Are there really no two snowflakes that are alike?

It is a common cliché that no two snowflakes are alike. Of course, for every cliché in one direction there is another in the opposite direction. Consider the infinite number of monkeys typing on an infinite number of typewriters, eventually they will produce Hamlet. Even if you are a one in a million kind of guy, there are a thousand people just like you in China.

So, is this snowflake truism true? With the number of molecules in a snowflake and the unique and variable environmental factors that lead to the formation of a snowflake, is it conceivable that there have never been two snowflakes that have been identical? All the snowflakes in all the snowstorms in all the world in all of history, surely it is not necessarily true that no two have been identical, but is it likely that there have never been? Or is it likely that there have been?

Does the idea of identity here get rendered meaningless by quantum mechanics in which objects get blurred out? Does the entire concept rest upon classical ideas that happen to be empirically false making this a pseudo-question?

Is this really what philosophers think about when their flights are delayed and they are stuck in an airport while it is snowing? (Credit where credit is due: TheWife was ranting about this on the way through the snow to the airport…)