Kalkudoku rules and solving steps
Kalkudoku combines a Latin-square grid with arithmetic cages. The board may be smaller than a standard Sudoku grid, but every placement must satisfy both the row-and-column rule and the clue written inside its cage.
What are the rules of Kalkudoku? Fill each row and column with the numbers from 1 to the board size without repeating a number. Cells grouped by a bold cage border must combine to reach the cage target using the shown operation. A 4×4 puzzle uses 1–4, a 5×5 uses 1–5 and a 6×6 uses 1–6.
Understand the grid size
The allowed numbers depend on the board. A 4×4 board uses 1, 2, 3 and 4 once in every row and column. A 6×6 board uses 1 through 6. Unlike classic Sudoku, there are no 3×3 boxes to complete. The arithmetic cages provide the extra constraints.
Read arithmetic cages
| Clue | Meaning | Example on a 4×4 board |
|---|---|---|
| 6+ | The cage values add to 6 | 1 + 2 + 3 |
| 12× | The cage values multiply to 12 | 3 × 4 |
| 2− | The difference between two values is 2 | 4 and 2 |
| 2÷ | One value divided by the other equals 2 | 4 and 2, or 2 and 1 |
| 3 | A single-cell cage contains that exact value | The cell must be 3 |
A reliable solving order
- Fill any single-cell cages first.
- Look for cages that have only one realistic combination for the board size.
- Remove combinations that would repeat a number in the same row or column.
- Recheck completed rows and columns for the one missing value.
- Return to larger cages after nearby placements reduce their possibilities.
Example of combined logic
Suppose a two-cell cage in a 4×4 puzzle is marked 12×. The values must be 3 and 4. If the first cell shares a row with an existing 4, that cell must be 3 and the other cell must be 4. The cage gives the pair, while the row rule determines the order.
Common mistakes to avoid
- Do not repeat a number in a row or column even when the cage arithmetic works.
- For subtraction and division cages, either order may be possible.
- Do not assume every cage contains different numbers; repetition is only forbidden when cells share a row or column.
- Check the full cage after every change instead of considering each cell separately.