Zen has nothing to do with Buddhism; It most certainly has something to do with the 'Buddha' but nothing at all with the religion buddhism. Simply by discussing these matters is missing all the essence. Once a beginner asked a zen master, "Master, what is the first principle?" Without hesitation the master replied, "If i could tell you, it would become the second principle."
The koan is not a puzzle because it cannot be solved, only dissolved. A zen master does not teach but devises methods to wake up. This is the purpose of the koan, to bring one to the state of no-mind in the present moment. Zen cannot be studied, only lived.