A census worker visits the home of a woman. After he knocks on her door, she answers and he can see three kids behind her. He asks about the ages of the children. She says, “The product of their ages is 72. And the sum of their ages is the number on the door.” He checks the door, thinks about it a minute, and then says “I need more information.” She replies, “The oldest one likes strawberries.” He immediately figures out their ages.
How old are the children?
So far all the solutions had went for the straightforward route - creating factor sets and ruling things out as more clues were presented in the later text.
But what if we switch up the order that we look at the clues?
So I'll start with “ 'The oldest one likes strawberries.' He immediately figures out their ages."
This pair of statements alone tells a lot. It can only be useful if there are twins and the twins are not the oldest of the siblings.
So now we can look at factorizations of 72 with a perfect square factor: 1^2*72, 2^2*18, 3^2*8, 6^2*2.
1,1,72 is too far apart for a set of children so is ruled out;
2,2,18 is a stretch but still plausible
3,3,8 is very reasonable
6,6,2 has the twins being the older which was ruled out.
So at this point there are two realistic options: 2,2,18 and 3,3,8. So last thing needed is to have a duplicate sum in some other factorization.
3,3,8 already has that as the previously discarded 6,6,2 has the same sum of 14. So this is an option
2,2,18 has a sum of 22, and to get a sum of 22 from we would need all even factors of 72, or two odd factors and one even factor; that does reduce the search space a bit, leaving factorizations of 72: 2,2,18; 2,6,6; 1,1,72; 1,3,24; 1,8,9; and 3,3,8. But none of the other five options have the same sum of 22 as 2,2,18, so this must be discarded.
The ages of the children are 3, 3, and 8.
Another solution
