22. Consider a list of six numbers. When the largest number is removed from the list, the average is decreased by 1 . When the smallest number is removed, the average is increased by 1 . When both the largest and the smallest numbers are removed, the average of the remaining four numbers is 20 . Find the product of the largest and the smallest numbers.
22. Answer: 375 .
Let $m$ and $M$ be the smallest and the largest numbers. Then
$$
\frac{m+80}{5}+1=\frac{M+80}{5}-1=\frac{m+M+80}{6}
$$

Solving the system, $m=15$ and $M=25$. Then $m M=375$.