The Odds

There is a slim chance that two people could choose the same set of images and that I might arrange them identically. A very slim chance.

The greatest possibility of that happening is with the smallest number of images - four. But within the full 7x7 grid there are 211,876 possible combinations of four. And each combination of four can be arranged in 24 different 2x2 permutations for a total of 5,085,024 possible arrangements.

Stepping up to nine images arranged 3x3, there are 2,054,455,634 combinations of nine available. Any combination of nine can be arranged 362,880 different ways (who knew?). When you multiply those two numbers you wind up with 745,520,860,465,920 possible arrangements of nine images. 745 trillion is a big number. But it's nothing compared to the numbers you get when calculating the odds with 16 or 25 images or for a full size 7x7 print.

There are 70+ septillion possible arrangements of 16. That's a seven with 25 zeroes behind it. One trillion times one trillion times seventy. Each 19x19" and estimating that there's 100 drawings per every 2 inches thick, 70 septillion 4x4 arrangements would create a stack of prints twice the area of the continental United States that would reach well past the moon.

9.8e+38. Nine hundred eighty undecillion possible arrangements of 25 images. It looks like this: 980,000,000,000,000,000,000,000,000,000,000,000,000. If each 23x23" print were the size of a grain of sand they would fill the beaches of close to 100 trillion earths.

A novemdecillion is a one with sixty zeroes following it. There are 600 novemdecillion or 6e+62 possible 7x7 arrangements. This is a staggering number, equal to a mass of prints that would fill the Milky Way galaxy four times or a stack of prints that would criss cross the known universe nearly two million septillion times. Essentially a meaningless number.

However, in this instance it does pretty well mean that no two prints will be identical and I think the same could be said for any of the smaller grids as well. There is the human element to consider. Certain drawings are bound to be more popular than others and I do have a loose set of unwritten rules by which I arrange them. But I don't believe either of these factors will affect the odds in any measurable way.

I'd like to invite anyone to doublecheck the numbers above. The total number of permutations (possible arrangements) for each size grid is correct. An online combinations and permutations calculator was used. For the examples (grains of sand etc.) I used assorted online references and a free online scientific calculator to the best of my limited ability. Confirmed corrections will be posted.