## 144. Math Puzzle $5 / 77$

Renate lives in a house with the number 149. She notices that the sum of the digits of this number is equal to the number formed by the first two digits. Can you name more three-digit numbers with this property?
The general three-digit number with the desired property is $100a + 10b + c$, where the sum of the digits equals the number formed by the first two digits: $a + b + c = 10a + b$ ($b, c = 0 \ldots 9$ and $a = 1 \ldots 9$) or $9a = c$ ($b$ arbitrary).

Given that $a$ can only take the digits $1, \ldots, 9$, it follows that: $a = 1, c = 9, b$ arbitrary, i.e., $b = 0, 1, 2, \ldots, 9$.

Thus, the following numbers satisfy the given condition: 109, 119, 129, 139, 149, 159, 169, 179, 189, 199.