Kája was supposed to multiply two two-digit numbers. Due to inattention, he switched the digits in one of the factors and got a product that was 4248 less than the correct result.

What should Kája have correctly obtained?

(L. Hozová)
Let $x$ and $y$ be Kája's two-digit numbers, and suppose he swapped the digits in the first number. If the digits of the number $x$ are denoted by $a$ and $b$, then we have

$$
(10 a+b) y-(10 b+a) y=4248 .
$$

After simplification, we get $9(a-b) y=4248$ or $(a-b) y=472$. This implies that the number $y$ is a two-digit divisor of 472.

The prime factorization of 472 is $472=2^{3} \cdot 59$, so its only two-digit divisor is 59. This means that $a-b=8$. The following two possibilities satisfy this condition:

- $a=8, b=0$, so $(10 a+b) y=80 \cdot 59=4720$,
- $a=9, b=1$, so $(10 a+b) y=91 \cdot 59=5369$.

Kája should have correctly obtained either 4720 or 5369.

Note. Swapping the digits in the first case results in 08. This does give a valid solution $(80 \cdot 59-8 \cdot 59=4248)$, but it is not a two-digit number. It seems unlikely that Kája, even being inattentive, would not notice this. Therefore, excluding this possibility is not considered an error.