THE AIM OF this chapter is to discuss various examples of constraint satisfaction problems (CSPs2 in short). The notion of a CSP is very general, so it is not surprising that these examples cover a wide range of topics. We limit ourselves here to the examples of CSPs that are simple to explain and that illustrate the use of general methods of constraint programming. In particular, we included here some perennial puzzles, since, as it has been recognised for some time, they form an excellent vehicle to explain certain principles of constraint programming.

As already mentioned in Chapter 1 the representation of a problem as a CSP is usually called modeling. The selected examples clarify a number of aspects of modeling. First, as we shall see, some of the problems can be formalised as a CSP in a straightforward way. For other problems the appropriate representation as a CSP is by no means straightforward and relies on a non-trivial ‘background’ theory that ensures correctness of the adopted representation. Also for several problems, more than one natural representation exists.

When presenting the CSPs it is useful to classify them according to some criterion. In general, the techniques used to solve CSPs depend both on the domains over which they are defined and on the syntax of the used constraints. In most examples we use some simple language to define the constraints. Later, in Chapters 4 and 6, we shall be more precise and shall discuss in detail specific languages in which the constraints will be defined.