#1
+4 Your question boils down to a geometric series, and is basically:
1+2+2^1+2^2+....+2^64
the general answer for a geometric series =a(1-r^m)/(1-r); where a=initial term(here 1), r=multiplicative factor(2 here because you are doubling in the next square ), m=number of terms(64, since a chess board has 64 squares)
hence, ans=1*(1-2^64)/(1-2)=2^(64)-1
that is, you need 2^(64)-1 grains of rice, which is a huge number!! It is approximately 2 thousand million billion grains of rice! Assuming you stack the grains of rice width wise, each grain has a width ~ 1/2 mm. This would require a length of 500 billion miles, whereas the Earth's circumference is only 25000 miles.
Hence, you would require 20000 million Earths, with rice stacked along the circumference, to fit your rice!!
