Sharing a Secret: Locks and Keys
Five people want to store a secret document in a safe. The rule is simple: any group of 3 or more people should be able to open the safe together, but no group of 2 (or fewer) people should ever be able to open it alone.
To enforce this, they decide to put multiple locks on the safe -- every single lock must be opened to access it. Each lock can have multiple copies of its key distributed to different people, but each physical key only opens one lock.
1. What is the minimum number of locks required?
2. How many keys will each person carry?
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