# Task 4.

Over two days, 50 financiers raised funds to combat a new virus. Each of them made a one-time contribution of a whole number of thousands of rubles, not exceeding 100. Each contribution on the first day did not exceed 50 thousand, while on the second day, it was more than this amount; and no pair of the 50 contributions differed by exactly 50 thousand. What amount was raised?
The solution significantly depends on whether all contributions were distinct or could repeat.

Let's first consider the case where all contributions are distinct. Any natural number greater than 50 but not exceeding 100 can be represented as $50+n$, where $n \in [1, 2, 3, \ldots, 50]$. According to the condition, there are no two numbers that differ exactly by 50, so $n$ takes all the remaining values from the first 25 numbers. Therefore, the sum of all 50 numbers is $1+2+3+\ldots+50+50 \cdot 25=2525$.

If contributions could repeat, a definitive answer cannot be given, but estimates can be made. Note that according to the condition, there was at least one contribution each day. The smallest sum would occur if there were 49 contributions of 1 on the first day, and one contribution of 52 on the second day (51 is not possible). The total sum would be $49 \cdot 1 + 52 = 101$. The largest sum would occur if there was 1 contribution of 49 on the first day, and 49 contributions of 100 on the second day. The total sum would be $49 \cdot 100 + 49 = 4949$.

Answer. If all contributions are distinct, then the total collected is 2525 thousand. If not, the minimum possible sum is 101 thousand, and the maximum possible sum is 4949 thousand.