For an upcoming international mathematics contest, the participating countries were asked to choose from nine combinatorics problems. Given how hard it usually is to agree, nobody was surprised that the following happened:
i) Every country voted for exactly three problems.
ii) Any two countries voted for different sets of problems.
iii) Given any three countries, there was a problem none of them voted for.
Find the maximal possible number of participating countries.
combinatorics unsolvedcombinatorics