Keen

Keen (also known as KenKen or Calcudoku) is a logic and arithmetic puzzle. Played on a square grid, Keen combines the Latin square constraint of Sudoku with mathematical operations to create a uniquely challenging and satisfying brain teaser.

The objective of Keen is to fill the grid with digits from 1 to N (where N is the size of the grid) so that each number appears exactly once in every row and every column. In addition, the grid is divided into outlined regions called “cages,” each containing a target number and an arithmetic operation (+, −, ×, or ÷). The digits within a cage must combine—using the specified operation—to produce the target number. For subtraction and division cages (which always contain exactly two cells), the order of operands doesn't matter; the result is the absolute difference or the larger number divided by the smaller.

Keen demands both logical deduction and mental arithmetic. Unlike Sudoku, it often requires trial, error, and strategic insight to resolve ambiguous cages. The game generates puzzles of varying sizes and difficulty levels, ensuring fresh challenges for beginners and experts alike.

Fill in the grid with digits from 1 to the grid size so that each digit appears exactly once in every row and column, and all arithmetic clues are satisfied. (That is, the clue number in each bold-bordered box must be obtainable by applying the specified arithmetic operation to the digits in that box.)

To enter a number, click on a square to select it, then type the number using your keyboard. To erase a number, click to select the square and press Backspace.

To add or remove a pencil mark—indicating a number you think might belong in that square—right-click the square and then type the number.