Calcudoku, also called KenKen or Mathdoku, is a grid puzzle that mixes Sudoku-style logic with arithmetic. You fill an N by N grid so that each row and column holds the digits 1 through N once, while the digits in each outlined cage combine to hit a printed target using a given operation: addition, subtraction, multiplication or division.

How is Calcudoku different from Sudoku?

Calcudoku has no 3 by 3 boxes, so rows and columns are the only line constraints, and the grid size varies rather than always being 9 by 9. Instead of given digits it uses arithmetic cages, where the digits must reach a target through a stated operation. A digit can repeat inside a cage as long as it does not repeat in its row or column.

How do you start a Calcudoku?

Place the single-cell cages first, since their target is simply the digit in that cell. Then find cages whose target can only be made one way, especially two-cell subtraction and division cages and small addition or multiplication targets. These locked combinations tell you which digits live in a cage, letting you eliminate them from the rest of that row and column.

Can a digit repeat inside a Calcudoku cage?

Yes, as long as it does not break the once-per-row-and-column rule. Because cages can bend around the grid, the same digit can appear twice in one cage when the two cells sit in different rows and different columns. This is a key difference from Killer Sudoku, where a digit can never repeat within a cage.

Does solving Calcudoku ever require guessing?

No. A well-made Calcudoku has exactly one solution reachable by pure logic. Every Puzzle Lair Calcudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often a cage combination or line-sum check you have not run.

Solving guides

From the rulebook

How to Solve Calcudoku

Calcudoku, better known to many solvers as KenKen or Mathdoku, blends Sudoku logic with arithmetic. Each row and column must hold every digit once, and the grid is split into outlined cages, each printed with a target number and an operation the digits inside must satisfy. Those cages replace starting clues, and once you can read their maths they give you plenty to work with. This guide takes you from the rules to the techniques that crack hard grids.

Play Calcudoku

The rules of Calcudoku

A Calcudoku is an N by N grid, where N depends on the puzzle size, commonly anywhere from 4 by 4 up to 9 by 9. Fill every cell so that each row and each column contains the digits 1 through N exactly once. Unlike Sudoku there are no 3 by 3 boxes, so rows and columns are your only line constraints.

The grid is divided into cages marked by bold outlines, each printed with a small target and an operation: plus, minus, times or divide. The digits inside a cage must combine using that operation to produce the target. Addition and multiplication cages can hold any number of cells, while subtraction and division cages always hold exactly two. A digit may repeat inside a cage as long as it does not break the once-per-row-and-column rule.

Start with the single-cell cages

The fastest opening move is placing the free digits. A one-cell cage has no operation, just a target, so that target is simply the digit in that cell. Write every single-cell cage straight onto the grid before anything else, then use those known digits to start eliminating candidates from their rows and columns.

Next hunt for cages whose target can only be made one way. A two-cell subtraction or division cage is the easiest to pin down, and small addition or multiplication targets often lock to a single combination too.

Read each operation for forced combinations

Each operation gives its own shortcuts. A two-cell division cage of 3 must be a pair where one digit is three times the other, so 1 and 3, 2 and 6, or 3 and 9. A two-cell subtraction cage of 1 means two consecutive digits. A small multiplication target factors quickly: a two-cell times-6 cage is 1 and 6 or 2 and 3, while a times target with a large prime factor like 7 forces that 7 into the cage.

List the digit combinations that hit each cage's target, then cross off any blocked by digits already placed in the rows and columns the cage spans. As with Killer Sudoku, knowing which digits live in a cage, even before you know their order, lets you eliminate them elsewhere in those lines.

Use the sum of the grid

Each row and each column contains 1 through N, so each one sums to a fixed total: 15 for a 5 by 5 grid, 21 for a 6 by 6, 45 for a 9 by 9. This is the Calcudoku version of the rule of 45. Add the targets of the addition cages sitting inside a single row or column and compare against that line total to pin down stray cells, just as you would in Killer Sudoku.

Multiplication cages can join the trick too, since their digits still contribute to the line sum once you know the combination. When a cage pokes one cell out of an otherwise solved line, the line total fixes that cell exactly.

Combine cage logic with line logic

Calcudoku is still a Latin square underneath. Once cage maths places a few digits, switch on ordinary scanning: a digit already in a row or column cannot repeat there, so look for lines where a digit has only one legal cell left. Each placement from cage arithmetic feeds the line eliminations, and each line elimination narrows the cage combinations in turn.

Apply the techniques in order: drop in the single-cell cages, lock the forced two-cell combinations, list cage candidates, run the line-sum checks, then loop ordinary row and column logic as the grid fills. On Puzzle Lair every Calcudoku is guaranteed solvable by logic alone, so if you are stuck there is always a deduction waiting, never a guess. Bigger grids and division-heavy cages are what make the hard set a genuine workout.

Frequently asked questions

What is Calcudoku?: Calcudoku, also called KenKen or Mathdoku, is a grid puzzle that mixes Sudoku-style logic with arithmetic. You fill an N by N grid so that each row and column holds the digits 1 through N once, while the digits in each outlined cage combine to hit a printed target using a given operation: addition, subtraction, multiplication or division.
How is Calcudoku different from Sudoku?: Calcudoku has no 3 by 3 boxes, so rows and columns are the only line constraints, and the grid size varies rather than always being 9 by 9. Instead of given digits it uses arithmetic cages, where the digits must reach a target through a stated operation. A digit can repeat inside a cage as long as it does not repeat in its row or column.
How do you start a Calcudoku?: Place the single-cell cages first, since their target is simply the digit in that cell. Then find cages whose target can only be made one way, especially two-cell subtraction and division cages and small addition or multiplication targets. These locked combinations tell you which digits live in a cage, letting you eliminate them from the rest of that row and column.
Can a digit repeat inside a Calcudoku cage?: Yes, as long as it does not break the once-per-row-and-column rule. Because cages can bend around the grid, the same digit can appear twice in one cage when the two cells sit in different rows and different columns. This is a key difference from Killer Sudoku, where a digit can never repeat within a cage.
Does solving Calcudoku ever require guessing?: No. A well-made Calcudoku has exactly one solution reachable by pure logic. Every Puzzle Lair Calcudoku is generated and verified to be solvable without guessing, so being stuck means there is a deduction you have not spotted yet, often a cage combination or line-sum check you have not run.

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