IMC 2013 Problem 3

There are ${2n}$ students in a school ${\left( {n \in {\Bbb N},n \geqslant 2} \right)}$ . Each week ${n}$ students go on a trip. After several trips the following condition was fulfiled: every two students were together on at least one trip. What is the minimum number of trips needed for this to happen?

Proposed by Oleksandr Rybak, Kiev, Ukraine.