Friday Puzzle #107 - Better Know a Corral
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.