As a side note, if you enjoy playing Minesweeper but don't like losing to a bad guess, you might want to try the implementation in Simon Tatham's puzzle collection:<p><a href="http://www.chiark.greenend.org.uk/~sgtatham/puzzles/" rel="nofollow">http://www.chiark.greenend.org.uk/~sgtatham/puzzles/</a><p>Unlike most other implementations, it only generates boards that can be solved by logic, so you never need to guess; your first square is guaranteed to be safe and to reveal enough information to progress.<p>(IIRC, the algorithm used to pre-solve each generated level bottoms out in an exhaustive search, so I guess this game variant is still in NP.)
I've submitted an interview with Ian Stewart here:
<a href="http://news.ycombinator.com/item?id=1594526" rel="nofollow">http://news.ycombinator.com/item?id=1594526</a><p>He's a serious mathematician, and a serious writer of both fiction and non-fiction.
Figure 3 is incomplete; as the space depicted in it is not a valid board configuration. If either x or x' is false, then the respective 1s on the extreme sides will be invalid. This is either a crop of a real situation (in which we assume the wire repeats beyond the scope of the image), or an error.