How about some kind of resource scheduling like, say, conference rooms, labs, classrooms, etc.? You'd have to keep track of locations, available facilities, events, event priorities, times, what facilities are required for which events, etc. and try to balance these "fairly" in some way. That would be a major challenge for a conventional programming environment and would be immediately useful to boot.
Edited to add:
I found the paper I wanted to reference earlier. You'll have to pay for a copy, but it's worth it if you decide to go this route: School time table scheduling in Prolog
Abstract:
The school Time-Table Scheduling task is a very hard operations research and engineering problem, especially when-implemented in a conventional language. That is due to the imperative, deterministic nature of most conventional languages, such as BASIC and PASCAL and to the long series of constraints and goals inside the problem. The descriptive, logic-based and nondeterministic nature of Prolog language, and its ability to backtrack allows one to easily obtain a deductive data base, mixing the facts, rules, and constraints of the Time-table. Two systems, one nonmonotonic, and one monotonic with a non-monotonic reasoning structure are compared and their performances in a significant test are discussed. The approach may be easily generalized to other analogous engineering, scheduling and operations research problems.