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new here. some questions
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.06 15:34:02
Hi there. Nice place you have here.

I started doing your puzzles, and find that I get stuck in most of them, even the easy ones. I hate trial and error.

So, do you find that the puzzles here can all (or mostly) be solved purely by logic? If so, I'm feeling dense... The puzzles over at puzzleloops.com are all solvable (to me). I can do their hard 10x10 puzzles in under 5 minutes. But here, I have trouble... I have found a lot of basic patterns, and patterns that may be not so basic (the diagonal 2s ending on 3s), but.. I'm stuck

Also, are there any windows programs you use to simulate puzzle loop situations? Can you recomend any? I've seen posts here with a lot of @ signs and stuff.. do you use a program to "see" those puzzles?

Finally, I read about a so called highlander situation, with the middle square having a 2, and blank on the sides, top and bottom, and 2 "x"s on a corner of the "2" square.

I've drawn it on paper and stared at it, and I can't figure it out. I always see 2 options, and no "must be there" lines.
If this is on a corner, where is the corner?

So, nice meeting you all
I'm so hooked on sligherlink...

cheers,

James.
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2007.06.06 17:28:16
Quote:
Originally Posted by xjames
Hi there. Nice place you have here.
Glad you like it too.
Quote:
Are there any windows programs you use to simulate puzzle loop situations? Can you recomend any?
Try  Loopy.
Quote:
I've seen posts here with a lot of @ signs and stuff.. do you use a program to "see" those puzzles?
That is a great mistery to me too.
Quote:
... I read about a so called highlander situation, ... If this is on a corner, where is the corner?
The highlander argument is nothing but applying that it is given that any puzzle has a unique solution ("There can be only one."). The most common pattern that uses highlander is probably

although it is not the first described here on the forum. Drnull, who was the first to post about it, thought at first sight that it was an obscure idea, but the idea can be applied almost every day. The black lines on the north and west sides indicate the top and left border of the puzzle. In earlier posts, this feature was not available yet, so the author had to tell which borders are involved. It is customary to leave the squares that have to be blank to apply the highlander argument blank and to label the squares that may contain a clue with a question mark.

If you look at the pattern, you might infer quickly two lines:
These two lines must be linked alongside the 2. At first sight, this can be done in two ways. However, suppose this were the local solution:Then there is a violation with uniqueness, since we can leave all lines as they are but the two just added, and lead the loop along the other side of the two:
Here, you use the assumption that the two blanks are blank. So, the latter path is the right one. Furthermore, there must be a reason that the first path is not part of a (the) solution. That reason is that the solution comes across the dot down right of the two. So, the pattern is complete if we add two more lines:
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.06 21:22:38
I get it.
So you're saying there will never be a case like

where the ? is either a 0 or a 1, cause it would violate uniqueness, right?

I guess I'll read more about uniqueness, and why it's a rule. (or is it just a rule here?)

Also, how did you get your images to show up as 2x2? I only get 3x3 and up...

and thanks!
Fgnn
Kwon-Tom Obsessive
Puzzles: 717
Best Total: 19m 46s
Posted - 2007.06.06 23:17:18
A more general form is that if above below and the sides are blank you can infer the same idea.


becomes

Para
Kwon-Tom Obsessive
Puzzles: 1911
Best Total: 19m 28s
Posted - 2007.06.06 23:46:02
Quote:
Originally Posted by xjames

I guess I'll read more about uniqueness, and why it's a rule. (or is it just a rule here?)

The idea behind these uniqueness deductions("highlander arguments") is that the puzzlemaker assures us there is only one solution to the puzzle. And this should be the case in any proper logic puzzle (besides optimization puzzles). So it should be applicable everywhere.
So as long as you know there is only one solution you can use uniqueness-based deductions.

Para
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.07 00:24:17
i get it. I can understand the logic that leads to the figure above, but I can't deduce the logic from the figure.. sucks being limited..

thanks!
Nis
Kwon-Tom Obsessive
Puzzles: 1989
Best Total: 22m 1s
Posted - 2007.06.07 00:35:37
Quote:
Originally Posted by xjames

So, do you find that the puzzles here can all (or mostly) be solved purely by logic?

