1. The number 2019 has an interesting property: the sum of $2+019$ is exactly 10 times less than the sum of $201+9$. Find all four-digit numbers that have this property.
Answer: 2019, 3028, 4037, 5046, 6055, 7064, 8073, 9082.

Solution. Let's represent the desired number in the form $1000a + 100b + 10c + d$, where $a, b, c, d$ are digits, and $a \neq 0$. Since the number $100a + 10b + c + d$ must be divisible by 10, either $c + d = 0$ or $c + d = 10$. The first case is only possible when $c = d = 0$, and for this case, the conditions of the problem are not satisfied; hence, we only consider the second case. According to the problem, $(100b + 10c + a + d) \times 10 = 100a + 10b + c + d$. From this, taking into account the equality $c + d = 10$, we get $11b + c + 1 = a$. Since $0 < a < 10$, we have $b = 0$, $a = c + 1$. Thus, the digits of the desired number are: $a = t + 1, b = 0, c = t, d = 10 - t$, where $t$ can be any integer from 1 to 8. In the end, we get 8 numbers with the property specified in the problem: 2019, 3028, 4037, 5046, 6055, 7064, 8073, 9082.

Criteria. A generally correct solution (possibly with the loss of some answers) is rated 4 or more points; several correct answers without a general principle for finding them are rated no more than 3 points.