I have come across an article of one of my favorite authors Ian Stewart and he was analyzing a simple computer game most nerds (like me) play constantly minesweeper. The solution he came up with involves locating hidden mines on a grid by making guesses about where they are located and using clues provided by the computer.
The actual article length is pretty lengthy, so I am going to try to sum it up in about a paragraph. He was trying to initialize the mines using probabilities famous theorem stating P=NP and realizes that it may not be as simple as that and tries to prove that the problem is non-P, Stewart goes through many different proofs and realizes that it is really a hard problem to solve and ponders on the thoughts that such a simple game can have "intractable consequences, but mathematical games are like that."
Here is a quote that sums up the end, "If you're interested in those million-dollar prizes, a word of warning. The Clay Institute imposes strict rules before it will accept a solution as being valid. In particular, it must be published by a major refereed journal, and it must have been 'generally accepted' by the mathematical community within two years of publication. But even if you're not going to tackle anything as daunting as that, you can have a lot of fun playing Minesweeper, secure in the knowledge that it encompasses one of the great unsolved problems of our age."