As if to put us in the mood for winter, the *Washington Post* has a fascinating feature explaining why no two snowflakes are the same:

Newly formed snow crystals with only a handful of molecules would be nearly impossible to distinguish. But that’s not really the issue. We’re talking about real snowflakes, which have something on the order of a quintillion molecules. (That’s the number 1 with 18 zeros.)

Now, it’s not a law of nature that no two snowflakes could be truly identical. So, on a very technical level, it’s possible for two snowflakes to be identical. And it’s entirely possible that two snowflakes have been visibly indistinguishable. But probability dictates that this is incredibly unlikely. Libbrecht draws a helpful visual comparison.

“There are a limited number of ways to arrange a handful of bricks,” he says. “But if you have a lot of bricks, the number of combinations grows very quickly. With enough of them, you can make a driveway, a sidewalk or a house.”

Water molecules in a snowflake are like those bricks. As the number of building blocks increases, the number of possible combinations increases at an incredible rate.

Consider the math, which Libbrecht helps explain using a bookshelf analogy. He points out that, if you have only three books on your bookshelf, there are only six orders in which you can arrange them. (That’s 3 times 2 times 1.) If you have 15 books, there are 1.3 trillion possible arrangements. (Fifteen times 14 times 13, etc.) With 100 books, the number of combinations increases to a number that is far, far greater than the estimated number of atoms in the universe.

An ordinary snowflake has hundreds of branches ribs, and ridges, all arranged in minutely different geometries. To be sure, lots of snowflakes have fallen in the world, but not nearly enough to render two identical snowflakes a reasonable possibility.

If you’re skeptical, you’re more than welcome to undertake your own study. But you might want to block off a pretty big chunk of time. Libbrecht estimates that around a septillion — that’s a 1 with 24 zeros — snowflakes fall every year.

This also makes me want to re-arrange the books on my bookshelves. I think I’ll put 15 of them on a shelf and make it my life’s work to put them in every possible order!