Can you please help me with this problem?
There are \(n\) persons which live on a planet. It is known that their planet has \(6\) languages and each of the \(n\) persons knows every language. It is also known that any two people communicate with just one of the six languages. What is the minimum value of \(n\) such that there always exists a trio which mutually communicates with each other in the same language?