SOLUTION: During a recent census, a man told the census taker that he had 3 children. When asked their ages, he replied, "The product of their ages is 72. The sum of their ages is the same a

Question 927551: During a recent census, a man told the census taker that he had 3 children. When asked their ages, he replied, "The product of their ages is 72. The sum of their ages is the same as my house number." The census taker ran to the door and looked at the house number. "I still can't tell", she complained. "Oh that's right. I forgot to tell you that the oldest one likes apple pie." The census taker promptly wrote down the ages of the three children. How old are they?
Answer by Techpriest(29) (Show Source): You can put this solution on YOUR website!
The man had 3 children, so we will write these 3 children as a, b, and c.
When you multiply their ages, they will be 72, so:

We do not have any further information, so we write down all of the possible real numbers of the multiple of 72.
a,b,c
1,1,72
1,2,36
1,3,24
1,4,18
1,6,12
1,8,9
2,2,18
2,3,12
2,4,9
2,6,6
3,3,8
3,4,6
The problem also included their house number as being a sum of their ages. So:
1 + 1 + 72 = 74
1 + 2 + 36 = 39
1 + 3 + 24 = 28
1 + 4 + 18 = 23
1 + 6 + 12 = 19
1 + 8 + 9 = 18
2 + 3 + 12 = 15
2 + 4 + 9 = 15
2 + 6 + 6 = 14
3 + 3 + 8 = 14
3 + 4 + 6 = 13
The census taker says that she can't tell because there are two solution leading to the same answer.
2 + 6 + 6 = 14
3 + 3 + 8 = 14
So, he tells them that there is an oldest child that likes apple pie. The fact that there is an oldest child implies that there is only one set of solution that has a single highest number. The correct set of solution would then be
3 + 3 + 8 = 14
The ages of the three children are 3, 3, and 8.
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