Using your higher order thinking skills, such as logical reasoning and hypothesising, to work out the solution abstractly is the most challenging way to solve the game and results in the highest score.
In this method, you use all the problem-solving skills at your disposal to work out the solution to the puzzle before entering it.
Once you get fairly good at performing a means-end analysis, you’ll probably find you start to learn to do it in your head. Holding all the information in your head, rather than clicking the buttons as you go along, is a much more challenging brain workout and is rewarded in the scoring system. In the early stages of the game where the puzzles are easy it’s quite straightforward to work out the answers abstractly.
As the puzzles become increasingly complex, it gets much harder to use abstract reasoning and most of us will resort to a means-end analysis or even trial-and-error behaviour, least for some part of the puzzle analysis.