Census taker puzzle

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During a recent census, a man told the census taker that he had three 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 man’s front door and looked at the house number. “I still can’t tell,” she complained. The man replied, “Oh that’s right, I forgot to tell you that the oldest one likes chocolate pudding.” The census taker then promptly wrote down the ages of the three children.

How old are they?

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SherlockHolmes Expert Asked on 23rd February 2020 in Math Puzzles.
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  • 1 Answer(s)
    Best answer

    Answer is :

    1. 3
    2. 3
    3. 8

    Explanation :
    Here is a complete list of all possible solutions :
    Ages:                               Sum of ages:

    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
    Every combination of possible ages which has a product of 72 
    has its own unique sum of ages - except for 2, 6, 6 and 3, 3, 8, both 
    of which share the sum of 14.
    Based on the first clue. the census taker can't figure out 
    the ages after looking at the house number, the house number must be 
    14, because then the ages could be either 2, 6, 6 or 3, 3, 8,that is 
    confusing for the census taker. 
    
    Now, the next clue is that the oldest child likes chocolate pudding. 
    This means that there is only one oldest child. 
    
    There is no oldest child of the ages are 2, 6, 6, 
    so the ages of the children must be 3, 3, and 8 years old.
    Hack_King Guru Answered on 28th February 2020.
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