Translation guide
A number-placement puzzle where you fill a 9×9 grid so that each column, row, and 3×3 subgrid contains all digits 1–9.
Referring to the game or puzzle called sudoku
Describing the activity of doing a sudoku puzzle
I bought a sudoku magazine.
I like solving sudoku during my commute.
More general 'do/play sudoku'. Less specific than 解く but perfectly natural.
I do sudoku when I have free time.