What is a KenDoku cage?

A KenDoku cage is a bold-outlined group of cells with a target number and operation. The digits in the cage must satisfy the operation to reach the target.

How does this KenDoku calculator work?

Select your grid size, cage rule, number of cells, and target number. Valid combinations appear instantly. Use Filter numbers to exclude placed digits and Insights to see which numbers must or cannot appear.

Is KenDoku the same as Calcudoku?

Yes — KenDoku, Calcudoku and Mathdoku are the same puzzle. KenDoku is the name used by several European and independent publishers for the same arithmetic grid puzzle invented by Tetsuya Miyamoto.

Can numbers repeat in a KenDoku cage?

Numbers can repeat within a cage if they occupy different rows and columns. Toggle Number repetition to allow this when your puzzle permits it.

KenDoku Calculator – Find All Cage Combinations Instantly

Every Valid KenDoku Cage Combination for Any Puzzle

This KenDoku calculator instantly generates all valid number combinations for any cage. KenDoku (published by many newspapers and puzzle sites, also known as Calcudoku and Mathdoku) uses arithmetic cages on a number grid. Select your grid size, cage rule, and target to see every valid solution immediately.

Have a puzzle to solve? Use the step-by-step solver.

→ Calcudoku Solver

How to use

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KenDoku: rules, tips and more help

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.

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).

Tips

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.

The full guide, with a worked example and common mistakes: How to play Calcudoku.

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.

KenDoku Calculator – Find All Cage Combinations Instantly

Every Valid KenDoku Cage Combination for Any Puzzle

How to Use

Solving Strategies

What is KenDoku?

KenDoku: rules, tips and more help

The rules

Tips

Questions

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