one additional sub-grid at the top, bottom, left, and right.

The entire visible figure includes 297 active cells within 21 rows and 21 columns. The central Sudoku is the hub. Its four edge areas are shared with the neighboring arms.

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

Rules

• Exactly one number from 1 to 9 occupies each active cell.
• Each contained 9×9 Sudoku individually meets the normal row, column, and 3×3 block rules.
• Overlapping cells belong to all intersecting sub-grids simultaneously.
• Given numbers are not changed.
• Cells outside the grid cells are not part of the puzzle and are not filled in.
• The puzzle is only solved when each sub-grid is complete and contradiction-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 grid lines.

These total coordinates do not specify which Sudoku units apply. Further, it must be checked which 9×9 sub-grid the cell belongs to. An overlap cell can thus belong to multiple relevant rows, columns, and blocks.

Basic idea in solving

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

If progress stalls, overlaps are not a hindrance but additional information. A candidate is only allowed if it fits all relevant rows, columns, and 3×3 blocks.

1. Recognize sub-grids and their overlaps

Start not with individual numbers but with the shape. The blue outline shows the top sub-grid. The yellow area also shares the center sub-grid with it.

The shared area is in overall rows 7 to 9 and columns 7 to 15. Each of its 27 cells has only one value but belongs to both sub-grid units.

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

2. Close an almost complete unit

In the shown intermediate state, consider row 12 of the left sub-grid. Only row 12, column 4 is open there.

The eight visible entries contain all numbers from 1 to 9 except 9. Therefore, 9 must be in row 12, column 4. The other sub-grids are not needed for this first step.

Such complete houses are the fastest start. Check them separately in each sub-grid because a long visible line can belong to multiple different Sudoku rows.

3. Find a single cell candidate

Now look at row 2, 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, 5, 6, 7, 8, and 9 are already visible in at least one associated unit. They are eliminated as options. The only candidate left is 4; it can be safely placed.

Blue cells show matching exclusion clues. During your solving, you do not need to mark them: 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 sub-grid in overall rows 1 to 3 and columns 13 to 15, focusing on the number 9. Several cells of this unit are still empty.

The 9 only appears in the notes for row 1, column 15. Although 1 is also a candidate for this cell, within the considered unit, 9 has no other place.

Thus, the 9 belongs to row 1, column 15. The other empty cells here have notes: row 2, column 13: 4; row 3, column 13: 8; row 3, column 15: 1 and 8.

5. Cut candidates in the overlap cell

Row 7, column 7 belongs to multiple sub-grids. Therefore, it’s not enough to take its candidates from just one direction.

The individual tests yield candidates 1 and 4 for the top sub-grid, and 4 and 6 for the left sub-grid. Only the common intersection 4 satisfies all row, column, and block conditions simultaneously.

The intersection contains only 4. So, row 7, column 7 is already solved. Always update shared cells as soon as something changes in any involved sub-grid.

6. Securely solve a shared cell

This is the typical multi-doku step. Row 8, column 15 belongs to the top, middle, and right sub-grids.

After all eliminations, only the 8 remains for this cell. Place the 8 there. In the end, all involved sub-grids are considered. The final entry impacts all of them equally.

Check not only the unit where you found it but also its wider effect on the other side of the overlap.

7. Track the effect in the neighbor grid

Now, 8 is visible in row 8, column 15. Next, consider row 3, column 15. This cell shares the new entry with a unit of the neighboring sub-grid.

Before the entry, 1 and 8 were possible. Now, 8 is eliminated. Only 1 remains; thus, row 3, column 15 is also solved.

This sequential process is what makes multi-dokus easily solvable: a secure step, followed immediately by a control scan in the connected grid. This creates a chain without guesses.

8. Deduce from block to row or column

We examine the 3×3 block of the bottom sub-grid in overall rows 16 to 18 and columns 7 to 9. There, 1 can only be in row 16, column 8, or row 16, column 9.

All these options lie within the same overall row 16. So, 1 must appear in this line within this block.

Outside the block, 1 can be eliminated from the same sub-grid line, here in row 16, column 15. The red notes show these exact exclusions.

9. Evaluate a naked pair

We look at the 3×3 block of the rightmost sub-grid in overall rows 7 to 9 and columns 16 to 18. There, row 9, column 16, and row 9, column 18 both contain exactly the same two candidates: 1 and 8.

These two numbers must split into the two blue cells below. Therefore, 1 and 8 cannot appear in any other cells of this unit.

In row 8, column 16, the red notes are removed. A pair does not yet place either number but can prepare new singles within the same unit.

Typical solving process

1. Mentally mark the boundaries of all 9×9 sub-grids.
2. Look for almost complete rows, columns, and blocks in each sub-grid.
3. Note candidates whenever a cell is not immediately fixed.
4. Check shared cells from all involved sub-grids.
5. Immediately follow each new overlap entry into neighboring grids.
6. Use hidden singles, block-line interactions, and pairs next.
7. Repeat the cycle until all sub-grids are complete.

Common errors

• Treat the entire visible line as one Sudoku row. Always valid are the nine cells of a specific sub-grid.
• Check a shared cell only in the sub-grid where it was found.
• Erroneously consider empty areas outside the drawn shape as fillable cells.
• Force a sub-grid in isolation. Some puzzles only become clear through overlap information.
• Proceed after a secure overlap entry without renewing candidates in the connected sub-grid.
• Guess despite uncertainty, when switching to another sub-grid can provide new clues.

Tips for beginners

• Work with different colored outlines for sub-grids if the shape initially seems confusing.
• Start where many givens are present, then follow shared cells.
• Only note candidates allowed in all units of the cell.
• Check row, column, block, then overlap after each entry.
• If a region gets stuck, deliberately switch to another sub-grid instead of guessing.

Conclusion

Cross Sudoku does not require new rules. The true challenge is to properly apply the familiar Sudoku logic over multiple overlapping 9×9 grids. Tracking boundaries and shared cells consciously turns the big figure into a sequence of small, verifiable steps.