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23 June 2011 @ 11:59 pm
Friday Puzzle #107 - Better Know a Corral  
This is part 1 of a "Better Know the USPC" preview series. The United States Puzzle Championship is expected to occur in August, so there will probably be about 8 parts to this series in 2011.

Type: Corral (aka Cave)

USPC History: Appeared in 2002, 2003, 2004 (as hex variation), 2007, 2008, 2x2009 (as Inside/Outside variation, and regular), 2010. Dave Tuller provided the first six of these; Nikoli the two most recent "regulars".

Notation tips: While the rules say "draw a single closed loop", I absolutely never draw a loop. I instead mark white spaces with straight lines as I would in the similar region-division types Four Winds and Nurikabe, and shade the other cells black. While shading in the ends effectively marks a clue as done, I sometimes find myself circling all spent digits so that it is easier to remember they are finished. I'd never do this on a Nurikabe where a surrounded island is clear, but I will do it to save time on a Corral.

Here is a solved form of my favorite Corral puzzle, the 2007 USPC edition. The answer entry is often more problematic than the puzzle, since it involves lots of counting, and my time is that to get the puzzle done AND write the full entry string on the page.

Strategies: There are a few main types of logic to learn. The first is very Four Winds-like, involving sizes of numbers and how they interact with nearby neighbors. Considering all the ways a (large) number can go, ask yourself if there are certain places it must go because of collisions with smaller numbers. Equivalently, with small numbers, there may be cells that must be unused (such as a 2 with a clue two cells adjacent). These marked used/unused cells start to seed the grid. Midway through, another type of logic will pop up: "escape" logic. Shaded cells must eventually see the border, and often the grid is bisected with only one of two routes out being possible. Whenever you put in a shaded cell, you want to think about all of its escapes. If all escapes must use a particular cell, shade in that cell. The final major thing to keep in mind is "this is a single closed loop" which gives an anti-checkerboard rule. Basically, if three of the four cells in a 2x2 square are shaded like a checkerboard already, you cannot color the fourth square to complete a checkerboard pattern. This would lead to an intersecting loop. My notation won't show me this loop problem, but knowing to avoid a checkerboard saves the day more often than not so make this an "instant" thing when you are solving.

Comments: Corral is probably my favorite logic puzzle type that I don't see enough of. And one I consistently mispronounce even though it is distinct from Coral which is a different kind of shading puzzle that also forms coral-shaped things. I guess drawing the loop would make one set of answers look more like Corrals, but still.

Corral may be the second most quintessential USPC puzzle after the Battleships at puzzle 1. It is often a 20-point or harder puzzle, so getting familiar with the type should lead to a fair number of comfortable points. I'm typically much faster than my USPC average on Corral, and have solved them every year except my rookie attempt in 2004 when the "hidden hex" surprise was on the Corral and I simply wasn't that experienced and found a reason to skip it (I also was not, at the time, going about the test intending to solve everything).

You can find a lot of practice in the "Blue" Tuller/Rios Mensa book (but not the "Orange", which also seems to be out of print). It might come as a surprise that Nikoli made the 2009 and 2010 versions. Why? Because this is a pretty rare Nikoli type. I would pay lots of money to see more Corral and essentially zero Yajilin and Hashi as path/region puzzles go from that provider. Unfortunately, "interesting puzzles" is not the market driver. You can find some nice Corral puzzles on the web (here's a pretty nasty one from MellowMelon that you can learn from), and I was fortunate enough to get a set Roger Barkan had made -- he uses the name Cave -- right after the last WPC.

Rules: Draw a single closed loop along the grid lines so that all the numbered squares are inside the loop. Additionally, each number equals the count of interior squares that are directly in line (horizontally or vertically) with that number's square, including the square itself.

MellowMelonMellowMelon [wordpress.com] on June 24th, 2011 05:50 am (UTC)
Oh, you appear to have caved.* I thought when the US team got into a light argument about the name of this puzzle at the WPC, you and Roger were both firmly committed to calling this Cave instead of Corral. Or maybe it's more the fact that this is part of a USPC series so you're using the other name?
(* = This word came to mind before the pun did, and I decided to go with it anyway. My apologies.)

On that note, Roger is apparently quite interested in these. Besides that very nice set he sent out, I also gave him my puzzle 70 - same one linked to - at the WPC when he mentioned how much he enjoyed these, and he was done in a few minutes. Nick Baxter, who is the one that puts one of these on the test every year, had quite a bit more trouble.

Anyways, the puzzle itself was really nice. The USPC (except 2007) and Mensa book ones were never a hit with me, as they tended to reek of computer generation/aid and did not flow that well. This one was much better and more consistent about the logic, with several tricks applied multiple times.

Also, didn't the 2009 USPC have a standard in addition to an in/out variation?
motrismotris on June 24th, 2011 05:52 am (UTC)
2009 did have two; I cut off my "find" too early....

I definitely would have sided for calling these Caves in another setting, and not just because of my pronunciation issues which make me seem stupid.

Edited at 2011-06-24 06:00 am (UTC)
(Anonymous) on June 24th, 2011 03:37 pm (UTC)
Great educational puzzle
... great example of using all three strategies:
escape needs, anti-checkerboard steps, and interaction of neighboring numbers (especially the diagonally connected 2's). Good stuff.


(Anonymous) on June 25th, 2011 04:35 pm (UTC)
Nikoli's name for this puzzle type is "baggu" (romanji) which translates to the Englisch word "Bag".
(Anonymous) on June 26th, 2011 03:08 pm (UTC)
There's something about this puzzle that's tripping me up. At least, I've now run into the same contradiction on two separate solves. Maybe third try will work.

(Anonymous) on June 26th, 2011 08:41 pm (UTC)
Re: tricky…
Third-and-a-half did it…
hagriddler on June 26th, 2011 08:47 pm (UTC)
Thanx for introducing me to a (for me at least) new and very interesting puzzle type. I am hooked instantly !
I first took on your puzzle and then went on with the MellowMelon puzzle.

Kudos to MellowMelon for constructing a very beautiful puzzle.
I can see why he advises not to use trial and error.
The logic interaction between the 3 strategies is very nicely used.
(Anonymous) on June 28th, 2011 02:44 am (UTC)
'I would pay lots of money ... "interesting puzzles" is not the market driver.'

However, I think you correctly identified the market driver :P
Krysdreamrose on July 18th, 2011 09:40 pm (UTC)
I was very happy to read that all the strategies you suggest I already used, it made me feel clever... but then rather disappointed since it wouldn't help my puzzle solving. But then went I went to do the puzzle I was getting quite stuck when I realized that yes, when I have 3 of a 2x2 square I use that strategy, I had never thought about when it meant when having a certain 2 of a 2x2 square, so it ended up helping me after all!! Thanks for keeping this puzzle journal. I'm hoping learning from you will help me get closer to where I thought I already was :o)