logical thinking 
kiwigeek KwonTom Noob Puzzles: 4  Posted  2006.05.18 05:17:13 Is there an enumeration of patterns and strategies for this game? Could somebody define the 'highlander' and 'uniqueness argument'? I seem to have hit a wall in my loopy development. ( 
foilman KwonTom Admin Puzzles: 1721 Best Total: 24m 8s  Posted  2006.05.18 07:45:41 I think most people have derived their own set of patterns to look for, so we've probably all got slightly different ways of doing it. There are a few topics on the forums here where we discuss some of them, so have a browse and it might help... but it's a lot more fun working them out yourself instead of just learning them from someone else. 
kiwigeek KwonTom Noob Puzzles: 4  Posted  2006.05.18 10:38:02 I didn't mean a list of the answers, but a list of what to look for, and figure out the answer myself. Like on one thread where people were showing a configuration and saying "Place two lines and one X" or whatever. 
Burko KwonTom Fan Puzzles: 89  Posted  2006.05.18 12:10:46 How about some of these people with quick times doing a step by step tutorial on one of the puzzles? Including a description of each and every move and why they did it? 
drnull KwonTom Obsessive Puzzles: 901 Best Total: 23m 25s  Posted  2006.05.18 12:30:37 Actually... it's a whole lot easier if you were to take a puzzle as far as you can get it, then screenshot it or something and post it to tinypic.com, then ask for what could be added.
Have you ever played the card game Rook? Or how bout the simple board game of Clue? Now, once you've played these games for awhile, you realize that there is a lot of strategies and techniques that your brain is doing. And after you have played for awhile, you start doing this all relatively subconsciously. Trying to explain what you do each step of the way is more difficult than taking a given position and explaining what you would do in that step.
Also, that keeps us from having to explain something that you already understand, as you've already completed the puzzle as far as you can (without guessing).
But that's just my (lazy) opinion. Maybe somebody else will have more motivation and do what you ask.
But... here's a couple of samples. All the old foggies know these, and you might know them all already too.
Note that on all of these, I'm not saying that blank squares are blank (unless specified, i.e., no highlander arguments here) and I'll try to keep things off of the walls so that corners of the puzzle and walls of the puzzle aren't "implied" (again, unless specified)
2 x's: 2 x's: 2 x's, 1 line: 1 x: 4 x's:
1 x, 1 line: 2 x's: 2 lines: 2 lines: 3 lines, 2 x's: 1 x: 4 lines, 5 x's: 1 line, 2 x's: 4 lines, 2 x's: (this is the highlander puzzle, there can be no numbers up, left, right, or below the two  diagonal is ok, though) 1 line, 2 x's: (this is derived from the highlander argument...) 4 lines, 2 x's: 2 lines: 2 lines, 3 x's: 3 lines, 2 x's: 4 lines, 4 x's:
4 lines, 1 x: 2 x's: 3 x's: 2 lines:
Last edited by drnull  2006.05.18 12:53:08 
astrokath KwonTom Obsessive Puzzles: 3093 Best Total: 13m 42s  Posted  2006.05.18 13:20:30
Quote: Originally Posted by drnull 2 x's:

Plus two lines as well there, unless I'm going completely mad. 
drnull KwonTom Obsessive Puzzles: 901 Best Total: 23m 25s  Posted  2006.05.18 13:55:31 Ahh, so there is. 
prj KwonTom Obsessive Puzzles: 2356 Best Total: 18m 20s  Posted  2006.05.19 00:12:54
Quote: Originally Posted by kiwigeek Could somebody define the 'highlander' and 'uniqueness argument'? 
The Highlander pattern first came up here. Procrastinator gives a hint in that thread, but you still get to figure out the solution for yourself. 
procrastinator KwonTom Obsessive Puzzles: 1083 Best Total: 12m 56s  Posted  2006.05.21 14:00:31
Quote: Originally Posted by drnull 4 lines, 1 x:

Is there an implied corner here? Otherwise I get:

drnull KwonTom Obsessive Puzzles: 901 Best Total: 23m 25s  Posted  2006.05.22 19:34:04
Quote: Originally Posted by procrastinator Is there an implied corner here? Otherwise I get:

