An experimental system called QPS (Quantitative Problem Solver) has shown that a numerical database of quantities in the physical sciences can be enhanced by adding intelligence for problem-solving. The system needs to store not only numerical data but also the formulae that operate on the data. It needs also the logical software that enables the system to find and combine together data and formulae to solve problems. It is shown that this logical software is similar to the backward-chaining algorithm used in expert systems with factual data. It has been successfully tested on a large number of problems, including many taken from textbooks in physics and chemistry and some taken from practical problems in engineering, including problems that need the solution of simultaneous equations, and including a novel solution to the problem of choosing the optimum material for a component. It has an interface based on the well known symbols used in equations; it can work with any system of units and it can check the accuracy of the calculations. The principle can be used in any numerical database that contains data which can be manipulated using formulae, not just in the physical sciences.