This type of problem is sometimes called an 'inverse' problem. Rather than being given some data and having to find a solution based on the data, in an inverse problem you are given some information about an outcome or solution and have to make deductions about the data.

Inverse problems can really exercise your problem solving skills because they require more understanding of the mathematical concepts involved than the more 'direct' type of problem.

Being able to solve problems of this type is important as they arise in real life situations where mathematics can be used to model the real life situation and so help in getting answers to questions about that situation. In such circumstances you may have to be creative in finding a method because there may be no known (standard) method for solving the problem.