KenKen

How to play KenKen

KenKen (also called Calcudoku, Kendoku or MathDoku) is a grid puzzle with two rules. First, like Sudoku, every row and column must contain the numbers 1 to the grid size with no repeats — 1–4 in a 4×4, 1–6 in a 6×6. Second, the grid is divided into outlined cages, and each cage has a target with an operation, like "6×" or "1−". The numbers you place in a cage must combine with that operation to reach the target.

Tap a cell, then tap a number to place it. A single-cell cage just shows its number. For bigger cages, the small clue in the corner tells you the goal: + and × use all the cage's cells; − and ÷ are always two cells, where the numbers subtract or divide to the target in whichever order works.

Strategy

• Start with the singles. One-cell cages are free — place them first, then use the row/column rule to eliminate elsewhere.
• List a cage's options. For "12×" in two cells of a 6×6, the pair could be 2×6 or 3×4 — then the row and column rules narrow it down.
• Subtraction and division cages are pairs. "2÷" means the two numbers divide to 2 (so 1&2, 2&4, 3&6…); "3−" means they differ by 3.
• Use the totals. Each row and column of an n×n grid always sums to the same amount, which can pin down a stubborn cage.

Why KenKen is great practice

KenKen was invented by a Japanese maths teacher, Tetsuya Miyamoto, as a no-instruction way to build arithmetic and logic at once — the name means roughly "cleverness squared". Unlike Sudoku, it actually exercises your mental arithmetic: every cage is a little sum, product, difference or quotient to work out. That makes it a perfect fit if you want a puzzle that keeps your calculation skills sharp, not just your pattern-spotting.

The history of KenKen

KenKen was invented in 2004 by Tetsuya Miyamoto, a Japanese mathematics teacher who wanted a puzzle that would build his students' arithmetic and their persistence, without him having to explain how to solve it. The name comes from a Japanese word for cleverness, doubled. English-language newspapers took it up a few years later, with The Times in 2008 and The New York Times in 2009.

Because "KenKen" is a trademark, the same puzzle is often published under other names: Calcudoku, Mathdoku and KenDoku are all versions of the cage-and-target grid you play on this page.

Frequently asked questions

Is KenKen free here?

Yes, completely free with no sign-up. It runs in your browser and your best time is saved on your device.

Is KenKen the same as Calcudoku, Kendoku or MathDoku?

Yes — they are all names for the same puzzle. "KenKen" is the trademarked name; Calcudoku, Kendoku and MathDoku describe the identical grid of arithmetic cages, played by the same rules.

What's the difference between KenKen and Sudoku?

Both need each row and column to have no repeats. Sudoku adds 3×3 boxes and gives you starting numbers; KenKen instead adds arithmetic cages with targets, so you calculate as well as deduce.

Can a number repeat within a cage?

Yes, a number can repeat inside a cage as long as it doesn't repeat within the same row or column. The row/column rule is what prevents repeats.

Does every puzzle have one solution?

Yes. Each puzzle is generated and checked to have exactly one solution, so it can be solved by logic alone.

What do the corner clues mean?

The clue shows a target and an operation for that cage — for example "6+" means the cage's numbers add to 6, and "3−" means its two numbers differ by 3.