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04 February 2013 @ 06:18 pm
A new gift to Corral Fans: "Rubber Bands"  
I've spent at least a dozen hours in the past month arguing with people on "Corral" vs. "Cave" puzzles. It's caused a lot of stress, almost lost me one collaborator, and it continues to haunt me as others are sharing my puzzles in new settings and reviving old arguments.

I feel it is now some sort of dogmatically argued issue where there just will be no agreement between the two sides. Sure, mathematically the puzzle definitions are isomorphic, but Corral (originally "Bag" until renamed for the 2002 US Qualifying Test) is a loop puzzle, and Cave is a shading puzzle. The two just can't coexist in any solver's mind. I've found I clearly solve it as a shading style, with identical notation to most other shading styles, and therefore professionally I have chosen "Cave" as the name I use for this genre. No loops needed.

But, if "Cave" is controversial to you, we can reengage in the flame-war over here if you want. Instead I wanted to offer a gift to you, Corral fans. It seems you loopers just see the world differently. So I wanted to repackage my favorite shading puzzle style for you to better enjoy. It's a style I dare not name as you probably don't like it at all and I don't want to sour your new impression by bringing up memories of fully darkening cells or anything. But with an open mind searching for loops, I'm sure you'll love the new twist. It is a style I call "Rubber Bands."

Rules: Stretch some rubber bands over the posts in the grid, reaching vertically or horizontally only between posts. Each rubber band will surround exactly one given number, and each number in the grid will be surrounded by exactly one rubber band. The number indicates how many unit cells that rubber band surrounds. Rubber bands can touch at a post, but cannot share an edge and cannot overlap to both contain any square. Rubber bands cannot cross themselves. All internal (black) posts must either touch a rubber band or be inside a rubber band. Cells outside the rubber bands must form a single contiguous group.

I find it particularly challenging to solve Rubber Bands by just drawing the edges, but I also find particularly challenging puzzles to be very fun. So I hope you give this new style a try and solve it as the instructions intend. The new "internal post" rule is so much better than that 2x2 shaded square nonsense anyway. At least if you are being loopy.
nickbaxternickbaxter on February 5th, 2013 03:38 am (UTC)
Great new design. But I think the instructions would be clearer if you used shading instead of loops.
TH: pencilrpipuzzleguy on February 5th, 2013 06:35 am (UTC)
The sad thing is that it took me several moments to figure out what you were getting at.

Edited at 2013-02-05 06:36 am (UTC)
betaveros.wordpress.com on February 5th, 2013 06:45 am (UTC)
Heh, nice one. Although I think you may want to add a rule since it's not obvious to me whether rubber bands can still cross each other:
|3| | |
  | |
motrismotris on February 5th, 2013 02:22 pm (UTC)
Thanks - that is a necessary addition to the rules.
MellowMelonMellowMelon [wordpress.com] on February 5th, 2013 07:17 am (UTC)
There's at least one very nonobvious bit of parity logic that's possible in Yin-Yang, and it's far easier to see if you interpret it as a loop type instead.
motrismotris on February 5th, 2013 02:23 pm (UTC)
I think there is a lot to be learned by seeing how shading becomes loop and vice versa. Your point on Yin-Yang is well taken, but I don't think I've ever seen anyone recast that as a loop puzzle (yet).
(Deleted comment)
motrismotris on February 5th, 2013 02:25 pm (UTC)
Yes, that one bit of the instructions failed the field test and has been improved. There was a unique presentation description someone gave which was to start the grid out with a fully blackened outer loop. Then the end state has two contiguous groups, a "cave" inside a "border". In the absence of that I think I've now chosen to just clarify enclosed squares to mean they all are part of a connected group that touch a border.
motrismotris on February 5th, 2013 02:28 pm (UTC)
And I think I once saw (in Bulgaria) a Cave description where a no 2x2 rule was part of the definition of the puzzle. Unfortunately, it was for the non-shaded part (Blacken the rock of the cave to outline its tunnels. The tunnels may fork, but may not form loops. Each cell with a number indicates the number of tunnel cells, including the cell with the number, visible from that position. No part of the tunnel may have a size of 2x2. Grey cells are outside the tunnels.)

