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Minesweeper is a single-player computer game. The object of the game is to clear a minefield without detonating a mine. The game has been rewritten for nearly every system platform in use today. It is most famous for the version that comes with Microsoft Windows. This version credits Robert Donner and Curt Johnson as its creators, starting in 1981, but the game's origins can be traced back to Cube in 1973. The Game
History The earliest known ancestor of Minesweeper is Cube, found in the PDP-11 program library catalogue and credited only as "CONVERTED TO RSTS/E BY DAVID AHL, DIGITAL". * Cube was played in a 3x3x3 cube with 5 mines, where the player had to find their way from one corner (1,1,1) to the opposite corner (3,3,3). The player entered the co-ordinates of the next square they wished to explore. If the target was more than one square away or there was a mine there, the player lost. No information about the number of surrounding mines was given. Cube was succeeded by Relentless Logic (or RLogic for short), by Conway, Hong, and Smith, which was available for MS-DOS as early as 1985. In RLogic, the player is a private in the United States Marine Corps, delivering an important message to the U.S. Command Center. RLogic is more similar than Cube to Minesweeper in concept, but a number of differences exist: One connection between RLogic and Minesweeper appears to be Tom Anderson's mines, written in 1987 for the Sun workstation. * Tom wrote the game after a few minutes watching colleagues play RLogic. Mines added the ability to mark squares as safe or containing a mine by using the other two buttons on the mouse. From there, the final step to today's Minesweeper was to change the objective from navigating the grid to finding all the mines, removing the player from the grid in the process. Patterns There are many patterns of numbered squares that may arise during a game that can be recognized for allowing only one possible configuration of mines in their vicinity. In the interest of finishing quickly, it is often easiest to process the known patterns first, and continue on with the uncertain parts later. This is especially important if a guess is required (see below), because if the guess fails, all efforts spent on other parts of the board will be lost. In the advanced levels, a user may occasionally find the number eight when revealing a square. In this case, all of the surrounding squares contain mines. The number three placed against a flat "wall" (always with adjacent twos on the wall) indicates three mines in a row, with the center being at the number three. In a wall (no mines next to the side opposite the wall), where a two is beside a one, there will be a mine by the corner of the two that is away from the one. Many longer patterns can be derived from this one, including some of the following. In a wall where a two appears between ones, the center square can be opened to find a number, and the two squares touching the ones will contain the two mines indicated by the two. The reason this makes sense is because if the mine were to be placed over the center square, you could not find any other mines adjacent to the "two" square because then one of the "one" squares would be touching two mines. This may not be true, however, if the numbers adjacent to either of the ones are numbered three or higher; nevertheless, on open walls of cells, the pattern holds. Where there is a row of twos by a wall, four twos with ones at the ends means that the mines are beside the two middle twos, and beside the ones adjacent to the twos; five twos in the same setting means that all twos except the centermost two are beside mines. These patterns are like extended versions of the patterns where one or two twos appear between ones, and the mines are located by the same principles as with those shorter patterns. Two twos on a wall of cells perpendicular and adjacent to a border of the minefield guarantee that the adjacent cell on the border, and the next one up the wall, are mines; this is because it is the only possible way for the two on the border to have two adjacent mines. Two ones on a wall of cells perpendicular and adjacent to a border of the minefield guarantee that the third cell from the border is clear; this is because exactly one of the first two cells must be a mine, which satisfies the second one. In a wall of ones where one cell beside the wall has been cleared to reveal a one, the three cells on the far side of the cleared cell are also clear; this is because one of cells adjacent to both the wall and the cleared cell must be a mine, which satisfies the one in the cleared cell. Not always solvable without guessing
NP-completeness Because of Minesweeper's relation to mathematics, it is mentioned in the Clay Mathematics Institute's unofficial description of one of the Millennium Prize Problems, namely that as to whether complexity class P equals that of NP: the P versus NP problem. In 2000, a paper detailing the proof that Minesweeper is NP-complete was published *. Mine probabilities are not enough
Measuring board difficulty
History of 3BV Stephan Bechtel is supposedly the first person to count the minimum number of left clicks that are needed to solve a Minesweeper board. In June 2002, he wrote about this method in the official Minesweeper guestbook. Soon thereafter, Benny Benjamin coined the term 3BV to describe this method. During the next two months, Yoni Roll and Benny Benjamin programmed a tool named "Minesweeper Board Reader", which analyzes screenshots of Minesweeper boards and as a result shows the 3BV of that board. In 2003, Sorin Manea developed a program that records Minesweeper games, and displays the board's 3BV as well as the number of clicks. That was the first program that calculated the 3BV/s (3BV per second speed) of the played game. In 2004, Rodrigo Silveira Camargo published "Minesweeper Clone" with many 3BV-related features, like playing boards with a prefixed 3BV, ability to select the range of 3BV on the generated board and the main — it saved all the 3BV statistics of finished games in a single file. Due to an easier way to represent the gaming history, the distribution of boards with a certain 3BV (for finished games only) could be analyzed. Also, there were programs which could show 3BV distribution tables for generated boards. Method The 3BV of a board names the minimum number of left clicks required to open up all squares without a mine of a Minesweeper field. 