The monkey says to the fox: "Do you see the three 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. And if I tell you that the youngest of the three is the only blonde, can you now figure out their ages? Then the fox gives the ages of the three people.

Why can't the fox answer initially? And why can she answer after?
2450 is the product of the prime numbers $1,2,5,5,7$ and 7. The three ages correspond to a particular combination of these numbers or their products. The fox cannot determine the ages at the beginning because at least two of these combinations have a sum equal to twice its age. Of all possible combinations, only $5+10+49$ and $7+7+50$ have the same sum of 64.

1- conclusion: the fox is 32 years old.

After the new clue from the monkey, the fox figured out the ages because it can eliminate one combination, the one that contains two identical numbers, since one of them is the youngest of all.

$2^{\mathbf{a}}$ conclusion: the people are 5, 10, and 49 years old.