Task 1. What is greater: 1 or $\frac{23}{93}+\frac{41}{165}+\frac{71}{143}$?
Answer: One is greater.

## First solution.

$$
\frac{23}{93}+\frac{41}{165}+\frac{71}{143}<\frac{23}{92}+\frac{41}{164}+\frac{71}{142}=\frac{1}{4}+\frac{1}{4}+\frac{1}{2}=1 .
$$

## Second solution.

$$
\begin{aligned}
\frac{23}{93}+\frac{41}{165}+\frac{71}{143} & =\frac{23 \cdot 165 \cdot 143+93 \cdot 41 \cdot 143+93 \cdot 165 \cdot 71}{93 \cdot 165 \cdot 143}= \\
& =\frac{542685+545259+1089495}{2194335}=\frac{2177439}{2194335}\left[=\frac{65983}{66495}\right]<1
\end{aligned}
$$