1. The natural numbers from 1 to $n$, a multiple of 50, are written on the board. Vasya claims that if all numbers divisible by 50 are erased from the board, the sum of the remaining numbers is a square of some natural number. Is Vasya right?
Answer: Vasya is right.

Solution. Let $n=50 m$. Then the sum of the remaining numbers is

$$
(1+2+\cdots+50 m)-50(1+2+\cdots+m)=25 m(50 m+1)-25 m(m+1)=25 \cdot 49 m^{2}=(35 m)^{2}
$$

Comment. The correct answer is obtained based on the consideration of specific cases - 2 points. If the correct approach is used but computational errors are made - 3 points. For potentially useful ideas and approaches without a solution - 1-2 points. Answer without justification - 0 points.