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
 
 
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