Lincoln and Michael gets acquainted in a bar. Lincoln offers a drink to Michael and they begin chatting. After a small conversation, Lincoln comes to know that Michael is married and has three children. He asks him, "How old are your children?" Michael thinks and then replies that the product of his children's ages is 72. Lincoln is puzzled and says that the information is not enough.
Michael tells him that if he goes outside and look at the building number posted on the door to the bar, he will get the sum of their ages. Lincoln goes outside and returns. Still puzzled, He tells Michael that the information is still not enough. Michael smiles and tells him that his youngest child loves strawberry ice cream.
How old are the children?
Solution:
In this question, let us think through the mind of Lincoln. At the first information of the product of the ages being 72, he must have calculated the number of ways in which the three ages can be multiplied in order to obtain 72. Of course there are many ways and therefore he asked for more info. Then Michael tells him how to find the sum of the ages of his children. Of course, we don't know what he saw. But he said that the information was still not enough.
Now why did he say so? It is because there must be two permutations with the same sum or he would have identified the ages easily. Now what are those two permutations?
The two possible permutations are 8 3 3 and 6 6 2. Both of them adds up to 14 (which would be the bar's address).
The last hint by Michael was that his youngest child loves to eat strawberry ice cream. The term youngest means that there is only one youngest child. If you see the permutation 8 3 3, it will mean that there are two youngest children. Thus it does not stand valid with the third hint. So, we are only left with one possibility i.e. 6 6 2.
Thus the ages of his children are 6, 6 and 2.
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