# Corral

Corral, also called Bag or Cave, is a path-drawing logic puzzle in which solvers must fill in a loop along the perimeters of cells in a grid so that numbered clues properly indicate the number of cells visible from their position.

## Background

Corral first appeared in Puzzle Communication Nikoli, volume 60. The genre was invented by ゲサク ("Gesaku") with the title of バッグ, which means "bag". The genre was originally presented as a loop puzzle.[1]

Closely related genres to Corral include Kurodoko/Kuromasu (instead of a loop, shade squares in a "dynasty" formation instead) and Canal View.

## Puzzle Application

Corral puzzles are usually presented fairly minimally, usually only as a blank grid with some cells containing numbers. The goal of the puzzle is to create a 'corral' that contains all numbered cells and satisfies the constraints set by them.

The rules for solving a corral are as follows:

• The perimeter of the "corral" must be continuous. No breaks, no crossing.
• Numbers indicate the number of cells a particular can "see", in each of the cardinal directions, including the cell they are on.
• All numbers must be inside the 'corral'.

Visually, a Corral puzzle may appear very similar to a Slitherlink puzzle. A good way to tell them apart is that Slitherlinks can only contain number 0-3, while Corral can have any number from 2 to the sum of the dimensions of the grid minus 1.

### Variants and similar genres

In Kuromasu (also known as Kurodoko), shade cells to create a single unshaded region. The loop constraint is relaxed, so shaded cells do not need to reach the border of the grid. Instead, shaded cells may not be adjacent. Clues still count the number of visible unshaded cells.

One common Corral variant is Product Corral, where the number of visible unshaded cells horizontally is multiplied by the number of visible vertical ones.

In Canal View, shade cells to create a single shaded region. (The loop constraint is relaxed.) Clues must be unshaded; instead of counting the number of unshaded cells a clue can see, instead they count the number of shaded cells in any adjacent runs of orthogonal directions. There is additionally a no 2x2 shaded cell rule.

## Strategy

• A common reformulation of the loop is to consider the puzzle a shading puzzle instead, with the conditions that all shaded cells must be able to "escape" to the edge, and all unshaded cells are connected. (That is, consider which cells are inside versus outside the loop.)
• Under these rules, one very common pattern to avoid is the checkerboard (also known as a Battenberg) - you cannot make a 2x2 region with two unshaded and two shaded that are diagonally apart from each other. This follows because it would make a loop crossing, though you can alternatively derive this topologically as well.
• Clues along the edge, especially larger numbers, are good places to start, as they only have three directions to consider. If a number is larger than the grid size, then you can mark cells in this direction
• It's also generally useful to consider how many cells in a given direction (say, horizontal) a given clue is allowed to extend. If there is another relatively smaller clue, then that can serve to limit this.
• On the other hand, small clues can serve to limit connectivity and force the interior of the loop to escape in certain ways.

## Examples

• Chimera (MITMH 2008) (web) - Like the title says, this was a logic puzzle chimera, combining two genres into one. In this case, the given puzzle can be solved both as a Corral puzzle and a Nurikabe. While they don't interact during solving, the fact that the grid serves a dual purpose is unique.
• Cactus Ranch (MITMH 2020) (web) - The meta for the Cactus Canyon round, this puzzle combined answer-placement and a Corral puzzle. Numbers in the grid serve two purposes: they can be used to solve the Corral puzzle, but can also be used to place the answers. Each number is the centerpoint for an answer, where that answer can be placed in reading order within all of the cells visible by that number.