Debbie asked, ‘Can you guess the ages of my three girls?The product of their ages is 72.

Question

Debbie asked, ‘Can you guess the ages of my three girls?The product of their ages is 72.

The sum of their ages is the same as our house number.’Robert went outside to look at the house number.‘I can’t solve this problem!’ he cried.‘There still isn’t enough information.’

‘Okay,’ replied Debbie, ‘What if I tell you that Mikayla, the eldest, is left-handed?’

‘Thank you,’ said Robert, ‘I can work it out now!’

Answer 1

Ok, this is a fun metapuzzle.  The three girls have ages that are a product of 72, and there are many ways to come up with this, such as

 

2, 3, 12

1, 6, 12

1, 8, 9

 

This is not enough information clearly to solve the problem.  We now are told that the sum is equal to the house number.  We don't know the house number, but we do know that that is not enough information to solve the problem.  That must mean that there is at least one sum that can be achieved in multiple ways.

 

If the ages were 1, 1, 72, the sum would be 74 and there is no other way to get that, so if 74 was the house number, we would know for sure.  Since this isn't the case, we want instances where sums are duplicates:

6 + 6 + 2 = 14

8 + 3 + 3 = 14

 

We know it is one of these two, but not which one, which is where the last bit of information comes in, where the eldest is left-handed.  We don't care about the left-handed bit, but that there is an eldest, which means only one oldest child.  Because of this, it cannot be 6, 6, 2 and the ages must be 8, 3, and 3.