- Sandwich Sudoku: clue numbers outside the grid show the sum of digits between 1 and 9 in that row/column
- Miracle Sudoku: adds two new constraints — cells a knight's move or king's move apart cannot share a digit
- Both variants can be solved with very few given digits (Miracle sometimes needs only 2)
- Start by exploiting the variant constraints before applying standard Sudoku logic
- These variants are designed to feel impossible until one key deduction unlocks the whole grid
Sandwich Sudoku
In Sandwich Sudoku, the standard 9×9 rules apply, plus additional clue numbers are placed outside the grid. Each clue shows the sum of all digits that appear between the digits 1 and 9 in that row or column.
Example: If a row reads _ 3 5 1 _ 7 4 _ 9, the digits between 1 (position 4) and 9 (position 9) are 7 and 4, so the sandwich sum is 11. A clue of 0 means 1 and 9 are adjacent with nothing between them.
Key deductions: a sandwich sum of 0 means 1 and 9 are neighbors. A sum of 35 means all digits 2–8 are between 1 and 9, so 1 and 9 are at the ends. Every sandwich sum constrains the positions of 1 and 9 relative to each other.
Miracle Sudoku
Miracle Sudoku uses the standard 9×9 rules plus three additional constraints:
- Non-consecutive: No two cells that are orthogonally adjacent (sharing an edge) can contain consecutive digits (e.g., 4 and 5 cannot be neighbors)
- Knight's move: Any two cells a chess knight's move apart cannot contain the same digit
- King's move: Any two cells a chess king's move apart (diagonally adjacent) cannot contain the same digit
These three extra constraints are so powerful that a valid Miracle Sudoku puzzle typically requires only 2–4 given digits to have a unique solution.
Solving Strategy for Miracle
Miracle Sudoku solving is almost entirely driven by the variant constraints rather than standard Sudoku logic. Start by tracing the knight's-move eliminations for any given digit across the entire grid. The non-consecutive constraint is extremely powerful — in a valid arrangement, digits 1, 5, and 9 must be separated by significant spacing from their neighbors.
For both variants, the key insight is: master the variant constraint first, use it aggressively, and standard Sudoku logic cleans up the remaining cells. Explore more specialty variants in the variants section of the site.