Fill the grid so every row and column uses each number once and every outlined cage hits its target with the given operation. Puzzles are generated on the spot and checked to have exactly one solution.
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How to use the Calcudoku Math Puzzle
Pick a size, difficulty and operations, then press New puzzle. A 4×4 Easy grid is a good first game.
Select a cell and tap a number on the pad or type it. Each row and column must contain 1 to N exactly once.
Respect the cages: the numbers in each bold cage must produce the target in its corner with the shown operation (for − and ÷, take the larger number first).
Use Notes (or hold Shift while typing) to pencil in candidates, and read the cage helper under the grid for possible digit sets.
Check answers or take a hint when stuck. The puzzle is solved when every cell is correct.
Calcudoku rules and cage examples
Cage label
Cells
Meaning
Possible digits (4×4 grid)
3
1
Given number
3
7+
2
The two numbers add up to 7
3 and 4
1−
2
Larger minus smaller is 1
1&2, 2&3, 3&4
2÷
2
Larger divided by smaller is 2
1&2, 2&4
12×
2
The product is 12
3 and 4
6×
3 (L-shape)
The product is 6
1, 2 and 3 in some order
Subtraction and division cages always have two cells. Addition and multiplication cages can have any size, and a number may repeat in a cage only if the repeated cells are in different rows and columns.
Solving techniques
Row and column totals: every row and column of an N×N grid adds up to N×(N+1)÷2 (10 for 4×4, 21 for 6×6, 45 for 9×9) and multiplies to N! (24 for 4×4). If all but one cell of a row is inside known cages, the last cell is fixed.
Unique combinations: small sums and large products often have only one digit set. In a 6×6 grid, 11+ in two cells must be 5 and 6, and 30× in two cells must be 5 and 6.
Prime numbers: a product that contains a prime such as 5 or 7 tells you that digit must be in the cage.
Naked pairs: if two cells in a row can only be {2, 4}, no other cell in that row can be 2 or 4.
Parity: an odd sum over two cells needs one odd and one even number; an odd product means every digit in the cage is odd.
How the puzzles are made
Each puzzle starts from a random Latin square (rows, columns and symbols shuffled). The grid is split into random connected cages of the size allowed by the difficulty, and every cage gets an operation and the matching target. A solver that combines cage-combination filtering with row and column elimination then counts solutions; if it finds two, the cage that separates them is reshaped and the check repeats. Only puzzles with exactly one solution reach you.
Frequently asked questions
What is Calcudoku?
Calcudoku (also called Mathdoku, and similar to the KenKen puzzles) is a logic puzzle on an N×N grid. Each row and column must contain the numbers 1 to N exactly once, like a Latin square, and the grid is divided into outlined cages that show a target number and an arithmetic operation.
How do subtraction and division cages work?
Subtraction and division cages always have exactly two cells. Take the larger number minus or divided by the smaller one: a cage marked 2− could hold 3 and 1 or 4 and 2 in any order, and a cage marked 3÷ could hold 3 and 1, 6 and 2, or 9 and 3.
Can a number repeat inside a cage?
Yes, as long as the two equal numbers are not in the same row or column. For example an L-shaped 3-cell cage marked 5+ could hold 2, 1 and 2 when the two 2s sit in different rows and columns.
Does every puzzle have only one solution?
Yes. After generating a random Latin square and cages, the tool runs a constraint-propagation solver that searches for a second solution. If one exists, it changes the cages and checks again, so you only get puzzles with a single, logically reachable answer.
What is a good way to start?
Fill single-cell cages first, because they are given numbers. Then look for cages with only one possible digit set, such as 3+ in two cells (1 and 2) or a large product like 20× in two cells of a 5×5 grid (4 and 5). Use the rule that each row of an N×N grid adds up to N×(N+1)÷2.
What do the difficulty levels change?
Easy uses cages of up to two cells and more given numbers, Medium uses cages of up to three cells, and Hard uses cages of up to four cells with very few givens, which means fewer obvious starting points.
Is my progress saved?
Yes. Your current puzzle, entries, notes and best times are saved in your browser's local storage on this device, so you can close the page and continue later. Nothing is uploaded.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.