Kaye showed that the minesweeper puzzle is NP-complete by reducing instances of SAT (satisfiability of formulas of propositional logic) to instances of the puzzle. The SAT instances are given as circuits constructed of Boolean logic gates.
How difficult is minesweeper?
There are three difficulty levels for Minesweeper: beginner, intermediate, and expert. Beginner has a total of ten mines and the board size is either 8 × 8, 9 × 9, or 10 × 10. Intermediate has 40 mines and also varies in size between 13 × 15 and 16 × 16. Finally, expert has 99 mines and is always 16 × 30 (or 30 × 16).
How do you know if it is a NP problem?
A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete.
Is the consistency of minesweeper in NP hard?
Minesweeper Consistency is NP Complete Since Minesweeper Consistency has been shown to be in NP and is NP Hard, by de nition, it is NP Complete. Sources: A very approachable paper and summary on both the Minesweeper consistency problem and P versus NP in general: Stewert, Ian.
What do all the numbers mean in minesweeper?
‘M’ represents an unrevealed mine, ‘E’ represents an unrevealed empty square, ‘B’ represents a revealed blank square that has no adjacent (above, below, left, right, and all 4 diagonals) mines, digit (‘1’ to ‘8’) represents how many mines are adjacent to this revealed square, and finally ‘X’ represents a revealed mine.
Is there a mathematical problem to play minesweeper?
In fact, Minesweeper is in a class of mathematically di\cult problems known as co-NP-complete. Therefore, understanding the complexity of Minesweeper and designing algorithms to solve it may prove useful to other related problems. In this paper, I will analyze di\erent approaches to designing an algorithm to play Minesweeper.
How do you change the number of squares in minesweeper?
If an empty square ‘E’ with at least one adjacent mine is revealed, then change it to a digit ( ‘1’ to ‘8’) representing the number of adjacent mines. Return the board when no more squares will be revealed.
