KenKen

Tetsuya Miyamoto, a Japanese math teacher, invented KenKen in 2004 as a classroom tool to teach arithmetic through pure logic. He wanted students to discover math patterns on their own, without lectures. The puzzle combines Latin-square placement with arithmetic cages: each grouped region must produce a target number using addition, subtraction, multiplication, or division. A 2019 study in the International Journal of Geriatric Psychiatry found that regular number-puzzle solving keeps the brain up to 10 years younger in adults over 50. Start playing KenKen right now in your browser, no download needed.

1. Pick a grid size from 4x4 to 8x8. The grid uses digits 1 through N, where N is the grid size.
2. Tap any cell to select it. Type a digit on your keyboard or tap a number from the pad below the grid.
3. Press Backspace or Delete to clear a cell. Use arrow keys to move between cells without reaching for the mouse.
4. Toggle pencil mode to jot down candidate numbers in a cell without committing to them.
5. Each cage shows a target number and an operation in its top-left corner. For addition cages, the digits in that cage must sum to the target.
6. For multiplication cages, they must multiply to the target. Subtraction and division cages always contain two cells: subtract the smaller from the larger, or divide the larger by the smaller.
7. Single-cell cages show a target with no operation, meaning the answer is that number.
8. Fill every cell so no digit repeats in any row or column. The puzzle is complete when all rows, columns, and cages satisfy their rules.

• Every row must contain each digit from 1 to N exactly once.
• Every column must contain each digit from 1 to N exactly once.
• This Latin-square rule is the same constraint you find in Sudoku, but without 3x3 box regions.
• Cells are grouped into cages, outlined by thick borders. Each cage displays a target number and an operation.
• For addition, all digits in the cage must add up to the target.
• For multiplication, they must multiply to the target.
• For subtraction, the cage has two cells, and the absolute difference between them equals the target.
• For division, the cage has two cells, and the larger divided by the smaller equals the target.
• A single-cell cage has no operation symbol: the digit is the target.
• Digits can repeat inside a cage as long as they do not repeat in the same row or column.
• Every well-formed KenKen puzzle has exactly one solution.

• Fill single-cell cages first. The target is the answer, so write it in immediately and eliminate that digit from the row and column.
• List all factor pairs for multiplication cages. In a 5x5 grid, a product of 12 can only be 3 and 4, or 2 and 6 (but 6 is invalid), so it must be 3 and 4.
• Use the sum extremes. A two-cell addition cage totaling 3 in a 6x6 grid must use 1 and 2. A sum of 11 must use 5 and 6. These forced pairs give you free placements.
• Scan for naked singles. After filling a few cages, a row or column may have only one empty cell. The missing digit goes there, no arithmetic needed.
• Cross-reference cage candidates with row and column constraints. A cage may allow two digit pairs, but if one pair conflicts with existing row or column values, only the other pair works. This elimination technique is the core of advanced KenKen solving.

• Calcudoku: The generic name for the same puzzle format. Many publishers use it to avoid the KenKen trademark. Follows identical rules.
• Killer Sudoku: Adds cage sums on top of a 9x9 Sudoku grid with 3x3 box constraints, combining two rule sets into one harder puzzle.
• Kakuro: Uses crossword-style sum clues in a grid with black cells and no Latin-square rule, so you rely on addition alone.
• Futoshiki: Replaces arithmetic with inequality symbols between adjacent cells, testing pure ordering logic instead of math.

• KenKen turns arithmetic into a deduction game. You calculate to eliminate possibilities, not for speed.
• The cage structure gives you multiple entry points into the puzzle, so you can always start somewhere productive.
• Small grids suit beginners and children learning multiplication tables.
• Larger grids challenge experienced solvers with longer chains of logic.
• 7x7 and 8x8 grids push your deduction to the limit with more cages and longer elimination chains.
• The puzzle rewards patience over guessing, since every digit follows from the rules.
• Miyamoto designed it to teach math through discovery, and that philosophy still works for self-taught players today.

Play KenKen online for free right here. Choose your grid size, generate a fresh puzzle, and start solving. Use the number pad or your keyboard to enter digits. Toggle pencil mode for candidates. The timer tracks your progress, and the hint button reveals a cell when you get stuck. No sign-up, no ads in the game area, no downloads. Just pure arithmetic logic.

KenKen combines Latin-square logic with arithmetic cages to create a puzzle that exercises both sides of your brain. Start with single-cell cages, work through the forced pairs, and let row-column elimination finish the grid. The more you play, the faster you spot patterns. Pick a size, hit new puzzle, and start solving now.

• KenKen - Wikipedia
• Brooker et al. (2019) - Number puzzle use and cognitive function in adults aged 50+, International Journal of Geriatric Psychiatry