MS Project is not allocating resources as per my calendar

Assume there are five people to whom tasks have to be allocated. I want one person to work on a task for complete day or until the task is complete whichever is earlier. How to define this requirement is MS project so that, first person will get to handle the task on Monday, the remaining task will be handled by the second person on Tuesday and so on? I have tried, but since the task almost gets over in two days, the other three persons are not getting the tasks only to be accomplished. What is the solution?