In the 1980's I was involved with three different research problems leading to questions still open today. Each problem was about sets of integers and the sums and differences one could form from them. The applications that provided the motivation were all different: public key systems based on the Knapsack problem, assigning frequencies to radio stations in a limited spectral band, and allocating storage to multi-dimensional arrays.
I shall describe the problems in turn, motivate them by their applications, and summarise the results. No prior technical knowledge is required.