1. After pulling out the turnip, a lot of earth was left. The Grandpa removed half of the pile, Grandma removed a third of the remaining earth, the Granddaughter removed a quarter of the remainder, the Dog removed a fifth of the remainder, the Cat removed a sixth, and the Mouse removed a seventh. What part of the pile is left?
Answer: $\frac{1}{7}$.

Solution: First, half of the pile remained, then $\frac{2}{3}$ of the remainder, then $\frac{3}{4}$ of the new remainder, and so on. In the end, $1 \cdot \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \cdot \frac{6}{7}=\frac{1}{7}$ of the original pile remained.

Comment: Correct solution - 20 points. Solution started, with some progress - 5 points. Solution started, but no significant progress - 1 point. Correct answer given without explanation - 0 points.