KenKen is a mathematical logic puzzle where you fill an NxN grid with digits 1-N so each row and column contains every digit exactly once, while groups of cells (cages) produce target values using arithmetic operations.

What does the equals sign (=) mean in KenKen?

A single-cell cage with just a number (no operation) is a "given" — that digit goes directly in that cell. These are free starting clues.

How to Play KenKen

Q: How is KenKen different from Sudoku?

Unlike Sudoku, KenKen includes arithmetic operations. Cells are grouped into cages with target numbers and operations (+, -, ×, ÷). KenKen also comes in various grid sizes (3x3 to 9x9), not just 9x9.

Q: Can digits repeat within a cage?

Yes! Unlike Killer Sudoku, KenKen allows digits to repeat within a cage, as long as they don't violate the row/column uniqueness rule.

Q: What is the best size for beginners?

3x3 and 4x4 easy puzzles are best for beginners. They use fewer digits and simpler operations, making them ideal for learning the rules.

A complete guide for beginners and intermediate players. Learn the rules, understand cage operations, and pick up essential solving techniques.

The Rules

Fill every cell with a digit

For an N×N grid, use digits 1 through N. A 4×4 grid uses 1-4; a 6×6 grid uses 1-6.

No repeats in rows or columns

Each digit appears exactly once in every row and exactly once in every column — just like Sudoku.

Satisfy cage constraints

Each cage (outlined group of cells) has a target number and operation. The digits in the cage must produce the target using that operation.

Understanding Cage Operations

Addition

All digits in the cage add up to the target. Example: 8+ in a 3-cell cage could be 1+3+4 = 8.

−

Subtraction

Always 2 cells. The larger digit minus the smaller equals the target. Example: 2− means the difference is 2 (e.g., 5-3).

Multiplication

All digits in the cage multiply to the target. Example: 12× in a 2-cell cage could be 3×4 or 2×6.

Division

Always 2 cells. The larger digit divided by the smaller equals the target. Example: 3÷ means one digit is 3 times the other (e.g., 6÷2).

Given (Single Cell)

A single-cell cage shows just a number — that's the digit that goes in the cell. These are free clues to help you start.

Step-by-Step Solving Guide

Step 1: Fill in Givens

Start by entering all single-cell cage values. These are definite and immediately reduce candidates in their rows and columns.

Step 2: Identify Forced Combinations

Look for cages with only one possible digit combination. For example, in a 4×4 grid, a 7+ cage of 2 cells can only be 4. Check our combination tables for reference.

Step 3: Apply Row/Column Elimination

If a digit is already placed in a row or column, eliminate it from candidates in all other cells of that row or column.

Step 4: Look for Naked Singles

If a cell has only one remaining candidate after elimination, fill it in. This often triggers a chain of further eliminations.

Step 5: Use Cross-Cage Logic

Sometimes the combination possibilities of one cage constrain what's possible in adjacent cages. Look for interactions between neighboring cages in the same row or column.

Ready for advanced techniques? See our strategies guide.

Frequently Asked Questions

What is KenKen?

KenKen is a mathematical logic puzzle invented by Japanese teacher Tetsuya Miyamoto in 2004. The name means "wisdom squared" in Japanese. You fill an N×N grid with digits 1-N so each row and column has every digit exactly once, while cell groups (cages) produce target values using arithmetic operations.

How is KenKen different from Sudoku?

Both share the Latin square constraint (no repeat digits in rows/columns), but KenKen adds arithmetic operations. KenKen also comes in various grid sizes (3×3 to 9×9), while Sudoku is always 9×9 with 3×3 boxes. Read our detailed KenKen vs Sudoku comparison.

What does the equals sign mean?

A single-cell cage showing just a number (no operation symbol) is a "given" — that digit goes directly in that cell. These are free starting clues that make the puzzle easier. Easier puzzles have more givens.

Can digits repeat within a cage?

Yes! Unlike Killer Sudoku, KenKen allows the same digit to appear in multiple cells of a cage, as long as those cells are not in the same row or column. This is an important distinction to remember.

What is the best size for beginners?

Start with 3×3 or 4×4 easy puzzles. They use fewer digits and simpler operations, letting you focus on learning the rules before tackling harder challenges.

Ready to Play?

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Advanced strategies → Cage combinations → For kids → KenKen vs Sudoku →