Sudoku Written and built by Brian Hamilton. Reviewed by Karan Hamilton.
Brian handles the technical puzzle logic, while Karan checks the page for clarity, usability, and player experience.
Puzzle tools are tested in the browser against Sudoku rules, example grids, and common player workflows. See how we make and test puzzles, our editorial standards, or report a problem.
Calcudoku Solver for KenKen-Style Math Puzzles
Our Calcudoku Solver helps you solve, check, and understand Calcudoku, KenKen, and MathDoku puzzles online. Calcudoku looks familiar if you already know Sudoku, but it replaces 3x3 boxes with arithmetic cages, so our classic Sudoku solver cannot read it. Every row and every column must contain each number from 1 up to the grid size, while each cage must also meet a target number using the listed operation. That combination of Latin-square logic and mental arithmetic is what makes the puzzle satisfying, and it is also why one copied cage error can make a perfectly good puzzle look impossible.
This page is designed as a KenKen solver, a MathDoku solver, and a practical online Calcudoku helper. You can draw cages, enter targets and operations, solve the grid, check whether the answer is unique, and export your setup as JSON. If you are rebuilding a puzzle from a newspaper, puzzle book, classroom worksheet, or screenshot, the tool gives you a structured way to confirm that your entry matches the original before you spend time chasing a contradiction.
Quick summary: choose the grid size, select the cells that belong to each cage, enter the cage target and operation, then run the solver. If the puzzle is valid, the tool returns a complete solution. If it is not valid, the checks point you toward missing cages, impossible arithmetic, repeated values, or a grid size that does not match the source puzzle.
How to Use the Calcudoku Solver
Start by selecting the correct size. A 4x4 Calcudoku uses the numbers 1 to 4, a 6x6 uses 1 to 6, and a 9x9 uses 1 to 9. Next, draw the cages exactly as they appear in the puzzle. A cage is a connected group of one or more cells. Each cage needs a target and an operation, such as 12x for multiplication, 7+ for addition, 2- for subtraction, or 3÷ for division.
Single-cell cages are fixed values, so the target is the number that belongs in that cell — and they must use the = operation; the tool will not accept a one-cell cage marked with anything else. Addition and multiplication cages can contain their numbers in any order, as long as the sum or product is correct. Subtraction and division cages must contain exactly two cells. That is not a convention here but a rule the editor enforces, so if your source puzzle has a three-cell minus cage it is using a variant this solver does not cover. The solver combines those cage rules with the row and column rule that no number can repeat.
For larger puzzles, a steady workflow helps. Draw all cage shapes first, add all targets second, then review the operations last. That makes it easier to catch a 15+ entered as 15x, a cell left outside every cage, or a cage that accidentally includes an extra square. Those small transcription errors are the most common reason a copied Calcudoku fails to solve.
What the cage clues are carrying
Calcudoku gives you no starting digits at all, which is easy to say and easy to underestimate. Here is a real 6×6, generated and then solution-counted.
Every one of those clues is load-bearing. That is the useful thing to hold on to when a copied puzzle refuses to solve: there is no redundancy to absorb a mistake.
Calcudoku Rules Explained
Calcudoku has two main rule families. The first is the row and column rule: each number appears once in every row and once in every column. In a 5x5 grid, every row and column must contain exactly 1, 2, 3, 4, and 5. This is the Latin-square foundation that also supports many Sudoku variants.
The second rule family is arithmetic. Each cage must match its clue — the same idea as Killer Sudoku, except Killer uses only addition and keeps the 3x3 boxes, which is why it has its own Killer Sudoku solver. A 10+ cage in a 6x6 puzzle might contain 1, 4, and 5. A 24x cage might contain 2, 3, and 4. A two-cell 3- cage might use 1 and 4 or 2 and 5. The solver builds the combinations that satisfy each cage, then removes any combination that conflicts with existing row or column constraints.
That is why Calcudoku feels more mathematical than classic Sudoku. You are not only eliminating candidates; you are also thinking about factors, sums, differences, and quotients. A good Calcudoku solver performs those checks consistently, which lets you focus on the puzzle logic instead of recalculating the same possibilities by hand.
What the Solver Checks
The solver does more than produce a final grid, though it is worth knowing exactly how much. Before it searches, it checks that no row or column already repeats a value and that every cell belongs to a cage — that second check is the one that catches a missed border. Cage rules are enforced as it goes: a target you could never reach is not flagged up front, it simply makes the search fail. So "no solution" covers both a genuinely impossible clue and a cage you drew a cell short.
Uniqueness is especially important. Many hand-made Calcudoku puzzles have more than one solution even though they look fine at first glance. For solvers, that is frustrating because two different paths may both be valid. For puzzle creators, it is a sign that the cage layout or clues need tightening. A useful solver should tell you whether the clues force exactly one answer.
