1. Determine which of the numbers is greater:

$$
\frac{\lg 2017}{2 \lg 2} \quad \text { or } \quad 2 \lg \frac{2017}{2}
$$
# Problem 1. 

Answer: the first number is smaller (in all cases).

Solution. Let $A$ denote the numbers 2011, 2013, 2015, or 2017, participating in the different variants, and compare the proposed numbers: $\frac{\lg A}{2 \lg 2} \equiv 0.5 \log _{2} A$ and $2 \lg (A / 2)$.

Since $2000<A<2^{11}$, then $0.5 \log _{2} A<\frac{11}{2}<6<2 \lg (A / 2)$.