I could be mistaken, but I think the folks in charge of the Examiner's "Games!" page decided to throw us a curve ball this weekend by featuring a "diabolical" puzzle for the Sudoku Classic (shown below). It's marked with 6 out of 6 stars, and about two-thirds of the way through working the puzzle, you reach a point where it becomes impossible to eliminate any more possibilities.
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You don't see many diabolical Sudoku puzzles in mainstream newspapers these days. (It tends to upset the so-called Sudoku purists who insist that all puzzles must be solved by logic alone and should never involve any guesswork.) There is a technique called "Ariadne's thread", which I have not mastered, that might address such situations-- but let's be honest here, it amounts to picking a cell with only two possible values, choosing one of those values and solving forwards from there until you either encounter a conflict or solve the puzzle. If you do find a conflict, you erase your way "backwards" to the point before you picked that value, and then you select the other option and progress forwards. Using a photo copier or different colored pencils makes this process much easier.