Two mathematicians, Peter and Paul, met in the
street, and started the following dialog:

- I don't see you for a
long time. Are you married Paul?

- Yes I am and I have three daughters. Peter the
product of theirs ages is 36. Guess how old they are.

- I can not guess. You know, Paul, that I need
more information.

- The sum of their ages is equal to the number of this house.
Do you see the number Peter?

- Yes Paul I see it, but the informations you gave me are not
yet enougth.

- The oldest play piano.

- Now I know their ages Paul

SOLUTION:

Case
Possible
ages
Product
Sum

1
36,1,1
36
38

2
18,2,1
36
21

3
12,3,1
36
16

4
9,2,2
36
13

5
9,4,1
36
14

6
6,3,2
36
11

7
6,6,1
36
13

If Peter knowing the product and the sum of ages could not
guess them, is because their sum was 13 (cases 4 and 7)..

With the information that the oldest plays piano he could
guess that their ages are 9,4,4 (case 4)

Haroldo C. Branco.

Rio de Janeiro, Brazil