Jacobian Locks Problem Solving

The problem from page 176 in Thinking Mathematically goes like this:
A certain village in Jacobean times had all the valuables locked in a chest in the church. The chest had a number of locks on it, each with its own individual and distinct key. The aim of the village was to ensure that any three people in the village would amongst them have enough keys to open the chest, but no two people would be able to . How many locks are required, and how many keys?

I initially figured that there had to be some kind of trick to this. I knew that if every villager had a key to each lock, then there would be no way to prevent two villagers from opening any number of locks. So I began to think of tricks. First, I thought that there is only one lock and each villager has one third of a key that together form a full key. But this would mean not every lock has its own individual key. Then, I thought maybe the chest is up in the air and it requires a human ladder to reach it, but two people could not. This would require only one lock and each villager to have one key. This might be the solution, but I doubt it. Then I thought maybe the chest is very big (it does hold all the valuables for the village) and has three locks spread far around it. Each villager has one key that opens a lock which closes again right away. Three villagers could do this but not two. The same would work for three locks with three keys that break upon their use. Then every villager would need only one key, but the keys would not be distinct. Then I got to thinking that there must be something in the order or way the locks are open.