Canonicalization of puzzle rules, particularly across countries, is a very hard business. And debates about instructions can get far too long and pointless after awhile as consensus just can't exist if there are two different ways to view the world that are internally consistent.

Edited at 2013-02-05 02:33 pm (UTC)
affpuzz on February 5th, 2013 04:11 pm (UTC)
Yeah, the Denksel magazine put out by the fine folks at croco-puzzle.de also used (uses? I haven't subscribed for several years) the no 2x2 rule. It would always confuse me when solving other corrals (Denksel was a significant part of my introduction to logic puzzles, I didn't have a pre-existing knowledge of puzzle rules to fall back on); I'd try to use deductions that weren't valid under the more usual set of rules.
cyrebjrcyrebjr on February 7th, 2013 03:17 am (UTC)
A sarcasm tag. "A style I dare not name." Oh, man. Yeah, I see the joke.
Adam R. Woodzotmeister on February 10th, 2013 11:04 pm (UTC)
Someone who shall remain unnamed made this comment to me, and now I'm passing it on to you: You are a magnificently clever bastard, though of course you already know that.

I'm reminded of a game Ian Schreiber likes to describe called Three to Fifteen. Two players take turns claiming an as-yet unclaimed whole number from 1 to 9. A player wins as soon as (s)he claims a number that can be added to exactly two other numbers (s)he's previously claimed to total exactly 15. If all nine numbers are claimed and neither player wins, then... well, it's a cat's game. - ZM
motrismotris on February 10th, 2013 11:43 pm (UTC)
Interesting game. It seems the only way to win is not to play.
(Anonymous) on February 12th, 2013 12:54 am (UTC)
Have you seen the solution to this? (This was also passed on to me, but by a fellow math competitor)
motrismotris on February 12th, 2013 01:19 am (UTC)
I figured the *magical* correspondence between the 15 game and something else from my childhood right after reading it. It's a pretty cute connection.
(Anonymous) on February 13th, 2013 07:15 am (UTC)
Atleast based on my preferred style,this is a completely unneeded, and why are you being so generous, formulation.As in cave(oops corral) puzzles, I find shading as the only possible way I can find myself even being able to start.
Andrew Feistandrewfeist96 on February 20th, 2013 04:32 am (UTC)
So surely someone has written the dual post, right? Where we re-cast slitherlink as a shading puzzle, or something similar?

(I've gotten so far as to convince myself that at least it's feasible, but I have no idea how difficult it would be to people who are actually good at those sorts of things.)
motrismotris on February 20th, 2013 05:07 am (UTC)
I'm not tempted to help that cause much. See, my war on Corral is that the clues in a Cave puzzle are clearly about the cells (a 15 talks about the loop how?). The 0-3 clues in Slitherlinks are cleanly about edges of the loop. The best you can do in a shading sense I think is to talk about region identity (inside or outside) and say the numbered cells describe how many of the edge-adjacent cells belong to the other type of region.

A 4-X clue flip makes that much more natural and now gives a puzzle with only 1-4 clues. In that case, define the clue rules as "A numbered cell may be in the 'slithercave' or not; the value of the number indicates how many edge-adjacent cells are in the same cell type as the clued cell."
Grant Fikes: pic#111602625Grant Fikes on March 4th, 2013 10:27 pm (UTC)
For me, Cave vs Corral is mostly "I grew up on Corral for a few years and I'm used to that". I probably don't think about the loop very much when solving on paper, using X's in indicate outside cells and dots to indicate inside ones, and drawing lines between inside and outside as I go; I always draw the loop, because the Nikoli instructions say to, and I'm not going to be in a competition of any sort anytime soon. Even when constructing on paper, I draw the loop as in Corral, because I'm just used to it. Solving in Paint, though, I probably solve it more like Cave than Corral.

Also, regarding Rubber Bands, consider a 10x10 puzzle with 1 at R5C5 and 92 at R6C6.

Edited at 2013-03-04 10:35 pm (UTC)