If you are not talking about the "user puzzles" in the archivet then yes.
I will quite often use "Fix position" for speed (or out of lazyness), but I have tried not doing so on a series of archive puzzles, and only got stuck on very few of them (perhaps 1 in 20)
Please note that "trial and error" is also pure logic (known in other contexts as "reductio ad absurdum").

My suggestion for getting better: Solve more puzzles!. Loopy is a good help - it doesn't allow "fix position", so you are forced to do all deductions in your head (or try to revert manually). And even the hard puzzles are in general a bit easier than most puzzles here.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2007.06.07 03:43:51
Quote:
Originally Posted by xjames

The puzzles over at puzzleloops.com are all solvable (to me). I can do their hard 10x10 puzzles in under 5 minutes. But here, I have trouble...

Don't worry, even the easiest puzzles here are significantly harder than puzzle-loop.com. They are based on a wider range of patterns and require you to think further ahead to find local loops and contradictions. Solving Fridays and some Thursdays/weekends without Fix Position may well require visualization beyond the capabilities you've developed so far. For the moment, if you do Monday problems from the archives, you'll hopefully learn a bunch of patterns that don't crop up on puzzle-loop, and Tuesdays often have good examples of situations where the patterns don't quite solve it and you have to think just a little way ahead. Wednesdays pretty much always require reading ahead, sometimes reasonably deeply.

Quote:
Originally Posted by xjames

I have found a lot of basic patterns, and patterns that may be not so basic (the diagonal 2s ending on 3s), but.. I'm stuck

Well you're in luck: This forum has threads and threads full of patterns (particularly the Logical Thinking thread) and a sprinkling of hints on higher-level strategy as well.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2007.06.07 04:39:47
Quote:
Originally Posted by chairman
Drnull, who was the first to post about it, thought at first sight that it was an obscure idea, but the idea can be applied almost every day.

To be fair to drnull, his original pattern (diagonal 1-2-1) is pretty rare, but yeah, I don't think anyone realized how commonly we could make use of the argument until we got better at spotting them - maybe we didn't have the brainspace for it until other simpler patterns and strategies (loops,counting) had become more automatic. These days I'd estimate I use a highlander nearly as often as not for hard or big puzzles. I didn't realize how much I'd come to rely on them until I started trying to do the user puzzles without them. (more than once I messed up a user puzzle because of making this flawed assumption)

The idea reached a tipping point with the (more common, more helpful) 2-in-a-corner version after which it seemed (from their times) like _someone_ would notice every time there was a simple non-pattern highlander to be found. But funnily enough when I asked whether it was a good idea to post patterns (with that 2-in-a-corner pattern in mind), astrokath's reply was "yes, for example I used this uniqueness argument in today's puzzle", so I think the first discussion of non-pattern uniqueness occurred by complete coincidence right there in the same thread! (entitled Help)
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.07 04:46:12
indeed I've found some new stuff I hadn't seen before, like

it would never occur to me that I can put 4 'x' at the intersection of the '1's before. Now (2 days later) it seems pretty basic.. lol

(that one I found on my own)
Last edited by xjames - 2007.06.07 04:46:45
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2007.06.07 10:54:54
Quote:
Originally Posted by xjames

So you're saying there will never be a case like

where the ? is either a 0 or a 1?
Right.
Quote:

Also, how did you get your images to show up as 2x2? I only get 3x3 and up...
If you look at the code, it is not difficult to see how to adapt it manually:
[puzzle]2x2:2..q....:01000001000000000000000000_9[[/puzzle]
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2007.06.07 11:03:31
Quote:
Originally Posted by procrastinator
To be fair to drnull, ...
You state it more accurate indeed.
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.08 00:48:45
First effective use of the highlander thingy
I'm doing the archives... and came across this

In the lower left, I can go around the 1 in two ways, and it wouldn't make a difference, unless I go around the three in a different way. So, given Connor McCleod of the Clan McCleod, I do this:


right, right?
heheh
gadget1903
Kwon-Tom Addict
Puzzles: 325
Best Total: 23m 39s
Posted - 2007.06.08 04:32:51
Sorry Xjames, you found a different deduction!

