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I've been reading several articles on difficult Sudoku puzzles and whether "guessing" is ever acceptable. The attached image shows the stage I reached using only deduction but at this point I could not see a purely logical correct next step. I eventually found the solution by "brute force" choosing one number from a pair and proceeding from there. (My first choice was the wrong one of course).

After posting this question I was introduced to a Sudoku solver, a fascinating insight into strategies I have never considered before. I could follow everything although whether I could manage it with just pen and paper is another matter. The only problem I have is at the step which requires use of the X-CYCLE. I cannot see how you decide that C9 is where we should try 4 as the potential solution. Once chosen I can see how the strategy works but why choose 4 in that Cell over 4 in any other cell?

A sudoku grid with theoretical numbers written on it

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  • $\begingroup$ @JLee I used that solver just now (with the original numbers, not the handwritten numbers) and it came back with "Very Hard Grade Overall Score: 251". Perhaps you entered a number wrong? $\endgroup$ Jul 26, 2022 at 15:08
  • $\begingroup$ According to this solver "Tough Grade Overall Score: 137 Comment: This puzzle could require strategies beyond its grade Note: a partially completed puzzle will have an easier grade than the original puzzle. Grading is most accurate if the number of clues is less than 30. $\endgroup$
    – JLee
    Jul 26, 2022 at 15:09
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    $\begingroup$ @IanMacDonald yep i did. Corrected now. I entered the numbers found so far, so that explains the difference between mine and yours. Does this solve path help? $\endgroup$
    – JLee
    Jul 26, 2022 at 15:15
  • $\begingroup$ Thank you for all your comments. The Solver is a fascinating insight into strategies I have never considered before. I could follow everythung although whether I could manage it with just pen and paper is another matter. The only problem I have is at the step which requires use of the X-CYCLE. I cannot see how you decide that C9 is where we should try 4 as the potential solution. Once chosen I can see how the strategy works but why choose 4 in that Cell over 4 in any other cell? $\endgroup$ Jul 27, 2022 at 9:11
  • $\begingroup$ @PaulFisher edit that comment/question into your question. Maybe someone well-versed in sudoku strategies will answer. $\endgroup$
    – JLee
    Jul 27, 2022 at 16:26

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For me, this one is easier to see if I start with simple alternation elsewhere.

Let's consider all the squares where 4 is still a possibility: sudoku board with remaining possible 4s highlighted

I can see that there are a number of rows and columns where I have 2 choices for where to put the 4, meaning I have a strong correlation there. For example if Row 3 Column 4 is NOT 4, then Row 9 Column for MUST be, and vice versa.

I'm going to choose red and yellow to color my squares. These do not (yet) correlate to making a choice about whether or not a particular square holds a 4, it just says that whatever is correct for that square, its partner must have the opposite. sudoku board with some squares highlighted either red or yellow

These are the only strongly linked pairs definite in this chain, but I can see that there is another chain possible, I'm going to color those orange and purple sudoku board with squares highlighted in red, yellow, orange, and purple

Now I can start thinking about which squares are at the intersection of these chains, in particular, I notice these guys sudoku board with colored arrows pointing at specific squares (the other intersections are either already solved, or not candidates for 4)

The square at the purple/ yellow intersection has too many inputs to be an easy check for if/then statements, but the red/orange intersection contributes a single input to each chain, so that's a good place to start checking.

Since it is at the intersection of 2 chains with strong connections on candidates of 4, I should first check to see if it can be 4. When I propagate that through the chains I have identified, I see that I get a contradiction.

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  • $\begingroup$ Many thanks for the explanation. It does make sense so I'll try to remember in future! $\endgroup$ Jul 28, 2022 at 7:47

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