The Strawberry Tart

Problem:

Luke: How old are your 3 children?
Eva: The product of their ages equals 36
Luke: I need more information
Eva: The sum of their ages is the house number you can see on the other side of the street
Luke: I’m sorry, but in hindsight I still can’t determine the age of your kids yet
Eva: The oldest one loves strawberry tarts
Luke: Ah, now it’s clear! I know how old your children are

Can you determine the ages of the 3 children?

Solution

The children are 2, 2 and 9 years old respectively.
Eva’s first answer, allows you to find 8 possibilities (hence Luke’s need for more information).

1-1-36 1-2-18 1-3-12 1-4-9 1-6-6 2-2-9 2-3-6 3-3-4

Luke’s second request for information (“I’m sorry, but...”), indicates that at least two of the possibilities have the same sum.

1+6+6=13 2+2+9=13

Since both possibilities indicate that two of the children are twins, Eva’s last clue (“The oldest one loves strawberry tarts”) allows you to find the right answer: where the oldest child is not one of the twins.