is this a google interview question? i love those........ NOT! first thing to do is to limit the number from above, so at least we know how large the playing field is:
assume a microprocessor is 1 cm³ on average. the slabs of silicone used to make such processors are 1 m³ in volume, so one of those can make 1 000 000 (10⁶) microprocessors. to make a single slab of silicone 453kg of raw manufacturing-grade gravel (sand) is used, together with 250kg of coal and other carbons. (http://www.answers.com/topic/silicon?cat=health). next we need to find how much sand there is in the world, and knowing that we have certainly not exhausted all of it to make silicone (there are still sandy beaches in some places of the world) we can calculate an upper limit for the number of microprocessors in existence: sand grains are 0.1mm across (on average), that means there are 1 trillion (10¹²) grains of sand in a cubic meter. the number of grains of sand on all earth's beaches has been estimated at 10²⁴ that 10 to the power of 24, (source: http://www.astro.utu.fi/~cflynn/sand.html), so about 10¹² m³. sand weighs at 1 500-1 800kg per m³ (http://www.answers.com/topic/sand?cat=health), which gives us about 1.65*10¹⁴kilograms of sand. that makes (combined with coal) roughly about 4*10¹¹ slabs, which, at 10⁶ microprocessors per slab, gives us a maximum number of microprocessors that can exist on an Earth with observable sandy beaches to be 4*10¹⁷ although i'm much more inclined to just start counting from 1 when i'm asked this type of questions. ps: limiting that number from below is left as an exercise to the reader :)
