You can use constraint programming to find every possible color combination for a map that shows four countries, each a different color. None of the neighboring countries can be the same color. This is a modified version of the example in How to: Apply a Constraint Programming Directive, where the colors of two countries are specified by a user and the solver reports the values for the remaining two countries.
The following steps demonstrate how to use Solver Foundation to create and solve the map coloring problem by using the Solver Foundation Services layer.