A village keep all their most precious belongings in a vault. The vault has a certain number of locks, each lock with an individual and specific key. The people in the village want to make sure that any group of three people can open the vault. No group of two people can open it. How many locks and keys?
Any ideas how this problem can be approached? The goal is to generalize the problem, so that there can be a lot of people in the village, starting with special cases where there are for example $3$,$4$,$5$,$6$ people etc. Hopefully someone can help!