KenKen Arithmetic Solver
A Latin square with arithmetic cages — each row and column must hold 1 to N, and each cage's digits must achieve the target using the given operation (+, −, ×, ÷).
About KenKen
KenKen (ケンケン) is an arithmetic and logic puzzle invented by Japanese math teacher Tetsuya Miyamoto. The n×n grid must be filled so that every row and column contains the digits 1 through n exactly once — like a Latin square. The grid is further divided into cages: outlined groups of cells, each labeled with a target number and an operation (+, −, ×, ÷). The digits in a cage, combined using the given operation in some order, must produce the target.
For single-cell cages, the digit is given directly (like a clue). For subtraction and division cages (always 2 cells), the larger value minus/divided-by the smaller must equal the target. Crucially, digits may repeat within a cage (unlike Killer Sudoku) as long as the row/column rule is satisfied.
Frequently Asked Questions
What operations appear in KenKen cages?
Addition (+), subtraction (−), multiplication (×), and division (÷). Subtraction and division cages always have exactly 2 cells. The target is always a positive integer.
Can digits repeat inside a KenKen cage?
Yes — unlike Killer Sudoku, KenKen allows repeating digits within a cage, as long as no digit repeats in any row or column.
How does the KenKen solver work?
The solver uses backtracking constrained by both the Latin square rule (no repeats in rows/columns) and the cage arithmetic rule. It evaluates partial cage assignments and prunes early if the target cannot be reached.
What grid sizes are available?
This solver offers 4×4 (beginner) and 6×6 (intermediate) KenKen puzzles. Select a size and difficulty using the buttons above the grid.
How to Play KenKen
1 Rules
- ✓ Each row must contain 1–N exactly once.
- ✓ Each column must contain 1–N exactly once.
- ✓ Each cage's digits must satisfy the arithmetic operation.
- ✓ Digits may repeat within a cage (unlike Killer Sudoku).
2 Operations
- 💡 + (Add): All digits in the cage sum to the target.
- 💡 − (Subtract): Larger minus smaller equals target (2 cells only).
- 💡 × (Multiply): All digits in the cage multiply to the target.
- 💡 ÷ (Divide): Larger divided by smaller equals target (2 cells only).
Tip: Single-cell cages are given values — fill them first. Then use the row/column constraint to narrow down which digits can go in each cage.