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