Task partitioning in multi-robot systems involves breaking down tasks or partitioning them into smaller tasks tackled by different robots in the system. Some of the benefits of this approach is less interference among the individual agents as they become more segregated, an improved scalability, and an improved transport efficiency. This approach allows for a better overall group performance, leads to specialization and aids in parallel task execution. In this paper, a new problem involving self-organized task allocation for partially sequential tasks in a two-robot environment is investigated. This partially sequential nature comes from the fact that some tasks are to be executed in a specific order while others can be executed in any order. The two robots are nonidentical. The first is equipped to do all the necessary computations and it has the ability to decide on the optimal order of executing the tasks, let's call him "Brain"; while the other has a set of simple behaviors that it keeps following at all times, let's call him "Pinky". There is no explicit communication between the two robots; instead, indirect communication is achieved through the concept of stigmergy.