Question 4
Alice chooses an odd number $k = 2l+1$, places $k$ plates around a circle and distributes 2013 beads into some of these plates as she wishes. After that Bob marks one of the plates. Determine the maximal possible value of $N$ such that no matter how Bob marks a plate Alice can choose exactly $l$ unmarked non-neighbouring plates containing at least $N$ beads in total.