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Not always. There is a practically infinite number of grids that cannot be solved using even the most advanced techniques, including some that blur the line between logic and trial and error. A software and puzzle designer known as Ruud has compiled a list of 50,000 such puzzles, which can be found here: http://www.sudokuvault.com/top50000.zip Unfortunately, nearly all sudoku puzzles found in American publications are computer generated, so there is no guarantee you won't come across puzzles that cannot be solved logically, but a majority of them still can.

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Q: Given a Sudoku puzzle with only one right answer is it always possible to solve it without using trail and error?
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