1. Grandpa Jordan and his grandson Ivan have their birthdays on the same day. The years of one and the other are written with the same digits. "The difference in their ages is equal to the number of your house" - Marko said to Petar. Petar quickly calculated how old Jordan and Ivan were. How old are the grandfather and the grandson?
Solution. The difference between the two-digit numbers $10a+b$ and $10b+a$ is $9(a-b)$. The difference $a-b$ is unique since $a$ and $b$ are non-zero digits, so this difference can be $1, 2, 3, 4, 5, 6, 7,$ or 8. Therefore, the product $9(a-b)$ is unique. For Petar, to determine $a$ and $b$, it is sufficient to know the number of his house. Therefore, the difference in age between the grandfather and the grandson is $9(a-b)=72$. Indeed, for the other cases, there would be at least two possibilities, so Petar would not be able to determine the solution. For example, if $a-b=6$, then there are three possible cases: $a-b=7-1=8-2=9-3$.

Thus, $a=9, b=1$, i.e., Grandfather Jordan is 91 years old, and the grandson Ivan is 19 years old.