3. What is the last digit of the number
$$
2^{2}+20^{20}+200^{200}+2006^{2006} ?
$$
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
3. Ans: $\mathrm{E}$
First we observe that $2^{2}=4$. Since $20^{20}$ is divisible by 10 , it follows that its last digit is 0 . Similarly, the last digit of $200^{200}$ is 0 . The last digit of $2006^{2006}$ is the same as that of $6^{2006}$. Since $6 \times 6=36$, it follows that the last digit of any positive integral power of 6 is 6 . Thus the last digit of $2006^{2006}$ is 6 . Now, $4+0+0+6=10$. Thus the last digit of $2^{2}+20^{20}+200^{200}+2006^{2006}$ is 0 .