[botexpert]

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.