Similar to the lottery problem and other covering problems. Let's say lottery has N numbers. Tickets contain K numbers. What is the least amount of tickets M t

Similar to the lottery problem and other covering problems. Let's say lottery has N numbers. Tickets contain K numbers. What is the least amount of tickets M that you need to buy so you guarantee when the winning ticket is pulled that you matched at least R numbers on that winning ticket with your pool of tickets? LP(N, K, R) = M. LP(N, K, K) = (N choose K), is winning the lottery and for that to be sure we need to buy all tickets. LP(N, K, 2) is solved, I believe, for many values (theoretically). LP(N, K, 3) is already a problem.