Posted in History & Literature

# Three Daughters

A man asked how old a man’s three daughters were. The father replied with the following statement.
“The product of their ages is 36.”
“It’s hard to determine their ages from just that.” the man asking replied.
“The sum of their ages is same as the number of my house.”
“I still can’t figure out the answer!” the man replied again.
“My eldest daughter is blonde.” the father said, and the man, now smiling, replied.
“Oh, is that so? Then I can figure out how old your daughters are.”

How old is each daughter? And how did the man figure it out?
A computer cannot solve this problem, as it can only be solved using human logic. To find the answer, you must first approach the question mathematically.
The only three numbers that multiply to produce 36 are:
1 × 1 × 36 = 36
1 × 2 × 18 = 36
1 × 3 × 12 = 36
1 × 4 × 9 = 36
1 × 6 × 6 = 36
2 × 2 × 9 = 36
2 × 3 × 6 = 36
3 × 3 × 4 = 36

Next, use the second hint to find the sum of the three numbers:
1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 2 + 9 = 13
2 + 3 + 6 = 11
3 + 3 + 4 = 10

As the questioner could not solve the problem from this hint, the sum must be 13 (all other answers are unique and would have given him the answer).
The remaining combinations are:
1 + 6 + 6 = 13
2 + 2 + 9 = 13
The last hint activates a logic that only a human being could think of. As there is an “eldest daughter”, the “twin” must be younger. Therefore, the only three numbers fulfilling the three criteria are 2, 2, 9.

(from The Encyclopaedia of Relative and Absolute Knowledge by Bernard Werber) 