Subject 2. Natural numbers $a, b, c (0<a<b<c)$ have a sum equal to 63. Knowing that when the sum of the numbers $b$ and $c$ is divided by $a$, the quotient is 2 and the remainder is 15, and one of the numbers $a, b, c$ has identical digits, determine the three numbers.
## Subject 2.

| $b+c=2 a+15, 15<a$ | $\mathbf{1 p}$ |
| :--- | :--- | :--- |
| $a+b+c=63 \Leftrightarrow 3 a+15=63 \Leftrightarrow a=16$ | $\mathbf{2 p}$ |
| One of the numbers $b$ or $c$ has equal digits and $b+c=47$ |  |
| $16<b<c \Rightarrow$ the numbers with equal digits are 22, 33, 44 | $\mathbf{1 p}$ |
| If $b=22$, then $c=25$ |  |
| The other values do not satisfy the conditions | $\mathbf{2 p}$ |