4
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How to solve the next step in this sudoku ? I tried X-wing, hidden pairs and many other popular techniques found here http://hodoku.sourceforge.net/en/tech_hidden.php

solve next step

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    $\begingroup$ What are the possibilities for each cell? $\endgroup$ – micsthepick Nov 24 '17 at 1:47
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    $\begingroup$ sudoku-solutions.com has a solver that has a "hint" option. $\endgroup$ – Chris Nov 24 '17 at 11:42
  • $\begingroup$ Perhaps, these types of puzzles must provide computers or no-computers tags explicitly. $\endgroup$ – Mea Culpa Nay Nov 25 '17 at 8:57
6
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Using the solver at http://www.sudoku-solutions.com/ (exact puzzle here) it suggested the following steps. Rows are lettered A to I from the top, columns 1 to 9 from the left.

  1. Column 1: 7 only appears in D1 and F1 so 7 cannot be in D2 or F2.
  2. Column 5: 9 only appears in D5 anf F5 so 9 cannot be in D4 or F4.
  3. Mid-right square: 9 only appears in D9 and F9 so 9 cannot be in H9.
  4. Row H: 7 only appears in H4 and H6 so 7 cannot be in I4 or I6.
  5. G5 and G9 can only be 3 or 8. Therefore 8 cannot be in G8.
  6. Column 9: 6 and 9 only occur in D9 and F9 so all other numbers can be removed from those cells.
  7. Column 9: 5 only occurs in B9 and C9 and so cannot be in C8.
  8. Columns 3 and 7: 1 can only occur in rows E and I. Therefore 1 cannot be in E4, I2 or I8. (xwing)
  9. Rows A, E and H: 5 can only occur in columns 3, 4 and 6. Therefore 5 cannot be in I3, D4, F4, I4, D6, F6, I6 (swordfish)
  10. I6 can now only be 8.

The rest at that stage falls out pretty easily though if you want more then the website linked will take you all the way to the end.

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  • $\begingroup$ But that won't lead to solving this particular puzzle. This is a listing of rules rather than logical deductions. $\endgroup$ – ibrahim mahrir Nov 24 '17 at 15:39
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    $\begingroup$ I have literally given the steps needed to make a logical deduction to find that I6 is 8. Can you tell me which of those steps above is guesswork? Candidates on there gives you only the most basic deductions (ie removes possibilities due to numbers in the same row/column/cell. You can then press hint and it will tell you the next way to eliminate candidates. sudoku-solutions.com/… is the link to this sudoko in case you've already closed the page. $\endgroup$ – Chris Nov 24 '17 at 15:50
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    $\begingroup$ @ibrahimmahrir: I will certainly not deny that guesswork can often be much easier than spotting things like xwings, swordfishes and some of the even more complicated ones. Thinking about it that does make your answer perfectly valid (upvoting it as we speak!) since more often than not that is the best way to proceed (I originally didn't upvote because I was looking down on a non-logical answer which was wrong of me). Sorry if I came off a little rude at any point. $\endgroup$ – Chris Nov 24 '17 at 17:20
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    $\begingroup$ Not at all! It is me who should appologize for doubting the powers of logical dedcutions hahaha. And I actually had a lot of fun (and headaches) going through those steps. $\endgroup$ – ibrahim mahrir Nov 24 '17 at 17:37
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    $\begingroup$ Thanks for the answer Chris and for highlighting the swordfish technique in this case ! I was almost sure that there should be a logical deduction approach $\endgroup$ – AnarKi Nov 24 '17 at 19:21
6
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What I usually do when I encounter such situation is:

Find a spot that only have two possiblities and fill it randomly with one possibility and keep playing untill it is solved or untill I encounter an error which then eleminates that possibility and makes the other possibility the correct one.

Using the method:

Notice the top left big square. There is only two small squares left blank, so each of those squares has only two possibilities, either 5 or 8. I randomly chose 8:
s1
and kept playing and after 6 fillings got an error
s2

So the next move will be:

s3

Final solution:

s4

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  • $\begingroup$ There are ways to do this through pure logical deductions without needing any guesswork. $\endgroup$ – Chris Nov 24 '17 at 12:07
  • $\begingroup$ That is what i actually did to solve it myself, but to me i would consider this as “cheating” not really but you know what i mean $\endgroup$ – AnarKi Nov 24 '17 at 13:47
  • $\begingroup$ So basically i wanted to see if there is an approach/techniques used at this point... this puzzle is supposed to be in the fiendish category $\endgroup$ – AnarKi Nov 24 '17 at 13:48
  • $\begingroup$ @Chris The pure logical deductions would be to do the above gueswork in your mind instead of on paper. $\endgroup$ – ibrahim mahrir Nov 24 '17 at 14:42
  • $\begingroup$ @ibrahimmahrir: The pure logical deductions are pure logical deductions, not guesses. I'm not sure how a guess, even in the mind, can be considered to be a logical deduction... I've added an answer now to explain these logical deduction. They are mostly simple deductions. Two of them are a bit harder than the others. but by now means impossible. $\endgroup$ – Chris Nov 24 '17 at 15:26

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