Specifying Constraint Problems:

However as with most successful "AI" techniques there constraint solving is all about solving problems as: somehow phrase the intelligent task you are interested in as a problem or then massage it into the format of a constraint satisfaction problem as CSP, put it through a constraint solver and see if you get a solution. Now here CSPs consist of the following parts as: 

• There a set of variables is X = {x1, x2, ..., xn} and
• There a finite set of values that each variable can take. This is known as the domain of the variable. In the domain of variable xi is written Di and
• There a set of constraints that specifies that values the variables can take simultaneously.

Furthermore in the high-IQ problem above, there are 25 variables: one for each of the 24 smaller square lengths or one for the length of the big square. In fact if we say that the smallest square is of length 1 so the big square is perhaps of length at most 1000. Thus the variables can each take values in the range 1 to 1000. Hence there are many constraints in this problem that including the fact that each length is different and that certain ones add up to give other lengths and for example the lengths of the three squares along the top must add up to the length of the big square.