KenKen (Calcudoku) Game

Fill the grid with numbers so that each row and column contains digits 1 to 4 without repetition. Respect the cage targets and operations shown in the top-left of each cage.

Puzzle
Time: 0:00
3+
7+
12×
1-
3+
3+
1-
7+

How to Play

KenKen, also known as Calcudoku, is a logic and arithmetic puzzle. The goal is to complete an N×N grid where each row and column contains the numbers 1 through N exactly once, while also satisfying the arithmetic constraints shown in each cage.

  • Each row and column must contain numbers 1 to 4 without repetition.
  • Each cage has a target and an operation; the numbers in that cage must produce the target.
  • Single-cell cages show a fixed value target.
  • Use Notes to pencil in candidates before committing a value.

Cage Operations Explained

Addition (+): All numbers in the cage add up to the target.

Multiplication (×): All numbers in the cage multiply to the target.

Subtraction (−): For a two-cell cage, the absolute difference must match the target, so both orders are valid.

Division (÷): For a two-cell cage, one value divided by the other must equal the target, so both orders are valid.

Single cell (=): The cage is fixed to the target value.

Strategy tips

  • Start with singleton cages (=): fill these fixed values first.
  • Scan rows/columns for near-complete lines to eliminate duplicates quickly.
  • For subtraction and division cages, test both orders (a − b and b − a) when listing candidates.
  • For × and ÷ cages, list factor pairs within 1 to 4 and rule out duplicates in the row/column.
  • Use Notes to track candidates and turn on error highlighting to spot conflicts early.

Example reasoning

In a 4×4 puzzle, a two-cell cage labeled 7+ can only be 3 and 4. A two-cell cage labeled 12× can only be 3 and 4 as well. Recognizing these forced pairs early helps you narrow down candidates across the whole row and column.

Common patterns

  • Sum cages close to min/max: e.g., in 4×4, 7(+) over two cells is usually 3+4.
  • Product cages with primes: limited pairs make deduction faster (e.g., 6 = 2×3).
  • Row/column uniqueness: if a number appears as the only candidate in a line, place it.

If you enjoy logic grids, try our Sudoku solver and helper too.