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April 20th, 2019, 11:32 PM   #1
Joined: Apr 2019
From: IRI

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Induction question about partitioning with a condition

We have $\displaystyle n$ students which are in $\displaystyle k$ classes. We know that between each two classes, there exist two persons A and B who know each other. Prove that we can put students in $\displaystyle n−k+1$ groups such that all the persons in a group know each other. (the proof is probably with induction) (I think it is safe to assume none of $\displaystyle k$ classes will be empty)

I don't know how should I approach this question. Should I use induction on n or $\displaystyle k$? how?
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