Question 512613: Sally and Bill had the following conversation.
Sally: I forgot how old your three kids are.
Bill: The product of their ages is 36.
Sally: I still don't know their ages.
Bill: The sum of their ages is the same as your house number.
Sally: I still don't know their ages.
Bill: The oldest one has red hair.
Sally: Now I know their ages!
How old are they?
(This was the only information given for this problem.)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Assuming the ages of the three children are integers, then there are a finite set of possibilities.
1, 1, 36 (Sum 38)
1, 2, 18 (Sum 21)
1, 3, 12 (Sum 16)
1, 4, 9 (Sum 14)
1, 6, 6 (Sum 13)
2, 2, 9 (Sum 13)
2, 3, 6 (Sum 11)
3, 3, 4 (Sum 10)
Note that the sums are all unique except for 1, 6, 6 and 2, 2, 9. So if it had been one of the other combinations, Sally would have known the ages when Bill told her it was the same as her house number. But she didn't know, therefore the ages are either 1, 6, 6, or 2, 2, 9. But knowing that the oldest has red hair means there IS an oldest, eliminating the 1, 6, 6 combination. The children are 2, 2, and 9 years old.
John
My calculator said it, I believe it, that settles it
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