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The Sudoku puzzles in the graduate level are very difficult to solve. In order to solve the puzzles at this level, you need to master the advanced techniques, including locked candidates, naked subset (naked pair, naked triplet, and naked quad), hidden subset (hidden pair, hidden triplet, and hidden quad), x-wing, swordfish, xy-wing, and xyz-wing. You do not need to use all these advanced techniques for one puzzle, but you certainly need some of them. Also, you may need to apply the advanced techniques early in the game, when not many cells have been filled with digits. In that situation, it may be quite difficult to observe the patterns for some advanced techniques.