I did think about the number of snowflakes that have ever fallen - it's not very big.

If the odds had been better than 1 in a googol my calculator should have coped.

I didn't bother trying to get a reliable estimate of the probabillity because there are estimated to be fewer tha a googol particles in the known universe. The number of snowflakes is clearly less than this.

Lets make a couple of aproximations. First off, rather than 1 in 6000 we might as well use 1 in 1000- this is never going to be a precise calculation.

That makes the calculation 0.999 to the power 600000000000000000000.

Lets just try a few numbers and see how the odds vary.

.999 ^ 3 is about .997

.999 ^ 10 is about .99

.999 ^ 100 is about .904

.999 ^ 692 in pretty near 0.5

so, by the time you were putting in the 692nd atom you would have a roughly 50:50 chance of having got the "wrong" atom somewhere in the snowflake.

Add another 692 atoms and theres a 50 50 chance one of these is wrong so, overall you have a 25% chance of getting all the atoms right.

Another 692 and the odds are down to one in 8 of a perfect copy.

By the time you have done this 10 times your odds are about 1 in 1024 of having the right atom in each place.

OK so that's how lucky you need to be with the first 6920 atoms

The next lot of 6920 atomstake the odds to one in about a million.

Each further 6920 makes it roughly another thousand fold more unlikely that you have the atoms all correct.

By the time you have used all 600000000000000000000 atoms you have added another 3 zeros to the odds 600000000000000000000 / 6920 times

The odds against getting all the atoms right is of the order of 1 followed by 86 thousand million million zeros.

That's just the hydrogens; then there's a comparable set of odds for the oxygen isotopes. Then think about all possible arangements in space (ie the numbet of possible ways to stick the atoms together).

The earth weighs something like 6*10^27 grammes or enough, if the entire earth were made into snowflakes, enough for about 6*10^30 snowflakes of 1mg each.

You are trying to compare 2 numbers, one has 30 digits the other has more than 85 thousand million million digits.

The number of possible combinations is so huge that it wouldn't matter much if you made snowflakes from something as much bigger than the earth, as the earth is bigger than a snowflake.

That's just the hydrogens; then there's a comparable set of odds for the oxygen isotopes. Then think about all possible arangements in space (ie the numbet of possible ways to stick the atoms together).

Trust me, I did think about the number of snowflakes.