## Subject 3.

Writing in base $10, \overline{a b c}+\overline{b c a}+\overline{c a b}=111(a+b+c)$

$M_{a}=[111(a+b+c)]: 3=37(a+b+c)$

Writing in base $10, \overline{a a b}+\overline{b b a}=111(a+b)$

$M_{a}=111(a+b): 2$

$[111(a+b)]: 2=37 \cdot(a+b+c) \Leftrightarrow 2 \cdot 37 \cdot(a+b+c)=111(a+b) \Leftrightarrow a+b=2 c$

$c=5$ (because $\mathrm{c}=0$ does not allow the existence of the number $\overline{c a b}$ ), so $\mathrm{a}+\mathrm{b}=10$

Finding all pairs (a,b) and the numbers 195, 285, 375, 465, 645, 735, 825, 915
## Subject 3.

Find all multiples of 5 of the form $\overline{a b c}$ such that the arithmetic mean of the numbers

![](https://cdn.mathpix.com/cropped/2024_06_07_f98a9d6c106196fc3d80g-2.jpg?height=60&width=1271&top_left_y=1929&top_left_x=198)