Imagine that you are teaching an american cultural component of an esl (english as a second language) course. you have a list of 3k people who are famous enough for your students to recognize (eg barak obama, george clooney, abraham lincoln, elvis presley, angelina jolie, john kennedy, tom cruise, ghandi, beyonce, you also have a k concepts for which you want to give examples (eg male, female, rich, tall, dead, president, singer, each person matches some of the categories (eg tom cruise is a rich, male, actor) and doesn't match others (eg tom cruise is not female, not tall, and not dead). you want to give three examples of each concept, but you do not want to use any of the people for more than one concept (eg if you use tom cruise as an example of a rich person then you do not want to also use him as an example of a actor). clearly describe an algorithm to determine whether (and how) you can give 3 examples of each concept without repeating any of the people.