As you do the harder levels, it does require a very good memory. Even at the beginner level, a good memory can help you solve puzzles faster. I used to do the puzzles in about 20 mins, and then i tried to memorize missing numbers in each block. That brought my time down to an average of 7 minutes, with my fastest being 5 mins and 30 secs for a beginner level puzzle. The higher the level, the more missing numbers you have and that is when it becomes tough. There are a number of strategies to use while solving sudoku puzzles. The secret is to know which one to apply when and that comes with practice and training yourself on memorizing missing numbers. My personal goal is to bring my average down to 4 mins for beginner level puzzles before I even try a medium level. Going by my progress, it may take me a few months to get there, but it is a worthy goal in my opinion.