So that the total mine number of a board is simply the number of the drawn segments. Since, the segments join blank squares to their mined neighbors, each segment is counted only once. The poor neighbor number of a cell is the number of segments emanating from its center. Let's join the centers of the blank squares with the centers of their poor neighbors. The following may be construed as a graphical elaboration of the proof in the conventional case of square cells and rectangular boards.
for toroidal boards) that are the union of arbitrarily shaped (not necessarily square) cells and also for any kind of adjacency that may be defined on such a board. The result is valid for boards of arbitrary shapes (e.g. To apply this fact to our puzzle, let A be the set of squares of the board, R the adjacency relation on A, B the set of mined squares and C = A - B the set of blank squares. Then we are simply counting the elements of (B×C)∩R in two different ways. To make the equation self-evident, think of R as a subset of A×A. Then, using |S| as the number of elements in a finite set S, Let A be a finite set and R a relation o A. The proof is based on the following obvious fact. When a board is overlapped by its complement, the result is a board of the same shape with every square carrying exactly one mine.Ī board and its complement have the same mine total number.įor the above board and the 8-adjacency relationship, the distribution of the poor neighbor numbers is as depicted in the diagram below. With any board we associate a complementary board which is the board of exactly the same shape, in which the previously blank squares carry a mine, and those that had a mine in them became blank. The mine total of the board is the sum of all poor neighbor numbers over all blank squares in the board. Adjacency may be 8-adjacency, as in the original minesweeper puzzle, or 4-adjacency, or in fact, any other kind that may come to mind. Each blank square in a board is assigned a poor neighbor number, which is the number of adjacent squares of the board that carry a mine. A board is any combination of grid squares, some of which are blank whilst some are marked with mines. The theorem is concerned with shapes on a square grid. The popular Minesweeper puzzle serves as the background. When a number touches the same number of squares, those squares must be mines.An engaging theorem has been published by Antonio Jara del las Heras from Avila, Spain ( Am Math Monthly, v 116, n 3, March 2009, p. You also can play Custom games up to 30x24 with a minimum of 10 mines and maximum of (x-1)(y-1) mines. Minesweeper saves your best time for each difficulty level. A counter shows the number of mines without flags, and a clock shows your time in seconds. The game ends when all safe squares have been opened. The three difficulty levels are Beginner (8x8 or 9x9 with 10 mines), Intermediate (16x16 with 40 mines) and Expert (30x16 with 99 mines). This can save you a lot of work! However, if you place the correct number of flags on the wrong squares, chording will explode the mines. Chording is when you press both mouse buttons at the same time. If you flag all of the mines touching a number, chording on the number opens the remaining squares.
#MINESWEEPER 8 HOW TO#
A common strategy for starting games is to randomly click until you get a big opening with lots of numbers. Want to install Minesweeper for PC We are show you, how to install Minesweeper For Pc Windows (10, 8, 8.1 & 7) - Free Download. When you open a square that does not touch any mines, it will be empty and the adjacent squares will automatically open in all directions until reaching squares that contain numbers. Pressing the right mouse button again changes your flag into a questionmark. You open squares with the left mouse button and put flags on mines with the right mouse button. Windows Minesweeper always makes the first click safe. If you click on a mine you lose the game! You can use the number clues to solve the game by opening all of the safe squares. Safe squares have numbers telling you how many mines touch the square. Then there are 81 9 72 squares left to place the remaining 2 mines. Suppose the upper left square in the middle 7 × 7 grid is surrounded by 8 mines. Minesweeper is a game where mines are hidden in a grid of squares. None of the border squares can be surrounded by 8 mines, only squares in the middle 7 × 7 portion of the grid can possibly be an 8. Minesweeper on Windows XP with 40 mines solved in 28 seconds
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