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Overview
Arithmetic Grid icon AG

Arithmetic Grid

산술 격자

Fill the grid with unique digits while every cage matches its arithmetic target.

Sudoku-like deduction plus quick arithmetic—every cage you solve unlocks the rest of the grid.

Players: 1P Session length: 5-20 min
Logic PuzzleNumber Puzzle

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.

Controls

Mouse

  • Click a cell/element to select
  • Use the input UI (numbers/marks/lines) to apply
  • Right click/secondary action: mark or erase (if supported)

Keyboard

  • Number keys: enter value (if supported)
  • Backspace/Delete: clear (if supported)
  • Arrow keys/Tab: move focus (if supported)

Touch

  • Tap: select/enter
  • Long-press: mark/secondary action (if supported)
  • Use the on-screen pad/buttons to input

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

  1. 2004 Tetsuya Miyamoto invents the KenKen puzzle format.
  2. 2008 KenKen appears in The Times (London), helping it reach a wider audience.
  3. 2009 KenKen debuts in The New York Times.

Notable People

  • Tetsuya Miyamoto Invented the KenKen format (2004)

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.

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