Suppose you’re helping to organize a summer sports camp, and the following problem comes up. The camp is supposed to have at least 506

one counselor who’s skilled at each of the n sports covered by the camp (baseball, volleyball, and so on). They have received job applications from m potential counselors. For each of the n sports, there is some subset of the m applicants qualified in that sport. The question is: For a given number k < m, is it possible to hire at most k of the counselors and have at least one counselor qualified in each of the n sports? We’ll call this the Efficient Recruiting Problem. Show that Efficient Recruiting is NP-complete.