## Task $9 / 87$

Calculate the sum $S$ of all three-digit natural numbers (in the decimal positional system) that are represented with distinct digits $1 ; 2 ; 3 ; \ldots ; 9$.
Since the digits must be different from each other, there are 9 possibilities for the first place, 8 for the second, and 7 for the third, if one wants to form one of the required numbers.

Thus, there are $9 \cdot 8 \cdot 7=504$ such numbers (variation of 9 elements of the 3rd class without repetition).

Since the 9 digits occur equally frequently at each position, each digit is found at each position $(9 \cdot 8 \cdot 7): 9=56$ times. Therefore, for the desired sum $S$,

$$
S=100 \cdot 56 \cdot \sum_{i_{1}}^{9} i+10 \cdot 56 \cdot \sum_{i_{1}}^{9} i+1 \cdot 56 \cdot \sum_{i_{1}}^{9} i=111 \cdot 56 \cdot \sum_{i_{1}}^{9} i=279720
$$