A diagram of a 5x5 grid of circles, with one red circle and its adjacent circles highlighted.

The game of Fiver involves a grid of circles that are green on one side and red on the other. Starting with all the green sides showing, in each move, the player flips one circle and its four adjacent circles until all the red sides are showing. Optimizing the Fiver solution is used to illustrate integer programming techniques. (Image by Prof. James Orlin.)