There are two ways around the 3 which are both valid


This one is valid too


The deduction really is:

     You can't put two lines where the ?'s are, because you would have either 3 line ends, or 1 line end in the corner

     

     So you are forced to have these two lines


     This is still a technique required to solve harder puzzles, especially the big weekend ones.  It's not highlander, because there are two ways around the three (actually 4 but the deduction discounts 2) and the solution can be unique both ways.

Quote:
Originally Posted by fgnn
A more general form is
Given the following 3 positions (they are all possible if the solution is not unique), tell me what you see.  There are no lines or x's to deduce, there is just something not quite right.  I have replaced all the ?'s from the standard pattern with 2's to demonstrate:





xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.08 05:46:33
Well, I don't know if that's what you mean, but this is what I see:

I know that any diagonal of 2 such as

will always generate a succession of the pattern thusly

(it's kinda the easiest pattern to discover, I guess)
However, it doesn't mean that the opposite follows. if you have

you could have the other options you outlined above...

Now, what I see wrong is that the top right 2 in this case would be dependent on whatever's outside the 3x3 sample pictured here. And any puzzle which would create this:

such as

(sorry about the clumsy example) would not be a unique puzzle because of the middle '2'. And since this site only has unique puzzles, you'll never have that pattern. So you'll always have something outside the 3x3 sample that'll necessitate this:

such as



Is that it?

About my original puzzle, I'm kinda puzzled at what I was thinking.. I tried to recreate my logic, but it was faulty. I guess my brain was out of order...

Anyway, thanks for taking the time to help me figure this stuff out...
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.08 07:37:37
Highlander in practice, part deux

I'm doing this easy puzzle:


In it there's this section, where I can go around the rightmost '2' in two ways.
Let's call this following way, the "loose" way.

If I did this, and successfully finished the puzzle, it would mean the puzzle is not unique. Since the puzzle is unique, I should only be able to go around the '2' the other way. The restriction would become evident later on as I filled the missing parts. So, using Highlander logic, I do this:

and also this, to add the restriction in the only way possible:


clear as crystal
.... or, I'm way off my rocker in this late hour where brains ought to be playing in their private holodecks and not doing slave labor...
astrokath
Kwon-Tom Obsessive
Puzzles: 3086
Best Total: 13m 42s
Posted - 2007.06.08 08:04:09
You don't need to use highlander logic for that 2 - if you bound the 2 on the left and bottom sides, you won't be able to connect one of the loose ends to anything...

But in principle, yes, you've got the idea.
xjames
Kwon-Tom Obsessive
Puzzles: 1905
Best Total: 31m 41s
Posted - 2007.06.08 09:10:09
Quote:
Originally Posted by astrokath
You don't need to use highlander logic for that 2 - if you bound the 2 on the left and bottom sides, you won't be able to connect one of the loose ends to anything...

How do you mean? assuming I don't know anything else, I should be able to do this:

which, in this sample, is perfectly doable, but... Highlanderly wrong (can you say that fast many times over?).

Of course, looking far enough (outside the sample), one would see where whis would result in a conflict. But in that light, looking far enough, one could visualize the completed puzzle intuitively, and no complicated logic would be necessary.

Edit: well, you're right.. now I see the conflict very clearly only 3 line segments away... I'ts pretty evident... but sometimes you can't see the forest for the trees, or something...

But thanks.
Last edited by xjames - 2007.06.08 09:13:10
astrokath
Kwon-Tom Obsessive
Puzzles: 3086
Best Total: 13m 42s
Posted - 2007.06.08 10:05:17
For things like that, it often helps to go straight for inserting these lines:

...before worrying about whether the 2-loop points inwards or outwards.

When you have something like this:

...it resolves itself very obviously, as you've just found.
Last edited by astrokath - 2007.06.08 10:05:39

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