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Omni-MATH / There are 2n students in a school (n∈N,n≥2). Each week n students go on a trip. After several trips the following condition was fulfilled: every two students were together on at le…

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There are 2n2n students in a school (n∈N,n≥2)(n \in \mathbb{N}, n \geq 2). Each week nn students go on a trip. After several trips the following condition was fulfilled: every two students were together on at least one trip. What is the minimum number of trips needed for this to happen?
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There are 2n students in a school (n∈N,n≥2). Each week n students go on a trip. After several trips the following condition was fulfilled: every two students were together on at least one trip. What is the minimum number of trips needed for this to happen?
Original LaTeX notation
There are $2n$ students in a school $(n \in \mathbb{N}, n \geq 2)$. Each week $n$ students go on a trip. After several trips the following condition was fulfilled: every two students were together on at least one trip. What is the minimum number of trips needed for this to happen?

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