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logical thinking
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3904
Best Total: 9m 35s
Posted - 2008.03.21 05:30:54
highlander:

the middle blank should be 2

4 lines, 2 x's:

the middle blank should be larger than or equal to 2
Last edited by Jankonyex - 2008.08.19 11:32:52
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.03 02:52:36
First: Reposting Highlander Patterns so there are in this topic.
   - where ? can be anything, but a Blank square must be blank.

   6 Lines + 4 Crosses 

   6 Lines + 4 Crosses   
More specifically: one or both of the two middle "blank" squares in the first pattern can also be 2's
  - UPDATE: one of these 2 middle "blank" squares can be a 3 as well (but not a 1, neither a zero).
        - They can't both be 3's as it lead to an impossibility.     
        - Such a pattern with a 3 can be found in the "Highlander Patterns Are Gone" user puzzle series (#332-340).

They are derived from the basic Highlander 2 pattern, and can be extended diagonally indefinitely:
   8 Lines + 6 Crosses

Where one or more of the four middle blank squares can also be 2's or 3's.


Now here's are two Non Highlander patterns with a Square Block of 2's, (I don't think they were posted, but I could be wrong) which are not unusual, specially within explorations.  There are easy to figure out.     
                  --> Where Blank squares can be anything
  2 Lines + 2 Crosses     
  2 Crosses EDIT: + 1 Line (as MondSemmel correctly point out further down)
       - The input line can also be at the right of the top right 2.
       - One of the 2 output crosses is the result of a basic corner 2 pattern, but not the other.   


And a new (again I don't think it was posted before) Corner Highlander Pattern:
           - where ? can be anything, but a Blank square must be blank.
   8 Lines + 4 Crosses 

   - The ? square @c3r3 can't be a 1 because it creates an impossibility,
      neither a 3 because it would force an ambiguous position.
   - This pattern can be found in the "Highlander Patterns Are Gone" user puzzle series (#332-340).
Last edited by Naivoj - 2008.07.06 08:18:50
MadPAM
Kwon-Tom Obsessive
Puzzles: 735
Best Total: 29m 3s
Posted - 2008.07.03 07:42:17
Quote:
Originally Posted by naivoj
   - Can be found in the current "Highlander Patterns Are Gone" user puzzle series.
What do you mean by that? Googled for it but nothing came up...and since I am always eager to learn I'd like to know.
tobiwan
Kwon-Tom Obsessive
Puzzles: 3951
Best Total: 17m 44s
Posted - 2008.07.03 07:54:40
In the user puzzles section of the Archives on this site.

chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2008.07.04 19:47:59
Quote:
Originally Posted by naivoj
   

And a new (again I don't think it was posted before) Corner Highlander Pattern:
           - where ? can be anything, but a Blank square must be blank.
   8 Lines + 4 Crosses 

   - The ? square @c3r3 can't be a 1 because it creates an impossibility,
      neither a 3 because it would force an ambiguous position.
   - This pattern can be found in the "Highlander Patterns Are Gone" user puzzle series (#332-340).

This one can be found already here.

(btw. thanks once more for the extra puzzles, naivoj. Just returned from holidays and I have a lot of catching up to do. Guess I first try and solve the highlanders are gone series, then the botm of july and finally check whether I am alien after all...)
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.05 00:34:53
Quote:
Originally Posted by chairman
This one can be found already
Sorry, but there is too many topics to check. That is why I just reposted the extended highlander 2 patterns in logical thinking.

On this Corner Highlander Pattern, I think that your version has one unnecessary blank square (the corner), and mine has two. So more precisely it should be:

8 Lines + 4 Crosses 

The ? corner square can't be a 1 because it creates an impossibility, neither a 3 because it would force an ambiguous position.
   - But when memorizing a pattern you don't care about impossibilities.
   - So here we should just remember that the corner can be anything.

I am guessing you are solver #3 for user puzzles #337-340.

Btw, If you are an alien, don't forget to tell us from which star you're coming from   >-)      >-)            >-)
Tilps
Kwon-Tom Obsessive
Puzzles: 4411
Best Total: 20m 22s
Posted - 2008.07.05 00:51:04
The interesting thing about this scenario for me is that its also not a 0, which means that the only valid option is a 2. If its blank you can put the 2 in place.

I'm not sure any of the blanks are required...
Last edited by Tilps - 2008.07.05 00:54:29
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.05 01:07:45
Derived from the previous pattern, a new (I think?) non corner 232 highlander pattern:
EDIT: -----> this is a BAD pattern
   2 Lines + 2 Crosses

EDIT: I am now saying it is not a pattern after reviewing it following MondSemmel 2008.07.05 08:44:52 comment
"I knew the 232 highlander pattern (somewhat) in corner cases, but if it's usable in non-corner cases, that's interesting."

I got confused with the following Extended Highlander 2 Pattern with a 3:
  8 Lines + 8 Crosses

Last edited by Naivoj - 2008.07.06 09:33:16
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.05 01:48:48
Quote:
Originally Posted by tilps
I'm not sure any of the blanks are required...
Without these 2 two blanks it is not a highlander pattern anymore and you are only getting 4 lines as Chairman has explained here.

