Snowflake Conundrum

I remember, as a young lad, watching the powdery white snow drift down lazily from the sky. The shock and aw that the first snow utilized was flawless. Youth would stare and just wonder at this natural phenomena. The adults would then claim that each was unique. UNIQUE? There have been billion of snowflakes, and you expect me to believe that each is unique? That's how they get you. At such a young age, the kids believe that this is possible. You almost don't even realize the statement. The statement that every snowflake in the world could not have a counterpart is taken as fact without thought. This can not be true. My conjecture is that there is no possible way for every snowflake ever to have an individual design. There are only so many possible options.