Jiřina has a four-digit number written on a piece of paper. If she swaps the digits in the hundreds and units places and adds this new number to the original number, she gets a result of 3332. However, if she swaps the digits in the thousands and tens places and adds this number to the original, she gets a result of 7886. Determine what number Jiřina had written on the paper.

(E. Novotná)
Let the digits of Jiří's number be denoted by $a, b, c, d$. Then the information from the problem can be written as follows:

$$
\begin{array}{cccc}
a & b & c & d \\
a & d & c & b \\
\hline 3 & 3 & 3 & 2
\end{array} \quad \quad \begin{array}{llll}
a & b & c & d \\
c & b & a & d \\
7 & 8 & 8 & 6
\end{array}
$$

From the first sum, it follows that $a=1$ (if $a=0$, then the desired number would not be a four-digit number; if $a \geq 2$, then the sum would be greater than 4000). Substituting this into the previous expression and proceeding similarly:

$$
\begin{array}{llll}
1 & b & c & d \\
1 & d & c & b \\
3 & 3 & 3 & 2
\end{array} \quad \quad \begin{array}{llll}
1 & b & c & d \\
c & b & 1 & d \\
\hline 7 & 8 & 8 & 6
\end{array}
$$

From the first column of the second sum, it follows that $c$ is 5 or 6. From the third column of the same sum, it follows that $c$ is 6 or 7. Therefore, $c$ must be 6. Substituting this into the third column, we see that in this column, a 1 is carried over from the last column. This means that $d+d=16$, or $d=8$. After substitution, we get:

$$
\begin{array}{llll}
1 & b & 6 & 8 \\
1 & 8 & 6 & b \\
\hline 3 & 3 & 3 & 2
\end{array} \quad \quad \begin{array}{llll}
1 & b & 6 & 8 \\
6 & b & 1 & 8 \\
\hline 7 & 8 & 8 & 6
\end{array}
$$

Now, from the last column of the first sum, we deduce that $b=4$. This determines all the unknowns. Substituting $b$ in the other places and performing the verification:

$$
\begin{array}{llll}
1 & 4 & 6 & 8 \\
1 & 8 & 6 & 4 \\
\hline 3 & 3 & 3 & 2
\end{array} \quad \quad \begin{array}{llll}
1 & 4 & 6 & 8 \\
6 & 4 & 1 & 8 \\
\hline 7 & 8 & 8 & 6
\end{array}
$$

Since everything checks out, we know that Jiří had the number 1468 on the paper.

Evaluation: 1 point for formulating the problem using unknowns; 1 point for determining each unknown; 1 point for the verification.