1. If we insert a zero between the digits of a two-digit number, we get a number that is nine times larger. Write down all such two-digit numbers.
1. Let $a$ and $b$ be the digits of the sought two-digit number. We set up the equation $100a + b = 9(10a + b)$. Removing the parentheses, we get the relationship $4b = 5a$. Considering that $a$ and $b$ are digits, the only possible solution is $a = 4$ and $b = 5$. The sought number is 45.
Writing the relationship $100a + b = 9(10a + b)$ ..... 1 point
Rearranging the equation $100a + b = 90a + 9b \ldots$ ..... 1 point
Considering the relationship $4b = 5a$ ..... 1 point
Solution $a = 4$ and $b = 5$ ..... 1 point
Solution 45 ..... 1 point