$O$ monkey says to the fox:

- Do you see the 3 people running far away? I know that the product of their ages is 2450; and that the sum of their ages is double your age. Can you tell me their ages?
- No, the fox replies.
- If I tell you that the youngest of the three is the only blonde, can you now figure out their ages?

And the fox gives the ages of the 3 people.

Why can't the fox answer initially? And why can she answer after that?
2450 is the product of the prime numbers $1,2,5,5,7,7$. The 3 ages correspond to a particular combination of these numbers or their products.

The fox cannot figure out the ages at the beginning because at least two of these combinations have a sum equal to twice her age. Of all possible combinations, only $\{5,1049\}$ and $\{7,7,50\}$ have the same sum of 64.

First conclusion: the fox is 32 years old.

After the monkey's new clue, the fox discovered the ages because she can eliminate one combination: the one that contains two identical numbers, since one of them is the youngest of all.

Second conclusion: the people are 5, 10, and 49 years old.