Give the answer of following question

Question

Puzzle

 ⚪
+⚪
+⚪
__________
=⚪⚪⚪

Each symbol represents a digit, and identical symbols represent identical digits. Can you tell the digits represented by blue, red and white circles?

Answer 1

Clearly the open circle is $5$ or $0$: those are the only digits $d$ with the property that $3d$ ends in $d$. Since the sum is clearly not $0$, the open circle is $5$. The black circle is then a digit $d$ such that $3d+1$ ends in $5$, i.e., such that $3d$ ends in $4$; this means that it must be $8$. Finally, the remaining symbol must be a digit $d$ satisfying $3d+2=5$, so $d=1$. Thus, the addition is $185+185+185=555$.

Easier yet, once you know that the open circle is $5$, just observe that $\frac{555}3=185$.

Answer 2

For "blue", I will use the digit $x$. Similarly, for "red", I will use $y$ and for "white", I will use $z$.

Then we have $\overline{xyz}+\overline{xyz}+\overline{xyz}=\overline{zzz}$.

Since $3z \equiv z \pmod{10}$, we get $z = 5$ or $z = 0$. Clearly, $z = 0$ is not an option, so $z = 5$. Then we have $\overline{xy5}+\overline{xy5}+\overline{xy5}=555$. We notice that dividing $555$ by $3$ gives us $185$, which satisfies equation. Therefore the answer is $$x = 1, y = 8, z = 5$$