KenKen Puzzle

How to Play KenKen

KenKen — also called Calcudoku or Mathdoku — is a number logic puzzle with two simple rules. Every row and every column must contain each number from 1 to N exactly once, where N is the grid size (4, 6 or 9 here). What sets KenKen apart from other Latin-square puzzles is the cages: blocks outlined in thick lines, each carrying a small target number and an operator.

The numbers inside a cage must combine to its target using the operator:

• 6+ — the digits in the cage must add up to 6.
• 2− — a two-cell cage where the difference of the two digits is 2.
• 12× — the digits must multiply to 12.
• 2÷ — a two-cell cage where one digit divided by the other equals 2.
• A plain number with no operator — a single-cell cage: that cell is already fixed and acts as a clue.

Digits may repeat inside a cage — the row and column rule is the only thing that forbids repeats. Every GridPaw KenKen puzzle has a unique solution and can be solved with pure logic, no guessing required. Tap a cell, then type a number (or tap the on-screen number pad); tap the same number again to clear it. If you get stuck, the Hint button reveals the correct digit for the selected cell — you get 3 per puzzle.

What Is Calcudoku? KenKen vs Calcudoku vs Mathdoku

Calcudoku (sometimes written "Calcu-doku") is the generic name for the puzzle family most people know as KenKen. The puzzle was invented in 2004 by Japanese math teacher Tetsuya Miyamoto, who designed it to train his students' arithmetic and logical thinking together — the name loosely means "wisdom squared".

Because KenKen is a registered trademark of Nextoy LLC, newspapers, apps and puzzle sites that are not licensed use the identical puzzle under other names: Calcudoku and Mathdoku are the two most common. The rules are exactly the same — a Latin square with arithmetic cages. If you have solved one, you have solved them all, which is why you will sometimes see a single puzzle published as "KenKen" in one outlet and "Calcudoku" in another.

At GridPaw we call the game KenKen because that is the name players search for, but the footer of this page always credits the trademark so nobody walks away confused about the name game.

KenKen vs Sudoku

Sudoku and KenKen both use the same backbone rule: every row and every column contains 1–N exactly once. The difference is how the third constraint works. In Sudoku, an inner 3×3 box ties groups of 9 cells together; in KenKen, oddly shaped cages — two cells, five cells, anything — carry an arithmetic target instead.

That small change transforms the experience. Sudoku is pure pattern logic: you scan, cross-hatch and eliminate. KenKen mixes arithmetic into the deduction, so you keep your mental math sharp while solving — a 6+ cage in a 4×4 grid immediately narrows the possibilities, and a 3÷ cage forces you to think about 3 or 6 before you ever look at the rows. Because cages come in every shape, KenKen boards also look more varied and feel less repetitive than a wall of uniform Sudoku squares.

Difficulty-wise, neither game is inherently harder. A 4×4 KenKen is friendlier for total beginners than most Sudoku grids, and a hard 9×9 KenKen demands the same deep elimination technique as an expert Sudoku — just with multiplication tables attached.

KenKen Tips and Strategy

New to KenKen? Start with the fixed cells — single-cell cages with no operator are already filled for you. Then hunt the cages that have only one possible combination, especially on small boards:

1. Start with the tightest cages. In a 4×4 puzzle, a two-cell 3+ cage is always 2, and a two-cell 2÷ cage is 2 in some order. A 7+ in 4×4 is always 4. Lock those pairs down first.
2. Use the row-sum trick. Every row must total N(N+1)/2 — a 4×4 row sums to 10, a 6×6 row to 21, a 9×9 row to 45. When a row is nearly full, the last cell is forced: just subtract what you have.
3. Read multiplication cages through primes. A two-cell 5× cage is 5 in some order; a 3× in 4×4 is 3. Bigger targets like 12× give you 4, 6, 3 and friends — then the rows and columns decide.
4. Test both orders for − and ÷. A two-cell cage never says which digit goes where. When everything else is eliminated, the row and column constraints pick the order — walk through both placements mentally before writing anything.
5. Remember cage repeats are legal. The most common beginner mistake is banning repeats inside a cage. A two-cell 4+ cage filled with 2 is perfectly legal as long as the rows and columns stay legal.
6. Eliminate before you commit. If a digit completes a cage but duplicates a value already in its row or column, cross it out. With 3 hints per puzzle, you will rarely need them — but they are there when a 9×9 gets stubborn.