Notes and pencil marks
Notes are leftover possibilities. They are not answers. Write them when a cell still has more than one legal option.
In Sudoku, switch on Notes and mark the digits that still fit. In Star Battle, a dot means this cell is empty; dots are notes, and the rules only care about stars. Binary Puzzle has no third mark: you cycle empty, 0, and 1.
Erase a note when it stops being possible. When one note is the last one standing, that is the fill.
You do not have to note every cell. Note the ones you are watching. Notes make forced moves visible. They are a help, not a score.
Play when you want a board. How to play Sudoku, How to play Star Battle, and How to play Binary Puzzle show how marks work in each game.