Keys to a Pirate's Heart
2025-09-22
Problem
You have 8 pirates friends who jointly find a giant treasure chest. Since they don't trust each other, they decide to secure the chest by locking it with distinct locks and have you distribute keys among them such that:
- Any group of 5 or more pirates can unlock the chest
- Any group of 4 or fewer pirates cannot unlock the chest
What is the minimum number of locks you need, and how many keys will each pirate receive?
Clarifications
How many locks can a specific key unlock?
Each key can unlock exactly 1 lock. However, there can be any number of duplicates for each key.
How many keys can be given to each pirate?
You can give each pirate up to the keys, where is the number of locks there are.
Solution
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