Yeah, I guess I forgot to "specify" it there. 
kiwigeek KwonTom Noob Puzzles: 4  Posted  2006.05.23 06:18:04 Thanks! These will keep me busy for awhile. 
m2e KwonTom Obsessive Puzzles: 607 Best Total: 16m 43s  Posted  2006.05.23 09:01:55 sorry, but what do question marks mean? 
tzukanion KwonTom Addict Puzzles: 436 Best Total: 17m 39s  Posted  2006.05.23 12:16:39 Question marks mean it doesn't matter what number is in that square. 
procrastinator KwonTom Obsessive Puzzles: 1083 Best Total: 12m 56s  Posted  2006.05.23 16:16:30
Quote: Originally Posted by tzukanion Question marks mean it doesn't matter what number is in that square. 
Although we've been leaving the doesn'tmatter squares blank in most of our diagrams, so when you see question marks someone is probably trying to imply that the blank squares _have_ to be blank. 
m2e KwonTom Obsessive Puzzles: 607 Best Total: 16m 43s  Posted  2006.05.24 03:48:43 ah thanks. now i understand what you're talking about with the highlander argument! 
kiwigeek KwonTom Noob Puzzles: 4  Posted  2006.06.01 03:59:14 Hey, I finally had a chance to look through all these, and I totally don't get the question mark thing. Maybe I'm dense, but I can't figure out anything unless I know what number is in the square. 
Tilps KwonTom Obsessive Puzzles: 4411 Best Total: 20m 22s  Posted  2006.06.01 07:05:42 On the topic of strategies pretty much everything I do can be reduced down to: 'Trying both on and off for an edge and following simple rules from the resultant situation  if you find a contradiction, the other option is chosen, if you don't find a contradiction you can keep any common aspects of the two situations'
Whether this is enough to solve most puzzles is dependent on your list of simple rules. For some puzzles you have to choose the above process as a simple rule. (which makes it recursive  my sudoku program found 1 in a million puzzles required nesting the above process within it self, for looptheloop i've found its much more common, which probably indicates that my currently programmed set of simple rules is too incomplete.)
Categories I have are...
The basics: Trivial intersection rules to ensure either zero or 2 lines for every intersection. Trivial cell rules to satisfy number. Not closing the loop too early.
Locked edges (two edges which must have the same state either filled or x'd): locked on a 3 gives 2 edges locked on a 1 gives 2 x's Anything in a corner gives locked. ...
Antilocked edges (two edges which must be different states): Antilock on an intersection with a line coming into it puts crosses on the other edges. 2 edges on a 3 gives antilocked. ...
Locked edge/antilocked edge inference: Locked/antilocked on a 2 gives locked/antilocked on the other two edges. Antilocked on an intersection gives antilocked on the other 2 edges in the intersection. Locked on an intersection, gives locked on the other 2 edgs in the intersection. ...
Colouring, which is the concept of locked/antilocked generalized, and has many things it can do, but i haven't enumerated them all yet. Colouring could actually be called numbering; locked edges have the same number, antilocked edges are negative of each other  but you can do the same effect with colours.
I never use highlander, although I have found a couple of occasions where I could use it to save time, I consider it to be cheating. The solver should be verifying the puzzle is solveable while solving, highlander bypasses this.
Last edited by Tilps  2006.06.01 07:07:46 
kiwigeek KwonTom Noob Puzzles: 4  Posted  2006.06.01 07:26:11 Thanks. I think I'm using everything you said. However, I try to avoid trying possibilities and use patterns instead. I'm getting frustrated right now because I can't see any patterns in my current puzzles, and I just keep trying one thing after another to make slow progress. Argh. 
Tilps KwonTom Obsessive Puzzles: 4411 Best Total: 20m 22s  Posted  2006.06.01 07:28:26 Patterns are just trying possibilities, they are just skipping the step of actually trying the possibilities after you work it out the first time. 
foilman KwonTom Admin Puzzles: 1721 Best Total: 24m 8s  Posted  2006.06.01 07:56:59 Another very important strategy in some puzzles, that I don't think has been mentioned in this thread yet, is the "number of lines going into an enclosed area" rule. If there's an area of the board with just a few ways in/out, then you can often solve it by just ensuring that only an even number of lines can get into it. I use this a lot, but it can sometimes be difficult to see suitable areas to apply the rule. 