$\textbf{Children's Age}$
Joe and John meet at a bar and become acquainted. John tells Joe that he has three children. So Joe asks John "How old are they?". "Well, the product of their ages is $72$.", John replies, "and the sum of their ages is the street number of this bar." Joe walks out the door, checks the number, and comes back "The information is not sufficient." John says "I agree. Here is another piece of information: my youngest child likes ice cream." Joe thinks for a minute and says "Now I know your children's ages."
What are the ages of John's children?
$\textbf{Answer}$
They are $6$, $6$, and $2$.
$\textbf{Analysis}$
The list below shows all the possible combinations of ages whose product is $72$. The last column is the sum of the three ages.
$$\begin{array}{ccc|c}&&&sum\\ \hline 1 & 1 & 72 &74\\ 1&2&36 & 39 \\ 1&3&24 & 28 \\ 1&4&18 & 23\\ 1&6&12&19\\ 1 &8&9&18\\ 2&2&18&22\\ 2&3&12&17\\2&4&9&15\\2&6&6&14\\3&3&8&14\\3&4&6&13\end{array}$$
Given the fact that Joe is unable to determine the result by their sum, there must be at least two groups of candidates having the same sum. This means the final answer must be one of $(2, 6, 6)$ and $(3, 3, 8)$ whose sums are both $14$. The last hint is a riddle. John says the youngest child, not children. This means their youngest is not a twin. Hence, the result is $2$, $6$, and $6$.
$\textbf{Note}$
Remember to read the question word by word!