Battleship (logic puzzle)

Battleship, sometimes called Battleship Solitaire, is a grid-shading logic puzzle in which solvers must place 'ships' of various lengths within a grid based on numerical clues along the edges.

Background
Battleship puzzles were invented by Jaime Poniachik, founder of Argentinian magazine Humor & Juegos, and first appeared in the same magazine in 1982 under the name Batalla Naval (lit. 'naval battle'). At the time, it didn't gain enough popularity to become a consistent feature of the magazine, fading out of existence in 1982, before showing up again in 1987 after Humor & Juegos renamed itself to Juegos Para Gente De Mente. There, it found a more consistent place.

Outside of Argentina, it took until 1992 for the genre to find popularity when it was used as part of the first World Puzzle Championship in New York. By 1993, it was being published regularly in Games magazine, solidifying itself as a mainstay amongst modern logic puzzles.

The logic puzzle may have some roots in the, which first originated as a pencil and paper game in the 1930's and was published by Milton Bradley as a board game in 1967. The mechanism of placing a set of ships of known sizes on a rectangular grid is the same, though in the game players must guess the locations of the opponent's ships by calling out squares.

Puzzle Application
Similarly to the board game of the same name, a Battleship puzzle involves locating a series of 'ships' within a grid. In most cases, the types/sizes of ship are same as in the board game, but with a different distribution: 1 of length 4, 2 of length 3, 3 of length 2, and 4 of length 1. In order to determine their positions, solvers are given a series of clues in the form on numbers at the end of each row and column indicating the number of ship segments found in them.

Beyond the clues, there are some additional constraints to the placement of the ships. In particular, no ship can be adjacent to any other ship, even diagonally, and they must all be placed either horizontally or vertically (just like in the board game).

Often, Battleship puzzles will provide some Givens, indicating that certain cells contain either an unknown segment of a boat or just water.

Strategy

 * In a standard battleship puzzle, you can automatically mark all squares diagonal to a known ship piece as non-ships. (You can't mark squares adjacent unless you know the directionality of the ship, however.)
 * Long ships tend to be the most constrained in their placement. Consider the rows with numbers large enough and known non-ship positions to support such ships.
 * Large numbers in rows/columns are also helpful (for example, if you have a run of 6 squares, with 5 left, you know it splits either 4+1 or 3+2). However, remember that "1" can be a longer ship viewed in another direction, which may be required to satisfy adjacent rows or columns to the original one.

Played Straight

 * - While not a traditional Battleship puzzle, it still follows similar mechanics. Combined with a comprehensive rule set, this puzzle manages to be a relatively straightforward battleship puzzle without featuring a single battleship.
 * - The edge clues, like the flavortext explains, cover four separate battleship puzzles, with some overlap in the middles. As a result, submarines are used multiple times, but all ships still follow the usual rules: none of them are adjacent to each other, and everything is accounted for by the clues.

Notable Twists

 * - What would be a series of normal battleship puzzles is convoluted by the addition of a single, 3-length submersible vehicle. While submarines are usually treated normally for adjacency rules, these ships can actually appear next to or even directly underneath other ships, making them much more difficult to place.
 * - An upgraded version of the also-notable, minesweeper/battleship hybrid Shoal Patrol, this puzzle features many of the same mechanics as its predecessor, with one major difference. Rather than being 2D, this puzzle uses a single 7x7x7 cube filled with 4 4-length, 6 3-length, 9 2-length, and 4 1-length boats.