1. A snowdrift 468 cm high decreased in height by 6 cm in the first hour, by 12 cm in the second hour, ..., by $6 k$ cm in the -th hour. After some time $T$, the snowdrift melted completely. What fraction of the snowdrift's height melted in the time $\frac{T}{2}$?
Answer: $\frac{7}{26}$.

Solution: From the equation $6+12+\cdots+6n=468$, we find $6 \cdot \frac{n(n+1)}{2}=468$ or $n^{2}+n-$ $156=0$. From this, $n=12$, meaning the snowdrift melted in 12 hours. In 6 hours, it melted by $6 \cdot \frac{6 \cdot 7}{2}=126$ cm in height, which is $\frac{126}{468}=\frac{7}{26}$.

Comment: Correct solution - 20 points. Height of 126 cm found, but answer not obtained or incorrectly calculated - 18 points. Only $T=12$ found - 10 points. Correct approach but error in formula - 5 points. Solution started but progress insignificant - 1 point. Only correct answer without solution - 0 points.