[pitchka]

General problem - having ticket with k numbers where possible numbers are from 1 to n, find the minimal set of tickets that will cover all of the possible ones so that at least one ticket in your set has at least m equal numbers on the ticket that is drawn (m <= k). (Trivial example. To win the lottery - guarantee k matches - one has to buy all of the tickets.)

It is still unsolved although maths has provided some nice bounds for large amounts of (n,k,m) triplets, and solutions to (n,k,2). Although, for the (n,k,2) a simple greedy set cover finds the optimal solution always.