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determine which victory can be secured based on k (cut the rod in k pieces)

Source: Rioplatense Olympiad 2014 level 3 P3

September 5, 2018
game strategygamecombinatorics

Problem Statement

Kiko and Ñoño play with a rod of length 2n2n where n≤3n \le 3 is an integer. Kiko cuts the rod in k≤2n 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 kk.
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