You have a project to do using object technology and are wondering about how to go about designing the class structure. Your first task is to find those parts of the system that can best be modeled by objects. Brainstorm to do this without being overly conservative. If it might be an object, list it. One way to find many of the objects in a system is to read or develop a description of it and then list the important nouns in that description.
Nouns name things and objects model things.
Apply this to the description of Mancala and see what you come up with. Do the same for the Robot problem. In an initial design try to model the problem directly. In other words, make the program, and in particular the objects, as close to the real-world system as possible. An object in the software system should have an exact counterpart in the world being modeled.