You have a set of ten numbers, and you are trying to cover all 4-element subsets of this set. To do this, you choose 5 elements from the set every time and you cover all 4-element subsets of your choice. What is the minimum number of selections you need to complete all 4-element subsets of the ten number set?
For example if you choose 12345, you cover 1234,1235,1245,1345 and 2345. But as you go on, the overlaps seem to be inevitable. I couldn't figure out the strategy to minimize it.