I liked minesweeper very much and I want to explain here how I embraced it in my education and what are the things I believe we can learn from such game that according to Wikipedia has been there since the early mainframes in the 60's. The first thing I liked about the game is that it is very self contained, it's more exciting if you figure out the game rules by yourself while trying it. You will quickly realize what are the meanings of the numbers when you start uncovering cells: The number of bombs around that cell. Then you will start realizing how to use this information and start finding patterns: The 1's in the corners, the 2's in the corners, several combinations of 2's and 3's and so on, those patterns that allow you to become faster and really master the game. Shortly after I started playing, my father and sister also liked the game and started playing it, often challenging ourselves in our computer.
1. Be good at manipulating arrays/matrices: Obvious! The game even looks like a matrix so this is the data structure you will need. You will have to traverse the matrix up and down, forward and backwards in every way possible. I implemented this in Java so I didn't need to think about dynamic allocation of arrays explicitly but if you want your game dimensions to be variable (beginner, medium, expert), then in a language like C you will want to go dynamic.
Beyond these two things you can learn about the power of random number generation when you're writing the routine to place the mines and also a basic convolution-like operation when you're assigning the numbers to the cells after the placement of the mines. Also if you're really into it you will notice things from the Windows Minesweeper like the fact that you never hit a bomb in your first move.
In the realm of Object Oriented programming itself which was the excuse for getting into this project, you can also learn to encapsulate your objects so well as to have the ability to create a new game by instantiating a Minesweeper class. Things like: new Minesweeper(), new Minesweeper('expert'), new Minesweeper(width, height, mineCount). Or even more, generalize your game to add the extra features in this way: SuperMinesweeper extends Minesweeper. Which effectively addresses the whole purpose of programming with objects in mind.