3BV/s 3BV/s stands 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 (nf) whereas marking mines with right-clicks is called flagging-style. Windows implementations In the popular Microsoft Windows version, there are three sizes: Beginner: 9 × 9 field with 10 mines Intermediate: 16 × 16 field with 40 mines Expert: 30 × 16 field with 99 mines. Custom: Any values from 9 × 9 to 30 × 24 field, with 10 to 667 mines the maximum number of mines allowed for a field of size A × B is (A-1) × (B-1). Newer versions of Windows (from Windows 2000 onwards) feature a 9 x 9 Beginner field instead of an 8 x 8, with the same number of mines. This was apparently because with the previous dimensions, the chances of clicking on a mine were the same for Intermediate and Beginner: In fact, when you allow for the starting square never containing a mine, there was a slightly higher chance of randomly hitting a mine in one move of the Beginner game. However, the Beginner game was still easier because it had fewer total chances of hitting a mine, and a smaller chance of having a problem that cannot be solved without guessing. Alternatively, it could have been changed because controls had been increased in size in later Windows versions, thus allowing nine boxes to fit in a row of width equal to the title and score bars. Another alternative: The beginner field is now solvable without guessing if a straight row of numbers with an opening on one side and unknown squares on the other side appears. In 2003, Microsoft added a variation of the original Minesweeper, called Minesweeper Flags in MSN Messenger (from version 6 onwards). This game is played against an opponent, and the objective of this game is to find the mines by actually clicking on the squares where they're located, not by clicking the surrounding squares. The person who first uncovers 26 (out of 51) mines wins. Cheat codes Some Windows versions of Minesweeper have a cheat mode that uses the top-left pixel of the display to signal the presence or absence of a mine under the cursor. Start Minesweeper normally. When it has loaded, type "xyzzy In some Windows versions, the file "winmine.ini" contains the high score table data. Editing this file changes the high score table accordingly, and can be used to falsify "high scores". This does not work on Windows XP. In the most recent Windows version of Minesweeper, the high scores list has been moved into the registry (HKEY_CURRENT_USERSoftwareMicrosoftwinmine). One can forge "high scores" by using a registry editor to access the highscore name and time files and change the data in them. Another cheat code can be used to stop the timer. After the timer has started hold down both the right and left button on the cursor and press escape (ESC). This does not work on Windows XP. (In the Windows 2000 version, pressing the ESC key alone after the game has started will stop the timer.) Alternatively, the timer can be stopped any time after it has started by pressing The timer may also be stopped by clicking and holding the smiley face at the top of the minefield. Note that in order for this to work without simply causing a new game to start, you must move the pointer off of the face before releasing the mouse button. Another way to win the game easily is to set the game difficulty to "custom", then enter 100 and 100 for the number of squares on the grid. The number of bombs should remain at 10. After this is done, clicking any square will give a result that allows you to almost instantly win the game, and there are cases where the game can be won on the first click. KDE Kmines, in the official release, for KDE. Originally created in 1996 by Nicolas Hadacek. GNOME Mines, in the official release. Minesweeper is beast Best times On the Windows version, for Expert, a time under 85 seconds in Windows 2000 (and under 80 seconds in Windows 3.1) is considered to be very good. The official record for Intermediate is 9 seconds (Jake Warner, United States) and 1 second (many players) for the 9x9 Beginner board. The official record for Expert is 38 seconds (Dion Tiu, Australia). (Note that the timer instantly goes to 1 on the first click, rather than after a second.) Many people publish screenshots or video recordings of their best performances. The Minesweeper Community has compiled a bestever-list which includes videos of the fastest games ever played. In order to get on that list your records on beginner, intermediate and expert must sum up to no more than 99 (sub100). The odds for winning Beginner (9x9 board) in a single click are as follows. Out of 127,800,681 games played in a row, by clicking in the corner, and seeing if all the squares get uncovered at once, 1,519 won on the first click. This gives an approximately 0.00119% chance of winning instantly, by clicking in the corner. In 6,713,134 games, clicking in the middle, 39 won on first click, giving only an approximately 0.00058% chance of winning instantly. In 10,839,687 games, clicking in the middle of an edge, 103 won on first click, giving an approximately 0.00095% chance of winning instantly. This could be more precisely calculated using combinatorial mathematics rather than statistics. Examples of the classic game There are several implementations of the game in its classic form. Here are some examples: Image:Minesweeper_end.PNG|Minesweeper running in Windows XP Image:MinesweeperVistaRC1.png|Minesweeper utilising the .NET Framework 3.0 for updated graphics and running on Windows Vista Image:Minesweeper_end_Kmines.png|Minesweeper clone named KMines for KDE Image:Firefox_Minesweeper_-_fr.png|Minesweeper in Firefox Image:Minesweeper(game).jpg|GNOME Mines Image:Ace_of_penguins-minesweeper.png|The Ace of Penguins Image:Xbomb squares.png|XBomb Image:Xdemineur.png|xdémineur (Look-alike clone of Microsoft version) Variants There are variations of Minesweeper available for download at various places on the Internet. These are generally differently shaped minefields in two and three dimensions, or various 2D layouts (such as triangular or hexagonal grids). For example, X11-based XBomb adds triangular and hexagonal grids, and Professional Minesweeper for Windows includes these and many others. Examples of variants Image:MineSweeper3D.png|A game on a surface of a truncated cuboctahedron Image:Cube_Minesweeper_3D.png|3D version Image:Firefox_Hexagon_Minesweeper_-_fr.png|A game with hexagonal tiles Image:Xbomb_triangles.png|A game with triangular tiles Image:Freesweep.png|An ASCII version (played with the keyboard) Image:Mines_Simon_Tatham's.png|This program deliberately generates the mine layout in such a way that the player never has to guess. Minesweeper community Minesweeper in science Minesweeper strategies to get better times Tips and tricks - Lots of helpful hints to get faster if you already know the basics of Minesweeper. Minesweeper variants 3D variants Hexagonal variants Unusual tile-size variants Logical variants Others | |||||||||||||||
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