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I am trying to understand something that should be simple. I have a "easy" puzzle here, and immediately found where 8 should be in the middle box.

enter image description here

But in various Sudoku Apps, they show "candidates" to the user. And sometimes there is only one candidate available, essentially giving away an answer for free.

It says that 6 and 7 MUST be in those boxes, but I can't see why, it is not obvious at all to me.

Ideally I would rather disable 'candidates' and find such candidates myself. What strategy can be used to show, just by glancing, that 6 and 7 are the only possibilities in those boxes?

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    $\begingroup$ It is more obvious to me that the 4th cell down on the left must be a 7. I see from the Beastly answer that I overlooked the even more obvious. $\endgroup$
    – Weather Vane
    Sep 18, 2020 at 20:12
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    $\begingroup$ @WeatherVane I think the point here is not that the sudoku couldn't be solved (there's lots of numbers that can be easily placed) but why a naked single works and how to spot one $\endgroup$
    – Beastly Gerbil
    Sep 18, 2020 at 20:16
  • $\begingroup$ @BeastlyGerbil it perhaps depends on the sequence in which one applies the various techniques. $\endgroup$
    – Weather Vane
    Sep 18, 2020 at 20:19

1 Answer 1

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A naked single occurs when

all the possible candidates in a cell are listed, and there is only one value.

Basically, there will be numbers that rule out 8 of 9 possibilities. So for the 7 bottom right:

enter image description here

As all the others are ruled out in various ways, it must be a 7.

The strategy would be to look at a cell and go through 1-9 and see what is ruled out. If all but one number is ruled out, it must be that number!

Hope this helps!

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    $\begingroup$ Thanks, that explains it! I'll try to solve squares using this method $\endgroup$
    – bryc
    Sep 18, 2020 at 23:48
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    $\begingroup$ to put it another way, sometimes you know a 7 goes there because of where the other 7s are, but sometimes you know a 7 goes there because of where all the not-7s are. $\endgroup$
    – Kate Gregory
    Sep 19, 2020 at 14:00

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