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 has been written for many computing platforms in use today. It has many variations and offshoots.

Overview

The player is initially presented with a grid of undifferentiated squares. Some randomly selected squares, unknown to the player, are designated to contain mines. Typically, the size of the grid and the number of mines are set in advance by the user, either by entering the numbers or selecting from defined skill levels, depending on the implementation. (In the Microsoft variant, this is limited to 30 times 24 with 667 mines.)

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.

In some versions, a question mark may be placed in an unrevealed square to serve as an aid to logical deduction. Implementations may also allow players to quickly "clear around" a revealed square once the correct number of mines have been flagged around it. The game is won when all mine-free squares are revealed, because all mines have been located.

Minesweeper for versions of Windows protects the first square revealed; in Windows 7, players may elect to replay a board, in which case the first square may no longer be protected.

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 game genre during the 1980s, with such titles 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:

Distribution and variants

Versions of Minesweeper are frequently bundled with operating systems and GUIs, including Minesweeper for OS/2, Minesweeper in Windows, KMines in KDE (Unix-like OSes), Gnomine 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 and 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.

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 Pokemon HeartGold and SoulSilver is a variation of Minesweeper and Picross.

A tentaizu puzzle with three stars (mines) already located and four remaining to be found.

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.[1] These puzzles appeared under the name "tentaizu", Japanese for a star map, in Southwest Airlines' magazine Spirit in 2008–2009.

In the game Minecraft, the 2015 April Fools "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.

Cary Huang made a version[2] that has different "modes" where each cell has vision over a different set of neighbours.

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.[3] If, however, a minesweeper board is already guaranteed to be consistent, solving it is not known to be NP-complete, but interestingly it has been proven to be co-NP-complete.[4]

Kaye also proved that infinite minesweeper is Turing complete.[5]

See also

Notes

  1. ↑ Minesweeper Puzzle Magazine, accessed 2017-02-07.
  2. ↑ "Timed Minesweeper". htwins.net. Retrieved 2017-03-28.
  3. ↑ Kaye (2000)
  4. ↑ Allan Scott, Ulrike Stege, Iris van Rooij, Minesweeper may not be NP-complete but is hard nonetheless, The Mathematical Intelligencer 33:4 (2011), pp. 5-17.
  5. ↑ Kaye, Richard. "Infinite versions of minesweeper are Turing complete" (PDF). Retrieved 8 July 2016.

References

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