You can also use the tool without spoiling the whole puzzle. Enter the cages, confirm that the puzzle is coherent, then return to solving it yourself. That is a nice middle ground when you want confidence that the puzzle was copied correctly but do not want the full answer yet.
Calcudoku, KenKen, and MathDoku
These names often describe the same style of puzzle. Calcudoku is a generic name for a Latin-square puzzle with arithmetic cages. KenKen is the best-known branded version. MathDoku is another common term, usually emphasizing the arithmetic side. In practice, Calcudoku, KenKen, and MathDoku solvers usually need the same kind of tool: a way to enter cages, operations, and targets.
There can still be small differences between sources, and one of them matters enough to state plainly. Some publications allow a repeated number inside a cage as long as the repeats are not in the same row or column; others forbid repeats outright. This solver allows them. A three-cell cage may hold 3, 4 and 4 if the two 4s sit in different rows and different columns, because the only thing stopping a repeat is the Latin-square rule itself. If your puzzle comes from a source that bans repeats entirely, a grid can therefore solve here to an answer the setter did not intend.
Other differences are milder: easier puzzles often use only addition and multiplication, while harder ones lean on subtraction and division. Always read the rules printed with your puzzle before deciding a grid is wrong.
Choosing the Right Grid Size
A 4x4 Calcudoku is ideal for beginners, children, or quick practice — much like a 4x4 Sudoku, and a reasonable next step for anyone who has worked through sudoku for kids. The set of numbers is small, and most cage combinations can be checked mentally. 5x5 and 6x6 grids are often the best everyday size: large enough for real logic, but still compact enough to enter and review quickly.
At 7x7, 8x8, and 9x9, the search space grows quickly. A 9x9 Calcudoku can feel like a classic Sudoku with an extra arithmetic layer. In those larger grids, an online solver is useful not only for finding the final answer, but also for checking whether the cage clues are strong enough and whether the puzzle has a unique solution.
Counting every legal two-cell cage in a 6×6 — and a two-cell cage is always two adjacent cells, so its two values can never be the same — multiplication pins the pair down far harder than anything else. Of the 13 products a two-cell cage can show, 11 have only one possible pair: 85%. Addition manages 4 of 9, subtraction 1 of 5. The gap holds at 9×9 too, where multiplication forces 26 of 31 targets and addition only 4 of 15. When you are looking for a way in, the × clues are worth reading first.
Using the Solver as a Learning Tool
The best way to use a Calcudoku solver is not always to reveal every cell immediately. Use it as a study partner. Enter the puzzle, check that the cages are correct, and first look for the most constrained cages yourself. Single cells, large products, extreme sums, and simple divisions often provide the first real deduction.
When you get stuck, look for cages with very few possible combinations. A 48x cage in a 6x6 grid is much tighter than an open-ended sum. A 1- cage means two consecutive numbers must appear. A 2÷ cage limits the cells to pairs such as 1 and 2, 2 and 4, or 3 and 6. Once you recognize those patterns, you will need the solver less often.
Common Calcudoku Entry Mistakes
If the Calcudoku solver finds no solution, do not assume the puzzle is broken straight away. First check the entry. Was a cage border missed? Does one cage include an extra cell? Did 16x become 16+? Was a division sign entered as subtraction? One small local error can block every later combination.
Then check the grid size. A 5x5 puzzle entered as 6x6 uses a different range of numbers, so the cage targets no longer match. Imported JSON can also be stale if you edited cages after importing. Export again after major changes so the saved data and the visible grid describe the same puzzle.
What one wrong operator actually looks like
The entry mistakes above are led by "did 16x become 16+?" — so here is that exact mistake, on the same puzzle, with one symbol changed and nothing else touched.
That is the best case, because the solver tells you immediately. The worse case is an operator error that leaves the grid solvable — you get a clean answer that is not the one the setter published, and nothing warns you.
Importing and Exporting Calcudoku JSON
The JSON export is useful when you want to save, share, or continue a puzzle later. Instead of redrawing every cage, you can preserve the full structure: grid size, cage cells, targets, and operations. This is helpful for teachers, puzzle creators, and players who want to test several versions of a KenKen-style grid.
When importing, the structure needs to be complete and consistent. If an imported puzzle does not solve, first confirm that the data matches the visible grid size. Then check each cage one by one. The solver can detect mathematical contradictions, but it cannot know which number was printed in the original source.
What to Do If No Solution Is Found
Work systematically. Check single-cell cages first, then very small cages, then unusually high or low targets. Compare every cage shape with the source puzzle. If the entry is correct, the puzzle may genuinely be contradictory or may use a special rule outside the standard Calcudoku assumptions.
If the solver reports multiple solutions, the opposite problem is present: the clues are too weak. The puzzle needs additional constraints or a different cage layout. For puzzle authors, this feedback is valuable because a polished Calcudoku should be solvable and uniquely solvable.