20) What is the unit digit of the number: $\frac{66^{66}}{2}$?
(A) 1,
(B) 3,
(C) 6,
(D) 8,
(E) 9.
20. The answer is $(\mathbf{D})$.

The units digit of the product of two numbers that end in 6 is 6. Therefore, the units digit of $66^{66}=66 \times 66 \times \cdots \times 66$ is 6, and the units digit of its half can be either 3 or 8. Clearly, $\frac{66^{66}}{2}=33 \times 66^{65}$ is even, so its units digit cannot be 3, and must be 8.

[Problem proposed by X.Y. Lu.]