Butterfly Sudoku – Hard

Butterfly Sudoku

Butterfly Sudoku is a multi Sudoku. This means the puzzle isn't just a single classic Sudoku, but several interconnected 9x9 Sudokus. Each sub-Sudoku follows the normal Sudoku rules: each row, each column, and each 3x3 block must contain the numbers 1 to 9 exactly once.

Butterfly Sudoku arranges four classic 9x9 Sudokus in a compact, butterfly-shaped pattern. The four sub-Sudokus are offset within a 12x12 overall grid and overlap significantly.

The central overlap is the key driver of the puzzle: a single secure entry can simplify multiple sub-Sudokus simultaneously. Like all Sudokus, no calculations are involved. The numbers are symbols placed correctly through logical elimination.

Basic Rules

• The puzzle consists of multiple classic 9x9 Sudokus connected into a common figure.
• Exactly one number from 1 to 9 is entered into 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 sub-Sudokus at once. The value entered there must be the same for all involved sub-Sudokus.
• Given numbers cannot be changed.
• A multi Sudoku is solved when each contained 9x9 Sudoku is correctly solved and all shared cells match.
• Important: A long visible row is not automatically a Sudoku row. The boundaries of each 9x9 sub-Sudoku are what matter.

Solving Strategies

The basic techniques match those of classic Sudoku. The difference is that secure entries in one sub-Sudoku can influence others. Shared cells and overlapping areas are especially important.

1. Check a single sub-Sudoku like a normal Sudoku

Start with a sub-Sudoku that already has many clues. Simple secure entries can often be found there without looking at the entire multi Sudoku layout at once.

In the considered 9x9 sub-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 open cell in this sub-Sudoku row must be a 5.

This conclusion applies only to the nine cells of this particular sub-Sudoku row, not the entire visible width of the figure.

2. Hidden single candidate in a 3x3 block

Not every secure number appears via an almost complete row. Often, a number can only be placed in a single spot in a 3x3 block. In the full butterfly Sudoku grid below, we examine the top-left 3x3 block of a sub-Sudoku searching for the number 5.

In the sub-Sudoku, the 5 is checked within the top-left 3x3 block. The second and third rows of this sub-Sudoku already contain a 5, so it cannot be in these rows. Additionally, the first and second columns of this sub-Sudoku already contain a 5. This excludes the first two cells of the first row in the block. The only remaining cell in the first row of the block is the third cell, which must contain the 5.

This is a hidden single candidate. The cell might not seem obviously forced at first glance, but for the number 5, this is the only possible position within this block.

3. Use a shared cell as a bridge

Shared cells are the most important feature of Butterfly Sudoku. They belong to multiple sub-Sudokus. When a number in a shared cell is securely determined, it must be reflected immediately in all involved sub-Sudokus.

In the leftmost 9 cells of the example, the sequence 123456.78 is present. Only the 9 is missing within this sub-Sudoku. The open cell is also part of an adjacent sub-Sudoku. Once the 9 is entered here, it also affects the 9 in the neighboring sub-Sudoku's row.

The first entry isn’t just a local progress; it’s also an indicator for the adjacent sub-Sudoku because the same cell is part of a row, column, and 3x3 block in that sub-Sudoku as well.

4. Derive a follow-up step from an overlap

In the neighboring sub-Sudoku, the relevant 9-row reads 45697812. Only the 3 is missing. Therefore, this cell can also be securely filled.

This example demonstrates the typical multi Sudoku effect: first, a cell in one sub-Sudoku is solved securely. Because this cell is shared, it immediately leads to a further secure step in the adjacent sub-Sudoku.

5. Carefully check candidates in overlaps

A normal Sudoku cell is limited by a row, a column, and a 3x3 block. A shared cell may belong to multiple rows, columns, and blocks from different sub-Sudokus. Thus, a candidate in a shared cell must be allowed in all involved sub-Sudokus.

Practically, this means: do not check a shared cell only from the perspective of the sub-Sudoku you’re working on. Switch consciously to the other sub-Sudoku and verify the row, column, and block there as well. This often makes shared cells less ambiguous earlier, especially those at the outer edge.

6. Keep track of sub-Sudoku boundaries

Butterfly Sudoku appears as a large interconnected puzzle. Still, the logic derives from the individual 9x9 Sudokus. A visible row might contain several different sub-Sudoku rows. Always explicitly identify which 9x9 sub-Sudoku you are currently considering.

Typical solving sequence

1. Get an overview of the arrangement: four strongly overlapping 9x9 Sudokus in a compact 12x12 shape.
2. Choose a sub-Sudoku with many clues and look for secure classic Sudoku steps there.
3. Check nearly complete rows, columns, and 3x3 blocks.
4. Search 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 each secure entry in a shared cell to all involved sub-Sudokus.
7. Check whether new single candidates or eliminations emerge in adjacent sub-Sudokus afterward.
8. Switch regularly between sub-Sudokus instead of solving one region in isolation.
9. In each entry, verify its validity in all affected rows, columns, and 3x3 blocks.
10. Finish the puzzle only when every individual 9x9 Sudoku is complete and contradiction-free.

Common Mistakes

• Treating the entire figure as a single large Sudoku. The rules apply within each individual 9x9 Sudoku only.
• Updating shared cells in only one sub-Sudoku. A shared cell affects all sub-Sudokus it belongs to.
• Wrongly tracking boundaries. In offset grids, not every visible row is part of the same Sudoku row.
• Guessing too early. An incorrect entry can damage multiple sub-Sudokus simultaneously.
• Not checking candidates in overlaps thoroughly enough. A candidate must be permitted in all involved rows, columns, and blocks.
• Not continuing after a secure entry. Shared cells often create new eliminations immediately.

Tips for Beginners

• Start with one sub-Sudoku and solve only secure steps there.
• Early on, look for the shared areas. They often contain the most important connections.
• Strictly adhere to the 9x9 boundaries of each Sudoku.
• Always verify shared cells with all involved sub-Sudokus, not just the one you're working on.
• Use candidate notes as soon as multiple sub-Sudokus are in play.
• Shift perspective: if stuck in one sub-Sudoku, check the neighboring shared cells.
• Ask yourself with each entry: in which sub-Sudoku is this number secure, and does it also influence another sub-Sudoku?
• View overlaps not just as challenges but as additional clues.

Butterfly Sudoku extends classic Sudoku without changing its core logic. Each number still follows the known Sudoku rules. The challenge lies in neatly linking multiple sub-Sudokus. Those who use shared cells consistently can approach complex multi Sudoku patterns step-by-step logically.