Calcudoku

Calcudoku is the generic name often used for KenKen-style arithmetic grid puzzles. The format was invented in 2004 by Japanese math teacher Tetsuya Miyamoto, who wanted a puzzle that trained arithmetic through discovery. Each row and column uses digits 1 through N once, while cages give target numbers and operations. The logical challenge comes from combining Latin-square placement with arithmetic. Start with single-cell cages and forced products, then use row and column eliminations.

1. Choose a grid size. A 5x5 puzzle uses digits 1 through 5.
2. Fill every row and column without repeating a digit.
3. Read each cage's target number and operation.
4. Place digits in the cage so they make the target using that operation.
5. Use candidates to combine arithmetic possibilities with row-column rules.
6. Finish when every cage and every row-column rule is satisfied.

• Rows cannot repeat digits.
• Columns cannot repeat digits.
• Cage targets must be met exactly.
• Addition and multiplication cages can use digits in any order.
• Subtraction and division cages usually use two cells and allow either order.
• Digits may repeat inside a cage only if they do not repeat in the same row or column.

• Fill single-cell cages first. Their target gives the digit directly.
• List factor pairs for multiplication cages. In a 6x6 grid, a product of 30 can only use combinations like 5x6 or 1x5x6.
• Use row and column conflicts to remove arithmetic candidates.
• Watch cage size. A three-cell sum of 6 in a 6x6 grid must be 1, 2, and 3.
• Solve small cages near each other first because they create strong row-column pressure.

• Killer Sudoku: Uses cage sums on a 9x9 Sudoku grid.
• Futoshiki: Uses inequalities instead of arithmetic cages.
• Kakuro: Uses crossword-like sum runs.

• It turns arithmetic into deduction rather than speed math.
• Small grids work well for beginners.
• 7x7 and 8x8 grids offer extreme challenges with longer cage chains and more elimination steps.
• Cage operations create many routes into the puzzle.
• It teaches factors, sums, and row-column logic together.

Play Calcudoku online for free. Fill the grid, solve each arithmetic cage, and use row-column uniqueness to narrow every candidate.

Calcudoku blends arithmetic cages with Latin-square placement. Start with direct cages, list possible combinations, and let row-column conflicts finish the grid.

• KenKen and Calcudoku Background
• Calcudoku Rules Overview