RIOPLATENSE 2014 Problem 3

Kiko and Ñoño play with a rod of length $2n$ where $n \le 3$ is an integer. Kiko cuts the rod in $k \le 2n$ pieces of integer lengths. Then Ñoño has to arrange these pieces so that they form a hexagon of equal opposite sides and equal angles. The pieces can not be split and they all have to be used. If Ñoño achieves his goal, he wins, in any other case, Kiko wins. Determine which victory can be secured based on $k$ .