Proizvolov V.V.

Given fifty different natural numbers, twenty-five of which do not exceed 50, and the rest are greater than 50 but do not exceed 100. Moreover, no two of them differ exactly by 50. Find the sum of these numbers.
Subtract 50 from each number that is greater than 50. We will get 50 different numbers, that is, numbers from 1 to 50. Their sum is $1+2+\ldots+50=25 \cdot 51$, and the sum of the original numbers is $-25 \cdot 51+25 \cdot 50=25 \cdot 101$.

## Answer

2525.