Question 10
Let $\lfloor x \rfloor$ denote the greatest integer not exceeding $x$. Find the last two digits of
$$
\left\lfloor \frac{1}{3} \right\rfloor + \left\lfloor \frac{2}{3} \right\rfloor + \left\lfloor \frac{2^2}{3} \right\rfloor + \cdots + \left\lfloor \frac{2^{2^{2^{14}}}}{3} \right\rfloor
$$
$$
\left\lfloor \frac{1}{3} \right\rfloor + \left\lfloor \frac{2}{3} \right\rfloor + \left\lfloor \frac{2^2}{3} \right\rfloor + \cdots + \left\lfloor \frac{2^{2^{2^{14}}}}{3} \right\rfloor
$$