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Overview

Arithmetic Grid

1 player · 5-20 min per session

Complete an N×N grid with digits 1–N so no row or column repeats, and each cage’s digits satisfy its target number.

Players: 1P Session length: 5-20 min

PuzzleNumber

Goal & Core Rules

Complete an N×N grid with digits 1–N so no row or column repeats, and each cage’s digits satisfy its target number.

Each row and column must contain the digits 1–N exactly once.
The grid is divided into outlined cages; each cage has a target (and often an operation).
Digits in a cage must combine (using +, −, ×, ÷ as applicable) to reach the target.
Use logic and constraints from both cages and rows/columns—no guessing required in well-formed puzzles.

Classic

Standard cages with targets and operations.

Calcudoku Style

A similar style often used when not using the KenKen trademark.

Expert KenKen Rules

The expert 6×6 board leans on stricter KenKen-style row/column uniqueness plus cage arithmetic deduction.

Controls

Mouse

Click a cell to select it
Use the bottom/right number pad to enter a value
Click the same cell again to clear the selection

Keyboard

Number keys 1-9: enter a value
0 / Delete / Backspace: clear the current cell

Touch

Tap: select or deselect a cell
Tap the bottom/right number pad to enter digits
Tap the hint button to reveal one correct number

Beginner Tips

Start with 1-cell cages (they’re fixed) and cages that can only form one combination.
Scan a row/column for missing digits before doing arithmetic-heavy cages.
Write candidates only where a cage and a row/column constraint overlap tightly.

Advanced Tips

Use Latin-square logic: once a digit’s positions are blocked in a row, the remaining spots become forced.
For subtraction/division cages, treat them as unordered pairs and prune using row/column conflicts.
When stuck, pick the most constrained cage to generate candidate sets, then propagate.

Origins & History

KenKen-style arithmetic grids were invented in 2004 by Japanese math teacher Tetsuya Miyamoto and are widely known under names like KenKen, Calcudoku, and Mathdoku.

Timeline

2004 Tetsuya Miyamoto invents the KenKen puzzle format.
2008 KenKen appears in The Times (London), helping it reach a wider audience.
2009 KenKen debuts in The New York Times.

Notable People

Tetsuya Miyamoto Invented the KenKen format (2004)

Sources

FAQ

Do cages always show an operation symbol?

It depends on the variant. Some formats imply the operation, while others show it explicitly.

Are repeats allowed inside a cage?

Rules vary by publisher, but row/column uniqueness is always enforced.

Is guessing necessary?

Well-constructed puzzles are intended to be solvable by logic without guessing.