How to play Calcudoku

Fill an N×N grid with 1 to N — no repeats in a row or column — so every cage hits its target using its operation. Also known as Mathdoku, KenDoku, Calcu-doku.

▶ Play Calcudoku ⊞ Open the solver ∑ Combination calculator

The rules

An N×N grid uses the digits 1 to N. Each row and each column contains each digit exactly once.
Bold outlines group the cells into cages. Each cage shows a target and an operation: + − × or ÷.
The digits in a cage must make the target with that operation. For − and ÷ the cage has two cells, and you take the larger number first (6 − 2 = 4, 6 ÷ 2 = 3).
A one-cell cage simply gives you the digit.
A digit may repeat inside a cage, as long as the copies are not in the same row or column (possible only in L-shaped or larger cages).

Playing Calcudoku on Puzzle Solvers

Choose a grid size and a difficulty, then press Generate Puzzle.
Click a cell and type a digit, or use the on-screen keypad. Notes switches to pencil marks.
Undo steps back; Force places one digit that has only one possible value; Check marks mistakes in red without giving away the answer.
Operators Hidden mode hides the operation in every cage — the hardest way to play.
Stuck? Send to Solver opens the same puzzle in the step-by-step solver. Send to Slate opens it as a board on the Slate whiteboard, to solve in front of a class.

Open the Calcudoku game →

Using the Calcudoku solver

① Build puzzle: choose the grid size, select cells to make a cage, then set its operation and target.
② Check: the solver checks every cell is caged and the puzzle can be solved.
③ Solve: watch it solve cage by cage, with every deduction explained.
Load the sample puzzle to try it first.

Open the solver →

A worked example

On a 4×4 grid, the first two cells of row 1 form a cage reading 3−. The only digits from 1–4 that differ by 3 are 1 and 4, so those two cells hold 1 and 4.

The other two cells of row 1 form a 6× cage. They must be the digits row 1 still needs — 2 and 3 — and indeed 2 × 3 = 6. Which way round each pair goes is decided by the columns: if column 1 already has a 4 lower down, the 3− cage reads 1, 4 from the left.

Strategies

Fill the freebies. One-cell cages are given digits. Write them in first.
List the few options. A two-cell 3− cage in a 4×4 can only be 1 and 4. A 2÷ cage is 1&2, 2&4 or 3&6 depending on the grid size.
Use large products. Multiplication cages with big targets have few factorisations — 60× in three cells of a 5×5 must be 3, 4 and 5.
Row and column totals. Every row adds up to 1+2+…+N. On a 6×6 that is 21, so cages that share a row tell you about the leftover cells.
Operators hidden mode. In the hardest mode the operation is not shown — check which operation can make the target with the cage's cells before you choose digits.

Common mistakes

Taking the smaller number first in a − or ÷ cage. The order is always larger first.
Assuming digits can never repeat in a cage — in bent cages they can, if they are in different rows and columns.
Forgetting that every row and column must still be a complete set of 1 to N.

Where it comes from

The puzzle was invented in 2004 by Japanese maths teacher Tetsuya Miyamoto as a way to build arithmetic and logical thinking. It is published under several names, including Calcudoku and Mathdoku.

Frequently asked questions

Are Calcudoku, Mathdoku and KenDoku the same puzzle?

Yes — the same rules under different names. This site has a cage calculator under each name: Calcudoku, Mathdoku and KenDoku.

Which number comes first in a − or ÷ cage?

The larger. A 2÷ cage of 3 and 6 means 6 ÷ 3.

Can digits repeat inside a cage?

Only when the cage is bent so the repeated digits sit in different rows and different columns.

What is Operators Hidden mode?

A harder mode in the Calcudoku game where cages show only the target — you deduce the operation as well as the digits.

How do I see every combination for a cage?

Enter the grid size, operation, cells and target in the cage calculator, or browse the cage combinations tables.

Keep going

All guides: How to play every puzzle and game.