A Gazillion Different iPhones

So, Mashable reported recently that there are now 100,000 approved apps for the iPhone.

Which is a big number. 

But not as big as the number I think is more interesting, and maybe more important. 

How many different combinations of iPhones are there with 100,000 available apps?



We can get the average number of apps per iPhone from reports like this from networkworld)

It’s about 18, apparently (10 paid for, 8 free).

So from 100,000 apps, how many possible combinations of iPhone are there?

To work this out, I asked my brother, Andrew, who has a PHD in engineering and works at our sister agency BrandScience. 

Needless to say, he has a better grasp of numbers than I…

This is what he worked out:

No. of Apps   /   Total Combinations   

1        100,000       
2        4,999,950,000   
3        166,661,666,700,000   
4        4,166,416,671,249,980,000   
5        83,325,000,291,662,500,000,000
6        1,388,680,567,360,800,000,000,000,000
7        19,837,103,521,810,800,000,000,000,000,000
8        247,946,436,557,054,000,000,000,000,000,000,000   
9        2,754,740,009,356,990,000,000,000,000,000,000,000,000
11      250,383,330,322,534,000,000,000,000,000,000,000,000,000,000,000
12      2,086,298,234,634,990,000,000,000,000,000,000,000,000,000,000,000,000
13      16,046,522,144,975,600,000,000,000,000,000,000,000,000,000,000,000,000,000
14      114,603,114,979,263,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
15      763,913,803,621,103,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
16      4,773,745,103,441,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
17      28,076,360,613,085,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000




<o:p>Yep; if you select just eighteen apps from the app store, you are selecting one of the </o:p>1.56E+74 possible 18 app iPhone combinations.

Which is a very big number indeed. 

To put it in context, if you multiply the number of hydrogen atoms in the galaxy (5E+68) by 311,907, then you get to the number of possible iPhone permutations. 

(EDIT: This is an update on the maths from Andrew… I misinterpreted original email)



Interesting?  Maybe, depending on your take on what ‘interesting’ is… but it’s certainly important.

Why?  Because it represents just how unique and customisable the iPhone platform has become… the chances of you ever running into someone who has the same iPhone as you are entirely remote.

…which means that not only is your iPhone unique, it continues to be a social object even when everyone around you has one, because you’re always likely to have something new, different and interesting to show each other.

So next year, when the Orange and Vodafone iPhone deals have really kicked in, it’s not like everyone in the UK is going to have the same phone…

…they’re going to have the most unique phone they’ve ever owned. 

It’s just they’re all going to have the same case for it…