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Logic
Level
3
- Alex and Bob meet on the street.
- Alex tells Bob that he has three children.
- Bob asks how old they are.
- Alex tells him that the product of the ages of his children is 36, and the sum of their ages is equal to the number of houses on the other side of the street.
- Bob counts the number of houses and then says that this is not enough information for him to solve the problem.
- Alex then tells Bob that his oldest child's eyes are blue.
How old are Alex's children?
9, 2, 2
3, 3, 4
36, 1, 1
18, 2, 1
6, 3, 2
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1 solution
Consider all possible sets of three natural numbers where the product of these numbers is 36.
It's evident that only two of these sets have the same sum: 1, 6, 6; SUM = 13 and 2, 2, 9; SUM = 13. When Bob counts the number of houses, any number other than 13 would have identified the solution, which means that because he said this still wasn't enough information, there had to have been 13 houses. After that Alex reveals that he has an oldest son, therefore his children are 2, 2 and 9 years old.