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April 21st, 2019, 12:32 AM  #1 
Newbie Joined: Apr 2019 From: IRI Posts: 1 Thanks: 0  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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combinatorics, condition, induction, partitioning, question 
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