How Kalkudoku works
Kalkudoku combines a Latin-square rule with arithmetic cages. On a 4×4 board, each row and column must contain 1, 2, 3 and 4 exactly once. A 5×5 board uses 1–5, and a 6×6 board uses 1–6. Repeating a number in a row or column is never allowed, even when both values appear to satisfy their cage clues.
Bold outlines divide the board into cages. The small clue in a cage gives a target and, usually, an operation. Every number inside that cage must combine to make the target. A clue without an operation belongs to a one-cell cage, so that cell takes the displayed value. Rows, columns and cages must all agree before the puzzle is complete.
Addition cages
For a clue such as 9+, all values in the cage must total 9. Start with combinations allowed by the board size, then remove any combination that would repeat a digit in the same row or column.
Multiplication cages
For 12×, list factor combinations using only available digits. On a 6×6 board, 2×6 and 3×4 are possibilities for a two-cell cage; surrounding rows and columns decide which one fits.
Subtraction cages
A two-cell clue such as 2− means the difference between the larger and smaller value is 2. The order of the cells does not matter, so both 1 and 3, or 2 and 4, may be candidates.
Division cages
A two-cell clue such as 3÷ means the larger value divided by the smaller value equals 3. On a 6×6 grid, possible unordered pairs include 1 and 3 or 2 and 6.
A reliable solving order
- Place one-cell cages first. They are fixed values and immediately restrict both a row and a column.
- List narrow combinations. Large products, small differences and exact divisions often have fewer possible digit sets than a broad addition clue.
- Apply row and column restrictions. A cage combination may be arithmetically correct but impossible because it repeats a number in a line.
- Revisit intersecting cages. When one cell becomes fixed, update every cage and line that crosses it before moving elsewhere.
- Use Check as a review tool. A check highlights contradictions, but explaining the contradiction is more useful than repeatedly testing values.
Keyboard players can move with the arrow keys, enter a value with the number row, and erase with Backspace, Delete or 0. The game saves the current board in local browser storage, so refreshing the page on the same device normally restores the session.
Choosing a board size
| Board | What changes | Recommended use |
|---|
| 4×4 Beginner | Digits 1–4 and shorter cages make combinations easier to list. | Learn how line restrictions and arithmetic clues work together. |
| 5×5 Medium | An extra digit expands the possible sums, products and line patterns. | Practise cage combinations without the density of the largest board. |
| 6×6 Expert | More cells and wider factor choices require longer chains of elimination. | Use when you can already solve smaller boards without trial and error. |
The labels describe relative complexity within SudokuGG; they are not a universal standard shared by every puzzle publisher. A fresh board is generated for each new game from a valid completed grid and arithmetic clues derived from that grid. The game accepts a completion only when every line has no repeated values and every cage reaches its target.
For a compact rule reference and additional examples, read the complete Kalkudoku rules. If you prefer classic 9×9 logic without arithmetic, open Classic Sudoku.
Rules and controls were checked against the current SudokuGG game implementation. Updated July 21, 2026. Corrections can be reported through Contact; methodology is described in our editorial policy.