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I have managed to solve this puzzle thru guess and check technique, but I cannot figure out any techniques to elongate numbers and solve this puzzle methodically. Can anyone shed some light for me?

First of all, I see no puzzle, and secondly, I have no idea of what you mean by elongating numbers.

I use Hodoku which has a "Vague Hint" command which is very useful I follow a certain algorithm for all puzzles. I'm sure other people do the same. Maybe slightly different near the bottom of the sequence when more advance techniques are required because I usually only do the ones I know. Right now I don't know all the advance techniques so maybe people have other strategies. But for most easy and medium puzzles I think people pretty much follow the same sequence. There is a group of techniques I call the 7 base techniques (steps 1 through 7).

Step 1: Look for any Naked Singles. If found repeat Step 1.

Step 2: Look for any Hidden Singles. If found go back to Step 1.

Step 3-7: Look for Naked Pair, Locked Candidates, Hidden Pairs or Naked Double, Naked Triples, X-Wing. If found go back to Step 1.

Step 8: Look for Hidden Triples. If found go back to Step 1.

Step 9: If there are cells with lots of pairs then look for W-Wings. If found go back to Step 1.

Step 10-17: Look for Skyscraper, Empty Rectangle, 2-String Kite, Remote Pair, XYZ-Wing, XY-Wing, Swordfish, and X-Chains. If found go back to Step 1.

Step 18: Use Hodoku's Vague Hint command to see if the puzzle requires a technique you don't know. (then learn it, come back, and try to solve).

Step 19: Go back to step 1

The order you look for the advance techniques is not as important I don't think based on my current experiences. Step 18 is important because you can use it to help you learn new stuff. Once you know what you need to know, you can go learn it and come back and solve the puzzle. This algorithm is the basic idea of a general puzzle solving strategy.

If you are interested here is a video I did using the algorithm above. I do the next step in the puzzle every 5 seconds and cycle through the list above as needed:

https://www.youtube.com/watch?v=JGqYjBiEE_8

dxSudoku wrote:Step 9: If there are cells with lots of pairs then look for W-Wings. If found go back to Step 1.

Interesting! You prefer a w-wing over a skyscraper!? I'm sure that depends on the grid and how the candidates are presented. I agree that some of these pairs on a PM grid do stand out making it difficult to ignore them!!!

tarek

Hi dxSudoku,
I use Hodoku quite often to test the difficulty of my puzzles, and of course to see how it solves them.
I notice that apart from the basic techniques (single candidates, alignments, closed sets) and a few easy to see fish, it is the discontinuous loop or the continuous loop that he essentially uses to solve. I generally find these resolutions less efficient than the ones I do with TDP, because they don't make as many eliminations at once, which makes a lot of steps in the resolution.
This said Hodoku is an excellent reference to learn sudoku and to help oneself.
Sincerely
Robert

tarek wrote:

dxSudoku wrote:Step 9: If there are cells with lots of pairs then look for W-Wings. If found go back to Step 1.

Interesting! You prefer a w-wing over a skyscraper!? I'm sure that depends on the grid and how the candidates are presented. I agree that some of these pairs on a PM grid do stand out making it difficult to ignore them!!!
tarek

I'm not that intelligent. In practice Skyscraper's are easier to find than W-Wings. It's just I been giving a lot of help to people lately where W-Wing is the technique they get stuck on. I think you are right. Looking for Skyscraper first is probably the better approach.

I just helped someone with a puzzle that had a Skyscraper. It was pretty funny they responded in such a way like they did not believe me it was there. So I showed them this image:

https://imgur.com/aRhvkbW

Mauriès Robert wrote:Hi dxSudoku,
I use Hodoku quite often to test the difficulty of my puzzles, and of course to see how it solves them.
I notice that apart from the basic techniques (single candidates, alignments, closed sets) and a few easy to see fish, it is the discontinuous loop or the continuous loop that he essentially uses to solve. I generally find these resolutions less efficient than the ones I do with TDP, because they don't make as many eliminations at once, which makes a lot of steps in the resolution.
This said Hodoku is an excellent reference to learn sudoku and to help oneself.
Sincerely
Robert

Thanks Robert! If I understood it I would do a tutorial video on it. I will try to understand it. Right now I'm working on a tutorial video for Swordfish. I'm still working my way up to the harder techniques. I have a ways to go. Here is the last video I did which was on the XYZ-Wing which is probably pretty easy compared to what you are doing:

https://www.youtube.com/watch?v=IN71m6sXhqU&t=12s

At some point I want to do some videos on harder techniques but I'm not exactly sure what is worth doing. So your comment is very much appreciated. I will definitely try to learn your TDP method. Thanks!