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Unsolved Sudoku

I have solved up to this point. How do I proceed without guessing?

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    $\begingroup$ What would you consider guessing? Inserting 1 out of 2 possibilities and seeing if its consequences lead to a contradiction? $\endgroup$ – A. P. Feb 15 '18 at 7:29
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    $\begingroup$ @A.P. Good question; it occurred to me a while ago that the only difference between "guessing" and not in Sudoku is one of degree. One could consider it a "guess" to put in a "3" and then immediately notice that there's a contradiction because you already have a "3" in that same row. $\endgroup$ – GendoIkari Feb 15 '18 at 15:53
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Consider the three circled squares. It's easy to see that the top left and the bottom right circles have the same number. But if they were both 3, that would deprive the bottom left box of any possible 3's. That was the most direct step I could find at least. enter image description here

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  • $\begingroup$ This is the hint I was trying to give, but was struggling to word it. I should have used pictures! $\endgroup$ – James Webster Feb 15 '18 at 7:54
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I don't 100% trust this logical device myself, but if the top-left cell is not a 2 then we have a paradox with the 4 and 8's against the Sudoku being valid (i.e. a single solution). So the top left cell is a 2.

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  • $\begingroup$ I always feel a little dirty when I use this sort of reasoning; because it relies on the assumption that the puzzle has a unique solution.. but it works! $\endgroup$ – GendoIkari Feb 15 '18 at 15:56

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