I am thinking of three natural numbers. The product of the first and second is 24, the product of the second and third is 32, the product of the first and third is 48.

Which numbers am I thinking of?

(E. Novotná)
The product of 48 of the first and third number is twice the product of 24 of the first and second number. Therefore, the third number is twice the second number.

Thus, the product of 32 of the second and third number is twice the product of the second number with itself. The product of the second number with itself is $32: 2=16$, so the second number must be 4.

The third number is $2 \cdot 4=8$ and from the product of 24, it follows that the first number is $24: 4=6$. (To check, we can verify that the product of the first and third is $6 \cdot 8=48$.)

The numbers in question are 6, 4, and 8.

Another solution. The product of the first and second number is less than the product of the second and third, so the first number is less than the third. The product of the second and third number is less than the product of the first and third, so the second number is less than the first. The numbers in question are arranged as follows:

$$
\text { second }48$ |
| 2 | 12 | 16 | $12 \cdot 16>48$ |
| 3 | 8 | $32: 3$ | not an integer |
| 4 | 6 | 8 | $6 \cdot 8=48$ |

The only suitable option is on the last row of the table; the numbers in question are 6, 4, and 8.

Evaluation. 2 points for auxiliary considerations and insights; 2 points for the result; 2 points for the quality of the commentary.