Intel Corporation Software Developer interview questions

Which has been the most critical work situation I have ever faced and how I solved

You have a queue of tasks, all of which take a different amount of time to complete. You have n machines that can handle these tasks simultaneously. However, once each task finishes with its initial mission, the task must be further processed & only 1 machine can do this processing. Regardless of the time of the initial completion of the tasks, the last processing part must be done in order of the original queue. DS to do this?