During a census, a man told the census taker that he had threechildren. When ask

Question

During a census, a man told the census taker that he had threechildren. When asked their ages, the man said "The product oftheir ages is 72. The sum of their ages is the same as house number." The census-taker ran to the door and looked at the house number, "I still can't tell." she complained. the man replied "Oh, Iforget to tell you, the youngest child likes chocolatepudding." The census-taker promptly wrote down the ages of the three children. how old re they ?
During a census, a man told the census taker that he had threechildren. When asked their ages, the man said "The product oftheir ages is 72. The sum of their ages is the same as house number." The census-taker ran to the door and looked at the house number, "I still can't tell." she complained. the man replied "Oh, Iforget to tell you, the youngest child likes chocolatepudding." The census-taker promptly wrote down the ages of the three children. how old re they ?

Explanation / Answer

So their ages are one of these  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  I know that the first three cases are ridiculous because children can't be 24, 36 or 72.  But this just shows that the problem didn't have to say they were children.  They could have just been any three people that live in the house with them.    

The sum of their ages is the same as my house number."
The census taker ran to the front door, looked at the house

number and returned saying "I still cant tell!"

So we find all the sums:  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+2+18 = 22 2+3+12 = 17 2+4+9 = 15 2+6+6 = 14 3+3+8 = 14 3+4+6 = 13  So we see from the list he could have told their ages if the sum of their ages (and therefore the house number) had been  anything other than 14 because 14 is the only sum that occurs  more than once in the list.  So he has narrowed it down  to two possibilities:  2, 6, and 6  3, 3, and 8   an OLDER set of twins, and a YOUNGER set of twins. 

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