๐ KenKen Puzzle Solver
Stuck on a KenKen puzzle? Enter your cage constraints and get the solution instantly. Supports grids from 3ร3 to 9ร9 with all operations.
Cell Coordinates Reference (4ร4)
Format: "row,col row,col" (e.g., "0,0 0,1")
Cages
How to Use the Solver
- Select your puzzle grid size (3ร3 to 9ร9)
- For each cage, enter the target number and operation
- Enter the cell coordinates in "row,col" format, separated by spaces
- Use the coordinate reference grid above to find cell positions
- Single-cell cages: leave operation as "single"
- Click "Solve" to find the solution
Example: A cage with target "3" and operation "+" covering cells (0,0) and (0,1) would be entered as: target=3, op=+, cells="0,0 0,1"
What is a KenKen Solver?
A KenKen solver is a tool that finds the solution to a KenKen puzzle based on its cage constraints. Given the grid size and the target numbers with their operations (+, โ, ร, รท) for each cage, the solver uses backtracking algorithms to determine the unique arrangement of numbers that satisfies all rules:
- โข Each row contains numbers 1 to N without repetition
- โข Each column contains numbers 1 to N without repetition
- โข Numbers in each cage combine to equal the target using the given operation
How to Solve a KenKen Puzzle
Step 1: Identify Single-Cell Cages
Single-cell cages have no operation โ just a number. Fill these in first. They give you free anchor points to work from.
Step 2: Analyze Constrained Cages
Look for cages with limited possibilities. For example, a "2รท" cage in a 4ร4 grid can only be {1,2} or {2,4}. A "3โ" cage can be {1,4}, {2,5}, etc. Narrow down options before placing numbers.
Step 3: Apply Sudoku Logic
Use the no-repeat rule for rows and columns. If a row already has 2 and 4, the remaining cells must be filled from the other numbers. This eliminates possibilities in intersecting cages.
Step 4: Work Multiplication and Division Cages
These cages are highly constrained. A "6ร" cage with 2 cells in a 4ร4 grid must be {2,3} or {1,6} (but 6 is invalid in 4ร4), so it must be {2,3}. Use this logic to fill cells quickly.
Step 5: Use the Solver When Stuck
If you've exhausted logical deduction, enter your puzzle into the solver above. It will find the solution and tell you whether the puzzle has a unique answer โ a hallmark of well-constructed KenKen puzzles.
Tips for Using the Solver
- ๐กCoordinate system: Rows and columns are 0-indexed. Top-left is (0,0).
- ๐กCell format: Enter cells as "row,col" separated by spaces, e.g., "0,0 0,1 1,0".
- ๐กSingle-cell cages: Leave the operation as "single" โ just enter the target number.
- ๐กFull coverage: Every cell in the grid must belong to exactly one cage.
- ๐กMultiple solutions: If the solver finds more than one solution, the puzzle may be ambiguous.
Solving KenKen by Grid Size
3ร3 KenKen Solver
The easiest grid size. With only numbers 1-3, the solver finds solutions almost instantly. Great for beginners learning the rules.
4ร4 KenKen Solver
The classic KenKen size. Moderate complexity with enough cages to require real logical thinking. Most published puzzles use this size.
5ร5 KenKen Solver
Stepping up the challenge. Larger cages and more complex operations make hand-solving tricky โ the solver is a great help here.
6ร6 to 9ร9 KenKen Solver
Expert-level puzzles. The solver handles these efficiently with constraint propagation and backtracking, finding solutions in seconds.
Also Known As: MathDoku Solver & Calcudoku Solver
KenKen is a trademarked name. The same puzzle type is also known as MathDoku and Calcudoku. This solver works for all three โ the rules and cage mechanics are identical regardless of the name.
Frequently Asked Questions
Is this KenKen solver free?
Yes, completely free. No registration, no limits. Enter your puzzle and get the solution instantly.
Can the solver handle 9ร9 puzzles?
Yes! The solver supports all grid sizes from 3ร3 to 9ร9. Larger grids take slightly longer but typically solve in under a second.
What if my puzzle has multiple solutions?
The solver detects multiple solutions and displays up to two. A well-formed KenKen puzzle should have exactly one unique solution โ if yours has multiple, double-check the cage constraints.
Does this work for MathDoku and Calcudoku too?
Yes. KenKen, MathDoku, and Calcudoku are the same puzzle with different names. The solver works for all three.
Why does the solver say "No solution found"?
This means the cage constraints you entered are contradictory โ no valid arrangement of numbers can satisfy all the rules. Check that: (1) all cells are covered by cages, (2) targets and operations are correct, and (3) cell coordinates are within the grid.