## Task 2 - 130812

In $* * \cdot 9 *=* * *$, each asterisk $*$ must be replaced by one of the digits 0 to 9 so that a correct equation is formed.

Determine all solutions to this problem!
Assuming there is a solution to the problem, the first asterisk must be replaced by 1; otherwise, the product would become a four-digit number.

Furthermore, the second asterisk must be replaced by 0 or 1; otherwise, a four-digit number would also result (since $12 \cdot 90 = 1080$ is already four digits).

If 0 is used for the second asterisk, then any digit from 0 to 9 can be used for the third asterisk. If, however, 1 is used for the second asterisk, then the third asterisk must be replaced by 0; otherwise, a product that is at least $11 \cdot 91 = 1001$, and thus four digits, would result.

The remaining possibilities for the first three asterisks indeed lead to exactly one solution each, namely:

$$
\begin{array}{llll}
10 \cdot 90 = 900, & 10 \cdot 91 = 910, & 10 \cdot 92 = 920, & 10 \cdot 93 = 930 \\
10 \cdot 94 = 940, & 10 \cdot 95 = 950, & 10 \cdot 96 = 960, & 10 \cdot 97 = 970 \\
10 \cdot 98 = 980, & 10 \cdot 99 = 990, & 11 \cdot 90 = 990 &
\end{array}
$$