A way to assign tasks
Source: Japan Mathematical Olympiad Finals 2005, Problem 5
October 31, 2005
parameterizationalgorithmalgebra proposedalgebra
Problem Statement
You are the boss. You have ten men and there are ten tasks. Your men have two parameters to each task, one is enthusiasm, the other is ability.Now you are to assign the tasks to your men one by one.When man has more enthusiasm about task than about task and man has better ability in task than man does, though if you assign task to man and task to man man feel unsatisfied.Or, if there is a more efficient way than yours that you can assign each task to men with better ability, you will be brought to account by your employer.Prove that there is a way to assign tasks without any dissatisfaction or disadvantage.