A simple switch is a logic gate, when 2 switches are placed in parallel they form an OR gate, when in series they from a AND gate.
It looks to me that the goal of this project is to find an arrangement of the 3 switches which will control each of the lights. There are 8 possible positions therefore there should be a way to wire the circuit to control 8 different lights.
Sounds like an exercise in ladder logic. If you ever encounter a PLC this is very nice stuff to know.