Morgado's old challenge

There are many locks and 9 people. At least 5 people are needed to open all the locks. If the number of locks is small as possible, how many keys does each person have?

Details and Assumptions

  • Each lock needs a different key.
  • Each key has many copies.
  • Every group of 5 people is able to open all the locks
  • This question is in memory of the mathematician Augusto C. O. Morgado.

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