DE-MO 2013 Problem 5
Five people form several commissions to prepare a competition. Here any commission must be nonempty and any two commissions cannot contain the same members. Moreover, any two commissions have at least one common member. There are already commissions. Prove that at least one additional commission can be formed.
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.