Gattai-3 – Medium

Solving Gattai-3: Rules, Overlaps, and Strategies

Gattai-3 is a multi-sudoku consisting of 3 classic 9×9 sudokus. Three offset 9×9 sudokus interlock within a 15×15 frame.

Overall, the visible figure comprises 180 active cells within a frame of 15 rows and 15 columns. The three subgrids are not simply aligned in a straight row. Each touches at least one other over a larger common area.

The goal remains familiar: in each 9×9 subgrid, the numbers 1 through 9 must appear exactly once in every row, every column, and each 3×3 block. A shared cell has the same entry in all related subgrid references.

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 independently.
• Overlapping cells belong simultaneously to all the subgrids they connect.
• Given numbers are not altered.
• Areas outside the grid cells are not part of the puzzle and remain unfilled.
• The puzzle is only solved when each subgrid is complete and free of contradiction.

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 overall lines.

These overall coordinates do not specify which sudoku units are valid. It must always be checked which 9×9 subgrid the cell belongs to. An overlapping cell may consequently have multiple relevant rows, columns, and blocks.

Basic Idea in Solving

Start with known sudoku techniques: complete houses, individual cell candidates, and hidden single candidates. After each secure entry in a shared cell, move immediately to the adjacent subgrid and update candidates there.

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

1. Recognize the Subgrids and Their Overlaps

Begin not with individual numbers, but with the shape. The blue frame shows the subgrid above. The yellow area is used together with the right subgrid.

The shared area lies here in overall rows 4 to 9 and overall columns 7 to 12. Each of its 36 cells has only one value, but belongs to the units of both subgrids.

The thick lines help identify the 3×3 blocks. For rows and columns, the entire 9×9 subgrid always counts, not the full visible width or height.

2. Complete One Unit

In the displayed intermediate state, we look at row in overall row 13 of the bottom-left subgrid. Only row 13, column 7 is open there.

The eight visible entries contain all numbers from 1 to 9 except 1. Therefore, 1 must be in row 13, column 7. The other subgrids are not needed for this first step.

Such complete houses are the fastest entry points. Check them in each subgrid separately, as a long visible line can belong to several different sudoku rows.

3. Find a Single Cell Candidate

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

Blue fields show matching exclusion clues. When solving on your own, you need not mark them: it is crucial to eliminate candidates from all units of the cell.

4. Use a Hidden Single Candidate

Next, we check the 3×3 block of the top-left subgrid within overall rows 4 to 6 and columns 7 to 9 for the number 9. Several cells in this unit are still empty.

The 9 appears in the displayed notes only in row 4, column 9. The cell also has 2 as a candidate, but within this unit, 9 has no other place.

Therefore, 9 belongs to row 4, column 9. The other open cells have notes: row 5, column 8: 7; row 6, column 7: 4; row 6, column 9: 2.

5. Candidates in the Overlap Field are Cut

Row 5, column 11 belongs to multiple subgrids. It’s not enough to take its candidates from only one direction.

Individual tests yield candidates 2, 4, 5, and 7 for the top subgrid; candidates 4 and 7 for the right subgrid. Only the common intersection 4 and 7 fulfill all involved row, column, and block conditions simultaneously.

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

6. Solve a Shared Cell Securely

Next is the typical multi-sudoku step. Row 6, column 9 lies in both the top and right subgrids.

After exclusions, only 2 remains. Enter 2 there. For the final step, consider all involved subgrids. The completed entry also affects each of them.

After such an entry, don’t just 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

Now, 2 is visible in row 6, column 9. Next, look at row 4, column 9. This cell shares an area with the new entry in an adjacent subgrid.

Before the entry, 2 and 9 were possible there. Now, 2 is excluded. Only 9 remains; thus, row 4, column 9 is resolved.

This sequence exemplifies why multi-sudokus are solvable: a secure step followed immediately by a control scan in the connected grid. It creates a chain without guesswork.

8. Deduce from the Block to a Row or Column

Consider the 3×3 block of the right subgrid within overall rows 7 to 9 and columns 10 to 12. There, 2 can only be in row 7, column 10 or row 7, column 11.

All these options are within the same overall row 7. So, 2 must appear within this block on that line.

Outside the block, 2 can be eliminated from the same subgrid line, here at row 7, column 14. The highlighted notes show these exact exclusions.

9. Analyze a Naked Pair

We look at the column in overall column 11 of the top subgrid. Cells in row 5, column 11 and row 9, column 11 both have the same two candidates 4 and 7.

These two numbers must split the two blue cells below. Therefore, 4 and 7 cannot appear in any other cell of this unit.

Notes marked in red at row 4, column 11 are removed. A pair does not assign either number yet but can prepare new single candidates in the same unit.

Typical Solution Sequence

1. Mentally mark the borders of all 9×9 subgrids.
2. Search in each subgrid for nearly complete rows, columns, and blocks.
3. Record candidates when a cell is not directly confirmed.
4. Check shared cells from all involved subgrids perspectives.
5. Follow each new overlap entry immediately into neighboring grids.
6. Then utilize hidden single candidates, block-line interactions, and pairs.
7. Repeat until all subgrids are complete.

Common Mistakes

• Treat the entire visible line as a sudoku row. Always valid are only the nine cells of a specific subgrid.
• Check a shared cell only within the subgrid where it first appeared.
• Accidentally regard empty areas outside the drawn figure as fillable cells.
• Isolate a subgrid claim. Some puzzles are only clear through overlap information.
• Work on a secure overlap entry without updating candidates in the connected subgrid.
• Guess when unsure, although switching to another subgrid may provide clues.

Tips for Beginners

• Use different colored border markers if the shape initially seems confusing.
• Start where many clues are present, then follow shared fields.
• Only note candidates allowed in all units of the cell.
• Check rows, columns, and blocks first after each entry, then the overlap.
• If stuck, intentionally switch to another subgrid instead of guesswork.

Conclusion

Gattai-3 does not require new calculation rules. The real challenge is to carefully apply familiar sudoku logic to multiple overlapping 9×9 grids. By consciously tracking boundaries and shared cells, you turn the large figure into a sequence of smaller, verifiable steps.