KenKen (Calcudoku) Game
Fill the grid with numbers so that each row and column contains digits 1 to 4 without repetition. Respect the cage targets and operations shown in the top-left of each cage.
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How to Play
KenKen, also known as Calcudoku, is a logic and arithmetic puzzle. The goal is to complete an N×N grid where each row and column contains the numbers 1 through N exactly once, while also satisfying the arithmetic constraints shown in each cage.
- Each row and column must contain numbers 1 to 4 without repetition.
- Each cage has a target and an operation; the numbers in that cage must produce the target.
- Single-cell cages show a fixed value target.
- Use Notes to pencil in candidates before committing a value.
Cage Operations Explained
Addition (+): All numbers in the cage add up to the target.
Multiplication (×): All numbers in the cage multiply to the target.
Subtraction (−): For a two-cell cage, the absolute difference must match the target, so both orders are valid.
Division (÷): For a two-cell cage, one value divided by the other must equal the target, so both orders are valid.
Single cell (=): The cage is fixed to the target value.
Strategy tips
- Start with singleton cages (=): fill these fixed values first.
- Scan rows/columns for near-complete lines to eliminate duplicates quickly.
- For subtraction and division cages, test both orders (a − b and b − a) when listing candidates.
- For × and ÷ cages, list factor pairs within 1 to 4 and rule out duplicates in the row/column.
- Use Notes to track candidates and turn on error highlighting to spot conflicts early.
Example reasoning
In a 4×4 puzzle, a two-cell cage labeled 7+ can only be 3 and 4. A two-cell cage labeled 12× can only be 3 and 4 as well. Recognizing these forced pairs early helps you narrow down candidates across the whole row and column.
Common patterns
- Sum cages close to min/max: e.g., in 4×4, 7(+) over two cells is usually 3+4.
- Product cages with primes: limited pairs make deduction faster (e.g., 6 = 2×3).
- Row/column uniqueness: if a number appears as the only candidate in a line, place it.
If you enjoy logic grids, try our Sudoku solver and helper too.