Minesweeper is a single-player puzzle video game.
The objective of the game is to clear a rectangular board containing hidden "mines" without detonating
any of them, with help from clues about 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.
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.
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.
Some versions of Minesweeper will set up the board by never placing a mine on the first
square revealed, or by arranging the board so that the solution does not require guessing.
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, Yomp, and Cube.
Cube was succeeded by Relentless Logic, 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: In RLogic, the player must navigate through
the minefield, from the top left right angled corner to the bottom right right angled corner.
It is not necessary to clear all non-mine squares.
Also, there is no mechanism for marking mines or counting the number of mines found.
The number of steps taken is counted.
Although no high score functionality is included, players could attempt to beat their personal
best score for a given number of mines.
Unlike Minesweeper, the size of the minefield is fixed.
However, the player may still specify the number of mines.
Because the player must navigate through the minefield, it is sometimes impossible to win —
namely, when the mines block all possible paths.
The gameplay mechanics of Minesweeper are included in a variety of other software titles,
including: The mini-game Vinesweeper implemented into
the MMORPG RuneScape; in this iteration, the Minesweeper gameplay is given a large multiplayer
aspect and the "game board" adopts a continually resetting timer.
This allows for a never-ending game of Minesweeper where the skill is awarded assessed in points
rather than "game completion".
The PC game Mole Control; in this game, the minesweeper mechanic is integrated into a
puzzle adventure game based in a village called Molar Creek, which has been overrun with exploding
moles.
You play the local inventor's assistant, who is tasked with clearing the village of exploding
moles, and you can also take part in the Molar Creek Annual Mole Control competition in a
Time Attack Mode.
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, 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.
A minigame in FIFA 11 is a variation of Minesweeper.
The Voltorb Flip game in the non-Japanese releases of Pokemon HeartGold and SoulSilver
is a variation of Minesweeper and Picross.
The Coincentration minigame in Super Mario 64 DS and New Super Mario Bros. is similar
to Minesweeper.
Another derivative of Minesweeper is Tentaizu, which could be described as a Minesweeper
with some squares initially revealed, where the player doesn't reveal any squares, only
mark them, and whose objective is to mark all mines correctly.
Tentaizu puzzles usually have a unique solution.
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 interestingly it has been proven to be co-NP-complete.
Measuring board difficulty
The difficulty of a given minesweeper board is often measured using the 3BV measure.
Method The 3BV of a board is the total count of:
openings of the board, i.e. regions of orthogonally or diagonally contiguous squares having no
neighbouring mines, together with the immediately surrounding numbered squares
numbered squares that are not part of any openings.
For example, in the illustrated example, there is one opening and there are seven further
numbered squares, giving a 3BV rating of 8.
Equivalently, it is the minimum number of single clicks required in typical implementations
to reveal all of the mine-free squares.
3BV/s 3BV/s stand for 3BV per second.
Because the time that is needed to finish a Minesweeper board depends highly on the
difficulty of the board, it may not be the best way to compare records.
3BV/s on the other hand does consider the difficulty of the Minesweeper board as well
as the time needed to finish it.
Among the best Minesweeper players, 3BV/s records are not nearly as important as time
records, but they give a picture of how fast someone can play with regard to mouse-handling.
If flags are marked, it is possible to require fewer clicks than the 3BV of the respective
board.
Using only left clicks is called non-flagging whereas marking mines with right-clicks is
called flagging-style.
See also Board puzzles with algebra of binary variables
Trivia Commonly, the color code for the numbers is
blue for 1, green for 2, red for 3, purple or dark blue for 4, maroon for 5, cyan for
6, black for 7, and grey for 8.
Notes
References Adamatzky, Andrew.
"How cellular automaton plays Minesweeper".
Applied Mathematics and Computation 85: 127–137.
doi:10.1016/S0096-3003(96)00117-8.
Lakshtanov, Evgeny; Oleg German.
"‘Minesweeper’ and spectrum of discrete Laplacians".
Applicable analysis 89: 1907–1916.
doi:10.1080/00036811.2010.505189.
Kaye, Richard.
"Minesweeper is NP-complete".
Mathematical Intelligencer 22: 9–15.
doi:10.1007/BF03025367.
Further information available online at Richard Kaye's Minesweeper pages.
Blincoe, Robert.
"Windows Minesweeper is an 'offence to mine victims'".
The Register.
Retrieved 5 May 2009.
External links Constraint Processing Techniques for Minesweeper
[1] - Article by a lecturer in pure mathematics.
Minesweeper at DMOZ