How to Solve Calcudoku: Rules, Tips and Strategies for Beginners
Calcudoku is the arithmetic logic puzzle made famous by KenKen: a grid divided into cages, where every row and every column must hold the numbers 1 to N exactly once, and the numbers inside each cage must reach the cage's target with its operator — +, −, × or ÷. It takes sudoku's row-and-column logic and adds arithmetic, and once you learn to read the cages it's one of the most satisfying puzzles there is. Here's how it works and how to solve one step by step.
The rules in one minute
Fill every blank cell with a number from 1 to N, where N is the grid size (4, 5 or 6 on our generator). Every row and every column must contain each number 1 to N exactly once. The grid is divided into cages; each cage's numbers must reach its target: + sums them, × multiplies them, − takes the difference of a two-cell cage, and ÷ takes the exact quotient of a two-cell cage. Digits may repeat inside a cage — only rows and columns forbid repeats. Every calcudoku puzzle has exactly one solution.
How to read the cages
The thick lines mark the cages, and each cage shows its target and operator in the corner — "12+" means the cage's numbers add to 12, "6×" means they multiply to 6, "3−" means the two numbers differ by 3, "2÷" means the larger is twice the smaller. A cage with just a lone number is a one-cell cage: that number is simply given. On our calcudoku generator the cages are drawn with thick borders exactly this way, and you can type digits directly into the squares with instant checking. If you just want the plain rules without the strategies, our rules page has them all in one place.
1. Start with the one-cell cages
Every lone-number cage is a free clue — fill it in immediately. One-cell cages are the easiest given digits in the puzzle, and each one you place narrows the rows and columns that share it. Sweep the grid for them first; they're the footholds that unlock everything else.
2. Learn the unique cage combinations
Just like killer sudoku, many cages have only one way to reach their target. In a 4×4 puzzle, a 2-cell cage of "3+" can only be 1 and 2; "4+" can be 1 and 3 (or 2 and 2 — repeats are allowed in calcudoku); a 3-cell cage of "6+" is only 1, 2 and 3. Knowing these small facts cold means you recognize a cage's digits instantly instead of working out the sums by hand. The smaller the cage and the tighter the target, the more likely the combination is unique.
3. Use the rows and columns to decide
When a cage has two or three possible digit sets, the rows and columns pick the winner. If a 2-cell "7+" cage in a 5×5 puzzle could be 2+5 or 3+4, but the column already contains a 4 and a 5, only one arrangement survives. The arithmetic gives you the options; the sudoku-style rows and columns choose between them. This two-step — cage first, line second — is the heart of calcudoku.
4. Subtraction and division pairs
Two-cell cages with − and ÷ are the friendliest: they come from a small pool of pairs. "3−" means the pair is one of 1/4, 2/5, 3/6 and so on (in a grid large enough); "2÷" means the larger is double the smaller — 1/2, 2/4, 3/6. Because division here is always exact, the possible pairs are tiny, and the rows and columns usually decide between them quickly.
5. Remember: repeats are allowed inside a cage
This is the rule that trips up killer sudoku players. In calcudoku, a 2-cell "4+" cage in a 4×4 puzzle can legitimately hold 2 and 2 — a pair that would be illegal in killer sudoku, where cages never repeat. Only the rows and columns enforce uniqueness. Don't cross off a repeated digit inside a cage unless its row or column rules it out.
6. Pencil in the candidates
For each cage, jot its possible digit sets in the corner of the cells, then let the rows and columns strike out the arrangements that clash. Calcudoku grids are small and the cages give you most of the information, so tidy candidate marks turn the puzzle into a fast elimination chart rather than a scramble of arithmetic.
7. Avoid the classic mistakes
Four errors trip up beginners. First, forgetting that digits can repeat inside a cage. Second, treating a − or ÷ cage as if the order matters — the difference and the quotient work either way (larger divided by smaller). Third, filling a cage that reaches its target but breaks a row or column. Fourth, guessing instead of checking both constraints. Verify each finished cage and each finished line, and if you're stuck, the answer key shows how the cage arithmetic was meant to fit.
Practice with a printable calcudoku
The best way to learn the cage combinations is to see them over and over. Generate a fresh puzzle in seconds on the calcudoku generator — pick a difficulty and grid size, then print the blank grid or solve on screen with instant checking. Start on 4×4 easy, where addition and the unique combinations dominate, and work up to 6×6 hard, where multiplication, subtraction and division all appear. If you enjoy cage logic, killer sudoku is the natural next step — and if you like the arithmetic angle, our cross math guide has you covered.