48. On the way back from the Palace of Sports, the following dialogue took place between Nina and her coach:

- Do you have a brother?
- I have three brothers,- answered Nina.
- How old are they?
- The product of the numbers representing the age of each of them is 36, and the sum is the number of that bus standing at the stop.

Looking at the bus number, the coach said that this information was insufficient.

- And the oldest of them also loves sports,- added Nina.
- Now I know how old each of them is,- said the coach and accurately named the age of each boy. Name them too.

![](https://cdn.mathpix.com/cropped/2024_05_21_00604dc020e3721fc1f4g-111.jpg?height=428&width=434&top_left_y=1188&top_left_x=343)

## Search for solutions
48. The total number of triplets of numbers, the product of which is 36, will be: 1) 1,4 , 9 (then $1+4+9=14$ ); 2) $1,6,6$ (sum 13); 3) $1,3,12$ (sum 16); 4) $1,2,18$ (sum 21); 5) 2, 2, 9 (sum 13); 6) 3, 3, 4 (sum 10); 7) 2, 3, 6 (sum 11); 8) 1, 1, 36 (sum 38).

If the coach had seen a bus number different from 13, he would have named the age without additional data. Therefore, he saw 13. Nina's statement that the oldest brother loves sports is equivalent to the oldest boys not being twins, so the case $1+6+6=13$ is ruled out, leaving $2+2+9=13$. Therefore, the oldest brother is 9 years old, and the younger ones, who are twins, are 2 years old.