KenKen, which starts in The New York Times today next to the crossword puzzle, is a new numerical logic puzzle from Japan. The name means loosely “cleverness squared.”

KenKen shares some properties with sudoku. Each is a pure logic challenge in which numbers are filled in the squares of a grid. Unlike sudoku, though, in which the numbers act solely as symbols (letters or pictures would work as well), KenKen requires arithmetic.

The rules are simple: Fill the grid with digits so as not to repeat a digit within any row or column, and so the digits within each heavily outlined box (called a cage) go together using the arithmetic operation shown to make the target number indicated.

Two new KenKen puzzles will be presented in The Times each day from Monday through Saturday. The first is a four-by-four-square puzzle that increases in difficulty from easy to medium as the week progresses. The second is a six-by-six-square puzzle that goes from medium to hard.