Minesweeper (video game)
Minesweeper is a single-player puzzle video game. The objective of the game is to clear a rectangular board containing hidden "mines" or bombs without detonating any of them, with help from clues about the number of neighboring mines in each field. The game originates from the 1960s, and it has been written for many computing platforms in use today. It has many variations and offshoots. Some versions of "Minesweeper" set up the board (after the first click) so that the solution does not require guessing. "Minesweeper" for versions of Windows protects the first square revealed; from  Windows Vista onward, players may elect to replay a board, in which the game is played by revealing squares of the grid by clicking or otherwise indicating each square. If a square containing a mine is revealed, the player loses the game. If no mine is revealed, a digit is instead displayed in the square, indicating how many adjacent squares contain mines; if no mines are adjacent, the square becomes blank, and all adjacent squares will be recursively revealed. The player uses this information to deduce the contents of other squares and may either safely reveal each square or mark  the square as containing a mine. Gameplay. In "Minesweeper", mines (that resemble naval mines in the classic theme) are scattered throughout a board, which is divided into cells. Cells have three states: unopened, opened and flagged. An unopened cell is blank and clickable, while an opened cell is exposed. Flagged cells are those marked by the player to indicate a potential mine location. Controls. A player left-clicks a cell to open it. If a player opens a mined cell, the game ends, as there is only one life per game. Otherwise, the opened cell displays either a number, indicating  the number of mines diagonally and/or adjacent to it, or a blank tile (or "0"), and all adjacent non-mined cells will automatically be opened. Right-clicking on a cell will flag it, causing a flag to appear on it. Flagged cells are still considered unopened, and a player can click on them to open them, although typically they must first be unflagged with an additional right-click. If a player both left-clicks and right-clicks on an opened cell that has the number of adjacent mines equal to the number of adjacent flagged cells, all adjacent non-flagged  unopened cells will be opened. This is known as chording and in many variants it can be done by middle-clicking or by simply left-clicking. Gameplay. A game of "Minesweeper" begins when the player makes the first click on a board with all cells unopened. This click is guaranteed to be safe with some variants further guaranteeing that all adjacent cells are safe as well. During the game, the player uses information given from the opened cells to deduce further cells that are safe to open, iteratively gaining more information to solve the board. The player is also given  the number of remaining mines in the board, known as the "minecount", which is calculated as the total number of mines subtracted by the number of flagged cells (note that because of this, the minecount can be negative). The minecount is mainly useful when there are only a few remaining mines. Frequently when playing the game, the player encounters situations when they cannot deduce any further safe cells from the information given so they would need to make a guess. Some variants of "Minesweeper" ensure that the board can be solved without the need to guess. To win the  game, players must open all non-mine cells while not opening any mines. Flagging all the mined cells is not required. The "score" of the game is the time taken to complete it. The timer starts when the player makes their first click and ends when they make their last click. Common board configurations. Most variants of "Minesweeper" offer three default board configurations, usually known as beginner, intermediate and expert, in order of increasing difficulty. Beginner is usually on an 8x8 or 9x9 board containing 10 mines, Intermediate is usually on a 16x16 board with 40 mines and expert is  usually on a 30x16 board with 99 mines. Most variants also allow the player to play a custom board in which the player can choose both the dimensions and number of mines of that board. Example. Here is an example of how logic is used when solving a "Minesweeper" board. History. "Minesweeper" has its origins in the earliest mainframe games of the 1960s and 1970s. The earliest ancestor of Minesweeper was Jerimac Ratliff's "Cube". The basic gameplay style became a popular segment of the puzzle video game genre during the 1980s, with titles such as "Mined-Out" (Quicksilva, 1983 ), "Yomp" (Virgin Interactive, 1983), and "Cube". "Cube" was succeeded by "Relentless Logic" (or "RLogic" for short), by Conway, Hong, and Smith, available for MS-DOS as early as 1985; the player took the role of a private in the United States Marine Corps, delivering an important message to the U.S. Command Center. "RLogic" had greater similarity to "Minesweeper" than to "Cube" in concept, but a number of differences exist: The gameplay mechanics of "Minesweeper" are included in a variety of other software titles, including: Windows Minesweeper. First appearing in a game pack for Microsoft in 1990, a version of the  game called Microsoft Minesweeper was released as a standard part of Windows 3.1 in 1992. This saw an explosion in popularity and awareness of the game, with tech bloggers and journalists calling it "iconic", "famous", and even "the most successful game ever". Versions of the game continued to be included in standard installs of Windows up through Windows Vista in 2007, though in Windows 8 (2012) and later, it must be downloaded as an app from the Microsoft Store. Distribution and variants. Versions of "Minesweeper" are frequently bundled with operating systems and GUIs, including Minesweeper for IBM's OS/2, "Minesweeper  in Windows, KMines" in KDE (Unix-like OSes), GNOME Mines in GNOME and MineHunt in Palm OS. Many clones can be found on the Internet. Variants of the basic game generally have differently shaped minefields, in either two or three dimensions, and may have more than one mine per cell. For example, X11-based XBomb adds triangular and hexagonal grids, and "Professional Minesweeper" for Windows includes these and others. There are also variants for more than one player, in which the players compete against each other. The HP-48G graphing calculator includes a variation on the theme called "Minehunt", where  the player has to move safely from one corner of the playfield to the other. The only clues given are how many mines are in the squares surrounding the player's current position. The Voltorb Flip game in the non-Japanese releases of "Pokémon HeartGold and SoulSilver" is a variation of "Minesweeper" and "Picross". A logic puzzle variant of minesweeper, suitable for playing on paper, starts with some squares already revealed. The player cannot reveal any more squares, but must instead mark the remaining mines correctly. Unlike the usual form of minesweeper, these puzzles usually have a unique solution . These puzzles appeared under the name "tentaizu" (天体図), Japanese for a star map, in Southwest Airlines' magazine "Spirit" in 2008–2009. In the game "Minecraft", the 2015 April Fool's update "The Love and Hugs Update" added "Minescreeper". It is a near exact copy of "Minesweeper", except, instead of avoiding the mines, the player must avoid hidden Creepers. Computational complexity. In 2000, Richard Kaye published a proof that it is NP-complete to determine whether a given grid of uncovered, correctly flagged, and unknown squares, the labels of the foremost also given, has an arrangement of mines for which it is  possible within the rules of the game. The argument is constructive, a method to quickly convert any Boolean circuit into such a grid that is possible if and only if the circuit is satisfiable; membership in NP is established by using the arrangement of mines as a certificate. If, however, a minesweeper board is already guaranteed to be consistent, solving it is not known to be NP-complete, but it has been proven to be co-NP-complete. In the latter case, however, minesweeper exhibits a phase transition analogous to -SAT: when more than 25% squares are mined, solving a  board requires guessing an exponentially-unlikely set of mines. Kaye also proved that infinite "Minesweeper" is Turing-complete.