Question 2
All the positive integers $1,2,3,4,\ldots$ are grouped in the following way: $G_1=\{1,2\}$, $G_2=\{3,4,5,6\}$, $G_3=\{7,8,9,10,11,12,13,14\}$, that is, the set $G_n$ contains the next $2^n$ positive integers listed in ascending order after the set $G_{n-1}$, $n\gt 1$. If $S$ is the sum of all the positive integers from $G_1$ to $G_8$, find $\lfloor S/100\rfloor$.