Spanish Juggling problem
These are some notes to be shared about a specific kind of problem I am thinking about since yesterday.
Problem formulation
You are given a list of persons P, a list of capabilities (or skills) C, and a list of all the capabilities per person. A person can have any number of capabilities. For each capability, there is at least one person who possesses it. Find the smallest set of persons so that they, in total, have all capabilities.
(Optional:) If there are multiple possible smallest sets, find them all.