As a counter proof solve the following puzzle where one of the 2 blank squares was replaced by a 1:
Flash Link for this 4x4 puzzle A

Or this one where one of the 2 blank squares was replaced by a 2:
Flash Link for this 4x4 puzzle C

Last edited by Naivoj - 2008.07.05 03:03:24
chairman
Kwon-Tom Obsessive
Puzzles: 1395
Best Total: 17m 32s
Posted - 2008.07.05 09:51:44
Quote:
Originally Posted by naivoj
I am guessing you are solver #3 for user puzzles #337-340.
Wrong guess, I only solved up to #331 so far...
MondSemmel
Kwon-Tom Obsessive
Puzzles: 4071
Best Total: 7m 47s
Posted - 2008.07.05 12:44:52
Quote:
Originally Posted by naivoj
   2 Crosses.    The input line can also be at the right of the top right 2.
       - One of the 2 output crosses is the result of a basic corner 2 pattern, but not the other.
It should be 2 crosses 1 line in both cases, shouldn't it?

I knew the 232 highlander pattern (somewhat) in corner cases, but if it's usable in non-corner cases, that's interesting.
Tilps
Kwon-Tom Obsessive
Puzzles: 4411
Best Total: 20m 22s
Posted - 2008.07.06 04:13:44
Quote:
Originally Posted by naivoj
Quote:
Originally Posted by tilps
I'm not sure any of the blanks are required...
Without these 2 two blanks it is not a highlander pattern anymore and you are only getting 4 lines as Chairman has explained here.

Yeah, it was obvious I was spouting nonsense, chalk it up to avoiding highlander like the plague, my highlander skills aren't that good.
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.06 07:45:57
Quote:
Originally Posted by tilps
Yeah, it was obvious I was spouting nonsense, chalk it up to avoiding highlander like the plague, my highlander skills aren't that good.
I think you would call them "cheating pattern" instead of "highlander pattern"
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.06 09:00:45
Quote:
Originally Posted by mondsemmel
It should be 2 crosses 1 line in both cases, shouldn't it?
Agreed, I just wanted to see if somebody was paying attention
   - I made the correction in the original 2008.07.02 22:52:36 posting.

Quote:
Originally Posted by mondsemmel
I knew the 232 highlander pattern (somewhat) in corner cases, but if it's usable in non-corner cases, that's interesting.
This 232 non corner pattern is wrong: I add comments to clarify in the original 2008.07.04 21:07:45 posting.
Last edited by Naivoj - 2008.07.06 09:40:07
MondSemmel
Kwon-Tom Obsessive
Puzzles: 4071
Best Total: 7m 47s
Posted - 2008.07.06 19:34:52
Quote:
Originally Posted by naivoj
This 232 non corner pattern is wrong: I add comments to clarify in the original 2008.07.04 21:07:45 posting.

Ah, that makes sense. I already knew the updated pattern (the one you replaced it with), so I was surprised that there supposedly was an even more general pattern.
I rarely use any patterns involving more than 3 or 4 numbers, although they can be helpful at times.
My favorite pattern (which undoubtedly has already been posted - it's one of the most basic patterns) at the moment is this one:



It's very basic, but it sometimes (or rather, often - I use it all the time in bigger puzzles like your beasts) helps you get one line in cases like this one, by using the fact that there must be an even amount of lines going into every area.
One line. (And (EDIT: correction by Naivoj) four crosses, but those are only there because I didn't make a better example.)

Last edited by MondSemmel - 2008.07.07 11:37:17
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s
Posted - 2008.07.07 07:18:49
Quote:
Originally Posted by mondsemmel
... My favorite pattern (which undoubtedly has already been posted - it's one of the most basic patterns) at the moment ...
The Extended Highlander 2 Pattern with a 3 I posted yesterday is actually a combination of 2 patterns:
  - Your favorite pattern and the Extended Highlander 2 pattern.

I believe the 2nd position you posted gives 4 crosses (not 3).
Last edited by Naivoj - 2008.07.07 07:30:45
MondSemmel
Kwon-Tom Obsessive
Puzzles: 4071
Best Total: 7m 47s
Posted - 2008.07.07 11:36:30
Quote:
Originally Posted by naivoj
Quote:
Originally Posted by mondsemmel
... My favorite pattern (which undoubtedly has already been posted - it's one of the most basic patterns) at the moment ...
The Extended Highlander 2 Pattern with a 3 I posted yesterday is actually a combination of 2 patterns:
  - Your favorite pattern and the Extended Highlander 2 pattern.

I believe the 2nd position you posted gives 4 crosses (not 3).

Well, I screwed up even more than I thought, I guess^^.
What I meant was really that you can get one line even in a huge open section if this section contains an uneven number of lines (e.g. 7) and the only open section contains a 2 and a 3 in this form - then you can somtimes deduce that this pattern can't be applied here, therefore the line. The rest is all just due to a bad example by me.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 3904
Best Total: 9m 35s
Posted - 2008.08.19 14:17:46
4 lines, 2 x's; the middle blank should be larger than or equal to 2:




2 lines, 2 x's; no further deduction:




2 lines; connects each other through blanks near the wall:







8 lines, 4 x's; no further deduction:


Last edited by Jankonyex - 2008.08.19 14:18:58
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