Cross Sudoku – Hard

Cross Sudoku

Cross Sudoku is a multi Sudoku. This means: The puzzle is not made up of a single classic Sudoku, but several interconnected 9x9 Sudokus. Each partial Sudoku follows the normal Sudoku rules: The numbers 1 to 9 must appear exactly once in each row, each column, and each 3x3 block.

Cross Sudoku consists of five classic 9x9 Sudokus in a cross shape. A central Sudoku is touched or overlapped by four other Sudokus at the top, bottom, left, and right.

In Cross Sudoku, the middle Sudoku is the most important hub because progress there can be passed in multiple directions. As with all Sudokus, no calculations are involved. The numbers are symbols that are correctly placed through logical elimination.

Basic rules

• The puzzle consists of several classic 9x9 Sudokus connected into a common figure.
• Exactly one number from 1 to 9 is entered in each active cell.
• Within each individual 9x9 Sudoku, each row must contain the numbers 1 to 9 exactly once.
• Within each individual 9x9 Sudoku, each column must contain the numbers 1 to 9 exactly once.
• Within each individual 9x9 Sudoku, each 3x3 block must contain the numbers 1 to 9 exactly once.
• Shared cells belong to multiple partial Sudokus simultaneously. The entered value must be the same for all involved Sudokus.
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• Empty areas outside the visible grid are not part of the puzzle and are not filled in.
• A multi Sudoku is solved when each contained 9x9 Sudoku is correctly completed and all shared fields match.
• Important: A long visible row is not automatically a Sudoku row. Always focus on the boundaries of the respective 9x9 partial Sudoku.

Solving strategies

The basic techniques correspond to those of the classic Sudoku. The difference is that confirmed entries in one partial Sudoku can influence other Sudokus. Shared cells and overlapping areas are therefore especially important.

1. Checking a single partial Sudoku like a normal Sudoku

Start with a partial Sudoku that already has many numbers filled in. Often, simple confirmed entries can be found there without having to consider the entire multi Sudoku at once.

In the considered 9x9 partial Sudoku, one row reads 43172689. The numbers 1, 2, 3, 4, 6, 7, 8, and 9 are already present. The only missing number is 5. Therefore, the last empty cell in this partial Sudoku row must be a 5.

This conclusion applies not to the entire visible width of the figure, but specifically to these nine cells of this one partial Sudoku row.

2. Hidden single candidate in a 3x3 block

Not every confirmed number results from an almost complete row. Often, a number in a 3x3 block can only occupy a single position. In the following complete Cross Sudoku grid, we examine the top-left 3x3 block of a partial Sudoku to find the number 5.

In the considered partial Sudoku, the 5 in the top-left 3x3 block is checked. In the second and third rows of this partial Sudoku, a 5 is already present, so the 5 cannot be in those two rows within this block. Additionally, the first and second columns of this partial Sudoku already contain a 5 each. This excludes the first two cells of the first row within the block. Only the third cell of the first row remains; it must contain the 5.

This is a hidden single candidate. The cell may not seem obviously necessary at first glance, but for the number 5, only this position remains allowed within the examined block.

3. Using a shared cell as a bridge

Shared cells are the most important special feature of Cross Sudoku. A shared cell belongs to multiple partial Sudokus. When a number is securely determined there, it must be immediately considered in all involved Sudokus.

In the first 9-line of the example, the sequence 276314.89 appears. In this partial Sudoku, only the 5 is missing. The open cell also lies in the neighboring partial Sudoku. As soon as the 5 is entered, it also changes the corresponding line in the neighboring Sudoku.

The first entry thus is not only a local progress but also a hint for the adjacent partial Sudoku, since the same cell also belongs to a row, a column, and a 3x3 block there.

4. Developing a follow-up step from an overlap

In the adjacent partial Sudoku, the relevant 9-line is now 58912346. Only the 7th number is missing, so this cell can also be securely filled.

This example demonstrates the typical multi Sudoku effect: First, a cell in one partial Sudoku is securely solved. Because this cell is shared, it immediately triggers another secure step in the neighboring Sudoku.

5. Checking candidates in overlaps more strictly

A normal Sudoku cell is restricted by a row, a column, and a 3x3 block. A shared cell can additionally belong to other rows, columns, and blocks of other Sudokus. Therefore, a candidate in a shared cell can only remain if it is allowed in all involved Sudokus.

Practically, this means: Do not check a shared cell only from the perspective of the partial Sudoku you are working on. Deliberately switch to the other Sudoku and verify its row, column, and block as well. This often helps identify shared cells earlier as cells at the outer edge.

6. Carefully tracking the boundaries of partial Sudokus

Cross Sudoku looks like a large connected puzzle. Still, the logic originates from the individual 9x9 Sudokus. A visible row may contain parts of several different partial Sudoku rows. Therefore, always clearly specify which 9x9 Sudoku is currently being considered.

Typical solving process

1. First, get an overview of the layout: a cross-shaped arrangement of five 9x9 Sudokus.
2. Select a partial Sudoku with many givens and look for secure classic Sudoku steps there.
3. Check nearly complete rows, columns, and 3x3 blocks.
4. Look for hidden single candidates: numbers that can only appear in one position within a region.
5. Mentally mark shared cells and overlapping areas.
6. Immediately transfer any confirmed entry in a shared cell to all involved Sudokus.
7. Then check whether new candidates or exclusions arise in the neighboring Sudokus.
8. Regularly switch between the Sudokus instead of solving one area in isolation.
9. For every entry, verify if it is allowed in all affected rows, columns, and 3x3 blocks.
10. Finish the puzzle only when every individual 9x9 Sudoku is complete and contradiction-free.

Common errors

• Treating the whole figure as a single large Sudoku. The rules only apply within each individual 9x9 Sudoku.
• Updating shared cells only in one partial Sudoku. Shared cells affect all Sudokus they belong to.
• Incorrectly following boundaries. Not every visible row is part of the same Sudoku row in displaced grids.
• Interpreting empty areas as cells. Areas without grid lines are not filled.
• Rushing into guesses too early. A wrong entry can damage multiple Sudokus simultaneously.
• Not strictly checking candidates in overlaps. A candidate must be allowed in all involved rows, columns, and blocks.
• Not reviewing a secure entry further. Shared cells often produce immediate new exclusions.

Tips for beginners

• Start with a single partial Sudoku and only solve secure steps there.
• Early on, identify shared areas. They often create the most important connections.
• Strictly adhere to the 9x9 boundaries of each Sudoku.
• Always check all involved Sudokus for shared cells, not just the area you are working on.
• Use candidate notes as soon as multiple Sudokus are in play.
• Change perspective: If progress stalls in one Sudoku, review the neighboring shared cells.
• Ask yourself at each entry: In which Sudoku is this number certain, and does it also affect another Sudoku?
• View overlaps not only as difficulties but also as additional hints.

Cross Sudoku extends the classic Sudoku without changing the fundamental logic. Each number still follows the known Sudoku rules. The challenge is to neatly connect multiple partial Sudokus. By consistently using shared cells, even complex multi Sudoku puzzles can be logically solved step-by-step.