NCTM Problem to Ponder - Under Lock and Key

NCTM Problem to Ponder:
Under Lock and Key

In medieval times, the inhabitants of a remote village decided to lock the village valuables in a giant chest to protect them from marauding thieves. They placed a number of locks on the chest, with each lock needing its own distinct key. For additional security, the villagers made sure that any three people from the village would always have among them the keys needed to open the locks, but no two people would have the keys to do it.

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