# Russian mathematicians

Two Russian mathematicians who are on a plane start a conversation.

• I think I remember you have three children ... How old are they? Asks Ivan
• Yes, I have three kids. The product of their ages is 36 and the sum of the three is exactly the same number as today.
• mmm ... sorry Igor, but I don't have enough information, Ivan replies after thinking briefly.
• Ah, I forgot to tell you that my youngest son plays the piano.
• Ah, now I know exactly the age of your children.

And you?, Would you know how to discover the ages of Igor's three children?

#### Solution

There are eight possible combinations of 3 numbers that multiply 36 and can be obtained from the divisors of 36. Since Ivan is unable to solve the problem even knowing the value of the sum of the ages, it means that there are several combinations of ages that add up to the same number as the day they are.

 Case Age first child Second child age Age third child Product of the ages Sum of the ages 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38 1 1 1 36 36 38