Locks and keys so any six of eleven can open

Eleven pirates want to secure their treasure chest with several padlocks, distributing keys so that any group of $6$ or more pirates can open every lock, while any group of $5$ or fewer always finds at least one lock it cannot open. What is the smallest number of locks needed, and how many keys must each pirate carry?

$462$ locks, with $252$ keys per pirate. Every group of $5$ must be locked out of some lock whose keys all the other $6$ pirates hold, and two different groups of $5$ cannot share that lock (their union has at least $6$ pirates), so you need $\binom{11}{5}=462$ locks. Each pirate holds a key to every lock belonging to a $5$-group without them: $\binom{10}{5}=252$.