Difficulty levels are judged by the complexity of the techniques of deduction required to solve the puzzle: each level requires a mode of reasoning which was not necessary in the previous one. In particular, on difficulty levels ‘Trivial’ and ‘Basic’ there will be a square you can fill in with a single number at all times, whereas at ‘Intermediate’ level and beyond you will have to make partial deductions about the set of squares a number could be in (or the set of numbers that could be in a square). At ‘Unreasonable’ level, even this is not enough, and you will eventually have to make a guess, and then backtrack if it turns out to be wrong.The distinction between performing several levels of deduction at once, and guessing/backtracking seems like a subtle one to me--is it just a matter of what you hold in your head versus what you commit to paper or the screen?
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posted by smackfu at 1:13 PM on November 10, 2005