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IMC 2013/1/3

Source: Imc 2013 Problem 3

August 8, 2013
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Problem Statement

There are 2n\displaystyle{2n} students in a school (n∈N,n⩾2)\displaystyle{\left( {n \in {\Bbb N},n \geqslant 2} \right)}. Each week n\displaystyle{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.
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