KenKen
Play KenKen (KenDoku) puzzles online. Fill the grid 1–N with no repeats in any row or column while every cage hits its target with +, −, × or ÷. 4×4 to 6×6.
Click a cell, then type 1–4 (or use the pad). Arrow keys move, Backspace clears. Fill so every row and column has each digit once and every cage hits its corner target with its operation.
The rules
KenKen (sometimes “KenDoku” or “Calcudoku”) plays on an N×N grid filled with digits 1 to N — a Latin square: each row and each column must contain every digit exactly once.
The grid is then carved into heavily-outlined groups called cages. The little number in a cage's top-left corner is the target, followed by an operation: +, −, × or ÷. The digits you place inside the cage, combined with that operation, must equal the target.
A single-cell cage just shows the digit itself — a free starting hint.
Operations, precisely
| Op | Cells | How it's evaluated |
|---|---|---|
| + | any number | All digits added together. |
| × | any number | All digits multiplied together. |
| − | exactly 2 | Absolute difference, larger minus smaller. |
| ÷ | exactly 2 | Larger divided by smaller; must be a whole number. |
Important: digits may repeat inside a cage as long as they don't repeat in the same row or column. So a 3-cell L-shaped cage with target 6+ could be {1, 2, 3} or {2, 2, 2} — whichever fits the Latin square constraint.
How to solve
- Start with freebies. Single-cell cages give you a digit instantly. Then look for cages with very small/large targets — they pin down digit sets.
- Use divide and subtract cages. A “3÷” pair on a 5×5 grid must be {1, 3}. A “4−” pair on 5×5 is {1, 5}.
- Apply Latin square logic. Once a row or column is mostly filled, the missing digits are forced. Cross with cage constraints.
- Sum the whole grid. Every row sums to N(N+1)/2. If a partial-row or partial-cage sum nearly closes a row, the leftover digit is determined.
History & why it's addictive
KenKen was invented in 2004 by Japanese maths teacher Tetsuya Miyamoto, who designed it as a no-instruction classroom tool — students were meant to deduce the rules themselves. The name combines ken (cleverness) twice. Unlike Sudoku, KenKen forces real arithmetic at every step, so it doubles as mental-maths practice; the New York Times has run a daily KenKen since 2009.