Children were given an example with five empty squares:

$$
\square \cdot \square-\square:(\square+\square)=?
$$

They were to write one of the numbers $1,2,3,4,5$ in each square so that each number was used only once and the division came out without a remainder.

Find all the results the children could have obtained.

(M. Petrová)
The dividend can only be the given numbers, that is, numbers from 1 to 5. The divisor can only be the sums of the given numbers, that is, numbers from 3 to 9. Division without a remainder can only be constructed in the following way:

$$
3:(1+2), \quad 4:(1+3), \quad 5:(1+4), \quad 5:(2+3)
$$

The order of the addends in the parentheses is not significant; in all cases, the quotient is equal to 1.

Completing the remaining two numbers in the remaining two fields gives the following examples:

$$
\begin{aligned}
& 4 \cdot 5-3:(1+2)=19 \\
& 2 \cdot 5-4:(1+3)=9 \\
& 2 \cdot 3-5:(1+4)=5 \\
& 1 \cdot 4-5:(2+3)=3 .
\end{aligned}
$$

The order of the factors is not significant. The children could have obtained the results 19, 9, 5, or 3.

Evaluation. 1 point for each correct completion with a result; 2 points for the completeness of the commentary.