Originally posted by Campaigner
Okay we can't do that, but it would be still possible to store all the values between these extremeties i.e. 1 would be an all white board and 1^10000 would be an all black board. But I don't know how HDD space the number 1 with 10000 noughts takes up - I suppose I could work it out and then factorial that number.
One way to think about it is that the addressable memory space by a binary computer is 2^n, where n is the number of bits in the operating system's addresses.
To describe the pattern of squares on one of your boards, in the most compressed form would require 10000 bits. We would still have 2^10000 of them to store. So it looks like we might need a "10000 bit" operating system to do it.
In 1985, Windows was "16 bit", in 1992 it was "32 bit" and in 2005 the first "64 bit" Windows was released. So it looks like the number of bits roughly doubles every seven years. Note that this progression can also be written as "2^4 bit" .. "2^5 bit" .. "2^6 bit"
"10000 bit" is about "2^14" bit (rounding up), so we need 8 more doublings before we can process this problem. Given the rate of doubling we calculated above, that will take about 8*7 = 56 years from 2005.
i.e. we might be able to deal with these chessboards in the year 2060.