Three Daughters
Puzzle:
A man in my neighborhood has three daughters. One day when
I asked their ages he said, “The product of their ages
is 36.”
When I still couldn’t find their ages he said,
“Ok. I’ll give you another clue: the sum of their ages
is same as the number of my house.”
I knew the number but still couldn’t calculate their
ages. So the man gave me a last clue,
“My eldest daughter lives upstairs.”
Finally I was able to figure out their ages.
How old are they?
Show Hint
Hint:
There are only so many ways that three numbers can
have a product of 36.
Show Answer
Answer: The ages are
2, 2, and 9.
Show Solution
Solution:
There are only so many ways that three numbers can
have a product of 36:
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
It’s got to be one of these, but we don’t know
which one. The second clue is about the sum of their ages:
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
The narrator knew the number of the man’s house,
so the only way that this clue didn’t help him is
if the sum is 13, in which case it’s still ambiguous.
So we know the ages are either 1, 6, and 6, or
2, 2, and 9.
The third clue makes a reference to the oldest
daughter, so the ages must be 2, 2, and 9.
(It’s true that there could still be an
“oldest” daughter in the case of 1, 6, and 6, since
they could be 10 months apart and both be 6.
But since the man gave this as a clue, we can
assume that it’s suppose to push us towards
the 2, 2, and 9 solution.)
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