Back after 13 years! Seeking advice 
Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.16 07:29:34 Hi guys,
I haven't visited this site for 13 years! Nice that it's still here! Disappointed to see that it's fairly quiet  I thought by now it might grown to be huge. IMHO Slitherlink is the best game ever!
I could never understand why Sudoku was so popular! It's nowhere near as good as Slitherlink!
Well, the last time I came here, I was a total newbie and could only solve the ones in Nikoli books, which, in retrospect, are ridiculously easy! LOL
Over the last 10 years, I have developed my skills, but I've only been playing Simon Tatham's "Loopy". (I assume members here are familiar with the program? It is excellent.)
If you don't mind me saying, I prefer the way Loopy works to this site  I like that all the sides are yellow by default, and when you "cross" them they are simply blank, instead of having crosses. I personally find that a better way of playing the game. In fact, when I come back here, my brain finds it really difficult to adjust to the style here!
Over the last 10 years I've gone from Loopy's "Easy" setting, up to the "Hard" setting. I can now solve the majority of "Hard" puzzles, but there are just a few that I still struggle with. Obviously, there are still some "rules" I haven't yet worked out.
So I thought I would ask here. If I were to post some images of partly completed Loopy puzzles, would that be OK? (Given that the puzzles aren't from this site?) And would anyone be able to give me any hints?
For example, here's one I just can't finish...

Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.16 07:37:27 I've simplified the above image and converted it to the KwonTom Loop style, which might be easier to understand for those not familiar with Loopy...
Last edited by Dizzy  2021.04.16 11:12:28 
pqg KwonTom Obsessive Puzzles: 6033 Best Total: 15m 37s  Posted  2021.04.16 15:00:09 Top edge of the top 2 must be an x, or else there'll be 3 lines entering the top right square. Rest of it falls out pretty easily from there. 
Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.16 22:13:25 Ah, of course! That is a rule I'd never considered before  three lines can never enter a square!
Thank you so much! I may be back to post some more here! 
qqwref KwonTom Obsessive Puzzles: 3134 Best Total: 13m 3s  Posted  2021.04.17 03:52:28 This idea is more general than just a single square: _any_ area must have an even number of lines enter it. In that square area, you know that 1 line enters in through the bottom right, and 1 line enters in through the bottom left; therefore, as pqg said, the top left, where a line could be, must be empty. 
Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.17 20:51:41 OK how about this one then...? What would be my next move?
Converted to Kwontom Loop style:
Blank:

Tilps KwonTom Obsessive Puzzles: 6370 Best Total: 20m 22s  Posted  2021.04.18 01:35:26 The bottom left quarter of that puzzle can be solved statically by 'advanced logic' I think ... (finding pairs of edges that have to be opposite or equal to each other and deriving a contradiction based on two edges not being able to be both set)  but really I would just move on to 'trial and error' stage. A single additional set edge down the bottom causes a contradiction, thus the opposite must be true. The remainder of the puzzle looks like it'll fall out after that. (Okay maybe not all the remainder of the puzzle  I can't see that far ahead.)
Last edited by Tilps  2021.04.18 03:34:51 
Tilps KwonTom Obsessive Puzzles: 6370 Best Total: 20m 22s  Posted  2021.04.18 01:40:11 To be more specific, the bottom left corner there is a 3, above that 3 there are 4 two's in a square. The top two of those two's both of their top edges can be proven equal by chain of 'these two edges must be opposite' (part of the shortest way to make the chain involves the even number of lines concept above, but it can be done otherwise). Since there is already a line between them, they can't both be set as it would make a tjunction in the loop, thus they must both be crosses.
Last edited by Tilps  2021.04.18 01:48:27 
Jankonyex KwonTom Obsessive Puzzles: 5601 Best Total: 9m 35s  Posted  2021.04.18 04:32:40
Quote: Originally Posted by Dizzy OK how about this one then...? What would be my next move? 
This can be solved by coloring or simply counting lines entering the left bottom region containing 8 cells. 
Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.18 11:03:38 Thank you all for your great advice, very much appreciated, and I will consider what you said!
As for the "trial and error" strategy which was mentioned, that is something I personally prefer not to use. There are many times when I can plainly see where the line needs to go, but I just don't feel personally satisfied unless I've solved a puzzle using "rules" 
Tilps KwonTom Obsessive Puzzles: 6370 Best Total: 20m 22s  Posted  2021.04.18 13:07:36 Trial and *error* isn't about seeing where the line should go. Its either about where the line can't go, or where a cross can't go. Seeing where the line should go is good for 'trial and success', which can finish a puzzle, but cannot prove a puzzle.
Ultimately the main practical difference between something like edgecolouring and trial based contradiction finding is whether you can notate it on the puzzle without needing an 'eraser'. (Although merging edgecolouring chains derived separately might make you want an eraser if you are doing them by hand ) In this particular case the trial is almost short enough that you can probably see the contradiction in your head without ever making any notations.
I've been through phases of being strong 'constructive logic is the best logic' proponent myself, it certainly is a personal choice. But it is also not exactly a well defined boundary. 
Dizzy KwonTom Noob Puzzles: 9  Posted  2021.04.19 20:15:02 OK, here are three more I couldn't do…
Any ideas, folks?
Puzzle 3
Puzzle 4
Puzzle 5

