Problem solving that both requires and develops higher-order thinking skills is illustrated in the EQUATIONS Challenge Matches program, which consists of computer diskettes at the elementary, intermediate, and advanced levels plus a multi-level diskette. Samples of computer output are given, with the results of various types of experimentation with the program discussed and illustrated. Users are expected to design and perform experiments involving application of elementary mathematical ideas. The problem-solver can arrange for things to happen that will provide the information needed to deal with the problem. The series of exercises has been developed to provide users the opportunity to learn and use the fundamental reasoning and problem-solving skills of careful observation, logical deduction, mathematical analysis, asking good questions, scientific research by experimentation, and data gathering, organization, and analysis. (MNS)