Share $m$ candy bars for $n$ people Assume that we have $m$ candy bars and $n$ people. Each candy bar can be divided into at most two pieces (not necessarily equal). Find the necessary and sufficient condition of $(m,n)$ such that $m$ candy bars can be distributed evenly to $n$ people.
Hint (from my teacher): We consider the graph with $n$ vertices $A_1, A_2, \dots, A_n$ and connect $A_iA_j$ iff $i$-th person and $j$-th person share a candy bar, and show that if $m<n$ then the graph has no cycles.
But I don't understand how this is related to the part of the candy bar we give to each of them. It only shows that they share a candy bar, not how the bar was shared.
All ideas are appreciated!

If you are connecting 2 vertices then you are drawing a diagonal and we all know diagonal divides a polygon in equal or even parts and it has to be $m<n$ as diagonals are always less than vertices. Also if you think logically you cant evenly distribute eg $7$ candies in $8$ people.