Tilps KwonTom Obsessive Puzzles: 6370 Best Total: 20m 22s  Posted  2021.04.20 00:22:20 I don't have any suggestions for 4. 3. I'm not sure how to convert it to 'constructive logic', but there is a trivial contradiction flowing from putting a cross on the bottom of the bottom most unsolved 2. It results in an early loop close. I'm not sure what to do next there though. 5. There is a lot of progress to be made with counting here. The right hand edge of the 2 below the pair of 3's in the top right must be a cross for instance. Once that is done there is another counting opportunity on the bottom left area. Which solves the bottom middle section. After that the top left may fallout  if there is anything slightly tricking remaining it might be the diagonal pattern of 2's in a corner (corner appears as part of solving above) leading to a 3, which is a cascade of 'same/opposite' pairing logic which solves both the twos completely and half the 3. 
pqg KwonTom Obsessive Puzzles: 6033 Best Total: 15m 37s  Posted  2021.04.20 00:30:45 3. 2 at B7 must have an X at the bottom or else there'll be a dead end line going into top right corner. That gives you quite a lot.
4. The 3 at C1 can't have its x on the left (because there'd be 3 lines going into top left corner) or the bottom (early loop closure with the 3 below it). That gives you a couple of lines on the lower 3, one of which interacts with the 3 along the bottom to force an x above it, and a line on the right of C1. Again, lots of straightforward progression from there. 
qqwref KwonTom Obsessive Puzzles: 3134 Best Total: 13m 3s  Posted  2021.04.20 01:01:20 My interpretations: 3) If the A7 corner area has no line, then the 3 at B6 must connect to both the A5 and C7 areas which is impossible. A bit trialanderror feeling but it works. 4) A5 is entered by a line on the topright, bottomleft, and bottomright corners, therefore a line must exit on the topleft corner (which is the top of A4). 5) B2 is entered by a line on the topleft, bottomleft, and bottomright corners, so there is a line exiting the topright corner, which crosses the 2 at B2 to leave a line on the top of A3. 
Sam KwonTom Obsessive Puzzles: 2250 Best Total: 24m 39s  Posted  2021.04.20 07:52:37 3)If there's a line between E3 & E4 that makes a corner pointing into a diagonal line of 2s, and creates a quick dead line 
Sam KwonTom Obsessive Puzzles: 2250 Best Total: 24m 39s  Posted  2021.04.20 08:04:26 And by "3)" I mean "4)"... 
Jankonyex KwonTom Obsessive Puzzles: 5601 Best Total: 9m 35s  Posted  2021.04.20 14:28:25
Quote: Originally Posted by Dizzy OK, here are three more I couldn't do… Any ideas, folks? 
3: count lines entering region A6B7 4: count lines entering cell A5 5: count lines entering region A7C7 Also any region with diagonal 322.. or 122.. pattern opening can have one line or cross deduced. I would suggest you to have a look at the logical thinking thread in this forum. Many (but not all) solving technique have been mentioned there. 
MondSemmel KwonTom Obsessive Puzzles: 6030 Best Total: 7m 47s  Posted  2021.04.20 16:00:43 Here is an old thread full of tips and strategies to solve puzzles. 
Jankonyex KwonTom Obsessive Puzzles: 5601 Best Total: 9m 35s  Posted  2021.04.20 20:31:04
Quote: Originally Posted by Dizzy ...As for the "trial and error" strategy which was mentioned, that is something I personally prefer not to use.... 
Puzzles can be solved using different strategies, you can introduce many different type of markings: line and cross, virtual numbers, coloring, junction types, highlander notes etc. and discover their rules. Many years ago I created a simple solver for myself using many different logical rules with no assumption and pattern recognition needed. I introduced markings like (even corner) vs (odd corner) to handle diagonal2 propagation and markings like (<=1 lines across a corner) vs (>=1 lines across a corner) to handle Lshape131 pattern. They are simple and I believe there are way more advanced rules for solving difficult pattern and puzzles without any assumption. The problem is, even something can be deduced without trial and error, using too much marking notes makes puzzle extremely difficult to mark and handle, plus the rules are usually computer friendly but low efficiency for human. Therefore trial and error plus observation is still by far the most useful tool for me to finish the task. If you are interested in finding other strategic rule not found on this forum, you probably need more work and insight, and discover your own. I have created some user puzzles with Jsl prefix. Those are written by hand and have quite simple and nice logical solution, with minimal to no long assumption needed. I believe you can get many insight during solving those puzzles. 