You use trial-and-error behaviour to try to make sense of what you’re seeing and eventually you ‘get it’. Once your brain makes sense of what it’s being asked to do, you ditch the trial-and-error behaviour in favour of a more sophisticated problem-solving strategy.
In fact, a systematic trial-and-error search is a very effective way to find the answers to the puzzles if you’re writing a computer program to solve the puzzles. There are millions of permutations that can be created from each stencil set for each puzzle, but a computer can generate these permutations and identify matches in seconds. A computer can complete the game in seconds, achieving 100% time bonuses but 0% accuracy bonuses, using a systematic trial-and-error strategy.