line counting is a technique that shows up a lot in akari puzzles, especially the more advanced ones. here’s an example:
here, we know that one of the green squares must lit, and same for the blue squares. at the same time, each of the two red lines can only have at most one light. # of lines is the same as the # of lights that need to be placed ⇒ each line must contain exactly one light. thus, we can place X’s on all squares on the red lines that are NOT the green or blue squares.