Many Sudoku beginners treat Sudoku like a one-step-at-a-time linear game – first you find the right number for this missing space, then the next, then the next, and so on until you’re done. But a more advanced understanding of Sudoku shows that some of the most successful Sudoku players know how to solve Sudoku puzzles by thinking ahead.

Sudoku is a seemingly simple game that is actually built upon many levels of seemingly infinite complexity. Although Sudoku is played by millions of people throughout the world, only a tiny percentage of the most skilled Sudoku players ever rise to the level of playing in a Sudoku championship.

We wrote an article a while ago about Sudoku tips from World Champion Thomas Snyder, where we discussed some of the thought processes and habits of mind that American Sudoku master Thomas Snyder uses for solving Sudoku puzzles.