Multiple locks

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You belong to a club that has accumulated valuable jewelry. The treasure is kept in a chest. For security reasons, you want at least two of your 10 club members present when the chest is open. To ensure this, you put multiple locks on the chest and distribute keys to members so that no one member can open the chest, but any two members can. Each lock has a different key, but you can make several copies of the same key to distribute to the club members. What is the fewest number of locks and keys that you will need?


The first thing I would try is to make the problem easier by reducing the number of members in the club. It would be easy if there were only two members in the club. What if there were three?


Problem Solving by Thomas DeFranco and Charles Vinsonhaler.